WO2025189369A1

WO2025189369A1 - Mimo demodulation of probabilistically-shaped qam using lattice basis reduction

Info

Publication number: WO2025189369A1
Application number: PCT/CN2024/081317
Authority: WO
Inventors: Mahmoud Taherzadeh Boroujeni; Wei Yang; Qiaoyu Li
Original assignee: Qualcomm Inc
Current assignee: Qualcomm Inc
Priority date: 2024-03-13
Filing date: 2024-03-13
Publication date: 2025-09-18
Anticipated expiration: 2026-09-13

Abstract

This disclosure provides systems, methods and apparatuses for demodulating multiple-input multiple-output (MIMO) transmissions with N layers with probabilistic shaping according to a distribution such as the Maxwell-Boltzmann distribution. A demodulator at a receiving device projects a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point. The demodulator performs lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. The demodulator obtains a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

Description

MIMO DEMODULATION OF PROBABILISTICALLY-SHAPED QAM USING LATTICE BASIS REDUCTION

TECHNICAL FIELD

The present disclosure relates to wireless communications including multiple-input, multiple-output (MIMO) demodulation of probabilistically-shaped quadrature amplitude modulation (QAM) using lattice basis reduction.

DESCRIPTION OF THE RELATED TECHNOLOGY

Wireless communication systems are widely deployed to provide various telecommunication services such as telephony, video, data, messaging, and broadcasts. Typical wireless communication systems may employ multiple-access technologies capable of supporting communication with multiple users by sharing available system resources. Examples of such multiple-access technologies include code division multiple access (CDMA) systems, time division multiple access (TDMA) systems, frequency division multiple access (FDMA) systems, orthogonal frequency division multiple access (OFDMA) systems, single-carrier frequency division multiple access (SC-FDMA) systems, and time division synchronous code division multiple access (TD-SCDMA) systems.

These multiple access technologies have been adopted in various telecommunication standards to provide a common protocol that enables different wireless devices to communicate on a municipal, national, regional, and even global level. An example telecommunication standard is 5G New Radio (NR) . 5G NR is part of a continuous mobile broadband evolution promulgated by Third Generation Partnership Project (3GPP) to meet new requirements associated with latency, reliability, security, scalability (such as with Internet of Things (IoT) ) , and other requirements. 5G NR includes services associated with enhanced mobile broadband (eMBB) , massive machine type communications (mMTC) , and ultra-reliable low latency communications (URLLC) . Some aspects of 5G NR may be based on the 4G Long Term Evolution (LTE) standard.

SUMMARY

The systems, methods and devices of this disclosure each have several innovative aspects, no single one of which is solely responsible for the desirable attributes disclosed herein.

In some aspects, the techniques described herein relate to a method of demodulating a multiple-input multiple-output (MIMO) transmission with N layers, the method including: projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

In some aspects, the techniques described herein relate to an apparatus for wireless communication, including: one or more memories storing computer-executable instructions; and one or more processors coupled with the one or more memories and configured to execute the computer-executable instructions, individually or in combination, to cause the apparatus to: project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

In some aspects, the techniques described herein relate to an apparatus for wireless communication, including: means for projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; means for performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and means for obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

In some aspects, the techniques described herein relate to a non-transitory computer-readable medium storing computer-executable code that when executed by one or more processors of a receiving device causes the receiving device to: project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

The present disclosure also provides an apparatus (e.g., a BS) including means for performing at least one of the above methods, and a non-transitory computer-readable medium storing computer-executable instructions for performing at least one of the above methods.

Details of one or more implementations of the subject matter described in this disclosure are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, the drawings and the claims. Note that the relative dimensions of the following figures may not be drawn to scale.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating an example of a wireless communications system including an access network.

FIG. 2A is a diagram illustrating an example of a first frame.

FIG. 2B is a diagram illustrating an example of DL channels within a subframe.

FIG. 2C is a diagram illustrating an example of a second frame.

FIG. 2D is a diagram illustrating an example of a subframe.

FIG. 3 is a diagram illustrating an example of a base station (BS) and user equipment (UE) in an access network.

FIG. 4 is a diagram illustrating an example disaggregated base station architecture. FIG. 5 is a message diagram illustrating various messages and actions for MIMO transmissions with probabilistic shaping.

FIG. 6 is a diagram of uniform quadrature amplitude modulation (QAM) and probabilistic shaping.

FIG. 7 is a conceptual data flow diagram illustrating lattice basis reduction for MIMO demodulation of a constellation with probabilistic shaping.

FIG. 8 is a diagram showing a distance calculation using lattice basis reduction.

FIG. 9 is a conceptual data flow diagram illustrating the data flow between different means/components in an example receiving device.

FIG. 10 is a flowchart of an example method for a receiving device to receive a MIMO transmission with probabilistic shaping.

Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

The following description is directed to certain implementations for the purposes of describing the innovative aspects of this disclosure. However, a person having ordinary skill in the art will readily recognize that the teachings herein can be applied in a multitude of different ways. Some of the examples in this disclosure are based on wireless and wired local area network (LAN) communication according to the Institute of Electrical and Electronics Engineers (IEEE) 802.11 wireless standards, the IEEE 802.3 Ethernet standards, and the IEEE 1901 Powerline communication (PLC) standards. However, the described implementations may be implemented in any device, system or network that is capable of transmitting and receiving RF signals according to any of the wireless communication standards, including any of the IEEE 802.11 standards, thestandard, code division multiple access (CDMA) , frequency division multiple access (FDMA) , time division multiple access (TDMA) , Global System for Mobile communications (GSM) , GSM/General Packet Radio Service (GPRS) , Enhanced Data GSM Environment (EDGE) , Terrestrial Trunked Radio (TETRA) , Wideband-CDMA (W-CDMA) , Evolution Data Optimized (EV-DO) , 1xEV-DO, EV-DO Rev A, EV-DO Rev B, High Speed Packet Access (HSPA) , High Speed Downlink Packet Access (HSDPA) , High Speed Uplink Packet Access (HSUPA) , Evolved High Speed Packet Access (HSPA+) , Long Term Evolution (LTE) , AMPS, or other known signals that are used to communicate within a wireless, cellular or internet of things (IOT) network, such as a system utilizing 3G, 4G or 5G, or further implementations thereof, technology.

In a wireless communications network such as a 5G NR network, multiple-input, multiple-output (MIMO) transmissions utilize multiple antennas at a transmitter and a receiver to transmit data in multiple layers, thereby increasing throughput. Another technique to increase spectral efficiency is probabilistic shaping, which uses non-uniformly distributed quadrature amplitude modulation (QAM) constellations. Probabilistic shaping has shown gains for single-input single-output (SISO) transmissions, but the shaping gain has not been fully realized for MIMO transmissions. For example, linear demodulation techniques have been optimized for approximation using maximum likelihood (ML) decoding, whereas approximation of maximum a posteriori (MAP) probability is the appropriate objective in demodulation of probabilistically shaped constellations.

In an aspect, the present disclosure provides a demodulator that demodulates MIMO transmissions with N layers and probabilistic shaping. The demodulator utilizes lattice basis reduction to reduce the dimensionality of a lattice of constellation points that is translated as the result of channel matrix tilting due to the probabilistic shaping and MAP geometry. For example, for a MIMO transmission with N layers, each received constellation point is in a 4N dimensional space. The demodulator projects the received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point. The demodulator performs lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. The demodulator obtains a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice. The demodulator outputs the nearest point as the demodulated symbol.

In an aspect, the demodulation techniques described herein allow use of probabilistic shaping to increase spectral efficiency. The lattice basis reduction provides a relatively low complexity solution to efficiently demodulate probabilistically shaped constellations. Accordingly, the techniques disclosed herein allow realization of the gains of probabilistic shaping while utilizing accepted linear demodulation techniques.

Several aspects of telecommunication systems will now be presented with reference to various apparatus and methods. These apparatus and methods will be described in the following detailed description and illustrated in the accompanying drawings by various blocks, components, circuits, processes, algorithms, etc. (collectively referred to as “elements” ) . These elements may be implemented using electronic hardware, computer software, or any combination thereof. Whether such elements are implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system.

By way of example, an element, or any portion of an element, or any combination of elements may be implemented as a “processing system” that includes one or more processors. Examples of processors include microprocessors, microcontrollers, graphics processing units (GPUs) , central processing units (CPUs) , application processors, digital signal processors (DSPs) , reduced instruction set computing (RISC) processors, systems on a chip (SoC) , baseband processors, field programmable gate arrays (FPGAs) , programmable logic devices (PLDs) , state machines, gated logic, discrete hardware circuits, and other suitable hardware configured to perform the various functionality described throughout this disclosure. The processor may include an interface or be coupled to an interface that can obtain or output signals. The processor may obtain signals via the interface and output signals via the interface. In some implementations, the interface may be a printed circuit board (PCB) transmission line. In some other implementations, the interface may include a wireless transmitter, a wireless transceiver, or a combination thereof. For example, the interface may include a radio frequency (RF) transceiver which can be implemented to receive or transmit signals, or both. One or more processors in the processing system may execute software. Software shall be construed broadly to mean instructions, instruction sets, code, code segments, program code, programs, subprograms, software components, applications, software applications, software packages, routines, subroutines, objects, executables, threads of execution, procedures, functions, etc., whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise.

Accordingly, in one or more example implementations, the functions described may be implemented in hardware, software, or any combination thereof. If implemented in software, the functions may be stored on or encoded as one or more instructions or code on a computer-readable medium. Computer-readable media includes computer storage media, which may be referred to as non-transitory computer-readable media. Non-transitory computer-readable media may exclude transitory signals. Storage media may be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can include a random-access memory (RAM) , a read-only memory (ROM) , an electrically erasable programmable ROM (EEPROM) , optical disk storage, magnetic disk storage, other magnetic storage devices, combinations of the aforementioned types of computer-readable media, or any other medium that can be used to store computer executable code in the form of instructions or data structures that can be accessed by a computer.

FIG. 1 is a diagram illustrating an example of a wireless communications system and an access network 100. The wireless communications system (also referred to as a wireless wide area network (WWAN) ) includes base stations 102, UEs 104, an Evolved Packet Core (EPC) 160, and another core network 190 (such as a 5G Core (5GC) ) . The base stations 102 may include macrocells (high power cellular base station) or small cells (low power cellular base station) . The macrocells include base stations. The small cells include femtocells, picocells, and microcells. The small cells include femtocells, picocells, and microcells. The base stations 102 can be configured in a Disaggregated RAN (D-RAN) or Open RAN (O-RAN) architecture, where functionality is split between multiple units such as a central unit (CU) , one or more distributed units (DUs) , or a radio unit (RU) . Such architectures may be configured to utilize a protocol stack that is logically split between one or more units (such as one or more CUs and one or more DUs) . In some aspects, the CUs may be implemented within an edge RAN node, and in some aspects, one or more DUs may be co-located with a CU, or may be geographically distributed throughout one or multiple RAN nodes. The DUs may be implemented to communicate with one or more RUs.

In some implementations, one or more transmitting devices such as the base stations 102 include a probabilistic shaping component 120 configured to transmit MIMO transmissions using probabilistic shaping. For example, the probabilistic shaping component 120 may apply a Maxwell-Boltzmann (MB) distribution during modulation to maximize source entropy for a given average power. In some implementations, the probabilistic shaping component 120 may include a constant-composition distribution matcher (CCDM) with the MB distribution.

In some implementations, one or more of the UEs 104 include a MIMO demodulation component 140. The MIMO demodulation component 140 is configured to demodulate a multiple-input multiple-output (MIMO) transmission with N layers. The MIMO demodulation component 140 includes a projection component 142, a reduction component 144, and a linear demod component 146. The component 142 is configured to project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point. The reduction component 144 is configured to perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. The linear demod component 146 is configured to obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

In some implementations, one or more of the base stations 102 includes a MIMO demodulation component 140 configured to demodulate an uplink MIMO transmission with N layers. The MIMO demodulation component 140 at the base station 102 may also include a projection component 142, a reduction component 144, and a linear demod component 146. The MIMO demodulation component 140 at the base station may operate in the same manner as a MIMO demodulation component 140 UE 104, except on an uplink MIMO transmission instead of a downlink MIMO transmission.

The base stations 102 configured for 4G LTE (collectively referred to as Evolved Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access Network (E-UTRAN) ) may interface with the EPC 160 through first backhaul links 132 (such as S1 interface) , which may be wired or wireless. The base stations 102 configured for 5G NR (collectively referred to as Next Generation RAN (NG-RAN) ) may interface with core network 190 through second backhaul links 184, which may be wired or wireless. In addition to other functions, the base stations 102 may perform one or more of the following functions: transfer of user data, radio channel ciphering and deciphering, integrity protection, header compression, mobility control functions (such as handover, dual connectivity) , inter-cell interference coordination, connection setup and release, load balancing, distribution for non-access stratum (NAS) messages, NAS node selection, synchronization, radio access network (RAN) sharing, multimedia broadcast multicast service (MBMS) , subscriber and equipment trace, RAN information management (RIM) , paging, positioning, and delivery of warning messages. The base stations 102 may communicate directly or indirectly (such as through the EPC 160 or core network 190) with each other over third backhaul links 134 (such as X2 interface) . The third backhaul links 134 may be wired or wireless.

The base stations 102 may wirelessly communicate with the UEs 104. Each of the base stations 102 may provide communication coverage for a respective geographic coverage area 110. There may be overlapping geographic coverage areas 110. For example, the small cell 102' may have a coverage area 110' that overlaps the coverage area 110 of one or more macro base stations 102. A network that includes both small cell and macrocells may be known as a heterogeneous network. A heterogeneous network also may include Home Evolved Node Bs (eNBs) (HeNBs) , which may provide service to a restricted group known as a closed subscriber group (CSG) . The communication links 112 between the base stations 102 and the UEs 104 may include UL (also referred to as reverse link) transmissions from a UE 104 to a base station 102 or DL (also referred to as forward link) transmissions from a base station 102 to a UE 104. The communication links 112 may use multiple-input and multiple-output (MIMO) antenna technology, including spatial multiplexing, beamforming, or transmit diversity. The communication links may be through one or more carriers. The base stations 102 /UEs 104 may use spectrum up to Y MHz (such as 5, 10, 15, 20, 100, 400, etc. MHz) bandwidth per carrier allocated in a carrier aggregation of up to a total of Yx MHz (x component carriers) used for transmission in each direction. The carriers may or may not be adjacent to each other. Allocation of carriers may be asymmetric with respect to DL and UL (such as more or fewer carriers may be allocated for DL than for UL) . The component carriers may include a primary component carrier and one or more secondary component carriers. A primary component carrier may be referred to as a primary cell (PCell) and a secondary component carrier may be referred to as a secondary cell (SCell) .

Certain UEs 104 may communicate with each other using device-to-device (D2D) communication link 158. The D2D communication link 158 may use the DL/UL WWAN spectrum. The D2D communication link 158 may use one or more sidelink channels, such as a physical sidelink broadcast channel (PSBCH) , a physical sidelink discovery channel (PSDCH) , a physical sidelink shared channel (PSSCH) , and a physical sidelink control channel (PSCCH) . D2D communication may be through a variety of wireless D2D communications systems, such as for example, FlashLinQ, WiMedia, Bluetooth, ZigBee, Wi-Fi based on the IEEE 802.11 standard, LTE, or NR.

The wireless communications system may further include a Wi-Fi access point (AP) 150 in communication with Wi-Fi stations (STAs) 152 via communication links 154 in a 5 GHz unlicensed frequency spectrum. When communicating in an unlicensed frequency spectrum, the STAs 152 /AP 150 may perform a clear channel assessment (CCA) prior to communicating in order to determine whether the channel is available.

The small cell 102' may operate in a licensed or an unlicensed frequency spectrum. When operating in an unlicensed frequency spectrum, the small cell 102' may employ NR and use the same 5 GHz unlicensed frequency spectrum as used by the Wi-Fi AP 150. The small cell 102', employing NR in an unlicensed frequency spectrum, may boost coverage to or increase capacity of the access network.

A base station 102, whether a small cell 102' or a large cell (such as macro base station) , may include an eNB, gNodeB (gNB) , or other type of base station. Some base stations, such as gNB 180 may operate in one or more frequency bands within the electromagnetic spectrum.

The electromagnetic spectrum is often subdivided, based on frequency/wavelength, into various classes, bands, channels, etc. In 5G NR two initial operating bands have been identified as frequency range designations FR1 (410 MHz –7.125 GHz) and FR2 (24.25 GHz –52.6 GHz) . The frequencies between FR1 and FR2 are often referred to as mid-band frequencies. Although a portion of FR1 is greater than 6 GHz, FR1 is often referred to (interchangeably) as a “Sub-6 GHz” band in various documents and articles. A similar nomenclature issue sometimes occurs with regard to FR2, which is often referred to (interchangeably) as a “millimeter wave” (mmW) band in documents and articles, despite being different from the extremely high frequency (EHF) band (30 GHz –300 GHz) which is identified by the International Telecommunications Union (ITU) as a “millimeter wave” band.

With the above aspects in mind, unless specifically stated otherwise, it should be understood that the term “sub-6 GHz” or the like if used herein may broadly represent frequencies that may be less than 6 GHz, may be within FR1, or may include mid-band frequencies. Further, unless specifically stated otherwise, it should be understood that the term “millimeter wave” or the like if used herein may broadly represent frequencies that may include mid-band frequencies, may be within FR2, or may be within the EHF band. Communications using the mmW radio frequency band have extremely high path loss and a short range. The mmW base station 180 may utilize beamforming 182 with the UE 104 to compensate for the path loss and short range.

The EPC 160 may include a Mobility Management Entity (MME) 162, other MMEs 164, a Serving Gateway 166, a Multimedia Broadcast Multicast Service (MBMS) Gateway 168, a Broadcast Multicast Service Center (BM-SC) 170, and a Packet Data Network (PDN) Gateway 172. The MME 162 may be in communication with a Home Subscriber Server (HSS) 174. The MME 162 is the control node that processes the signaling between the UEs 104 and the EPC 160. Generally, the MME 162 provides bearer and connection management. All user Internet protocol (IP) packets are transferred through the Serving Gateway 166, which itself is connected to the PDN Gateway 172. The PDN Gateway 172 provides UE IP address allocation as well as other functions. The PDN Gateway 172 and the BM-SC 170 are connected to the IP Services 176. The IP Services 176 may include the Internet, an intranet, an IP Multimedia Subsystem (IMS) , a PS Streaming Service, or other IP services. The BM-SC 170 may provide functions for MBMS user service provisioning and delivery. The BM-SC 170 may serve as an entry point for content provider MBMS transmission, may be used to authorize and initiate MBMS Bearer Services within a public land mobile network (PLMN) , and may be used to schedule MBMS transmissions. The MBMS Gateway 168 may be used to distribute MBMS traffic to the base stations 102 belonging to a Multicast Broadcast Single Frequency Network (MBSFN) area broadcasting a particular service, and may be responsible for session management (start/stop) and for collecting eMBMS related charging information.

The core network 190 may include an Access and Mobility Management Function (AMF) 192, other AMFs 193, a Session Management Function (SMF) 194, and a User Plane Function (UPF) 195. The AMF 192 may be in communication with a Unified Data Management (UDM) 196. The AMF 192 is the control node that processes the signaling between the UEs 104 and the core network 190. Generally, the AMF 192 provides QoS flow and session management. All user Internet protocol (IP) packets are transferred through the UPF 195. The UPF 195 provides UE IP address allocation as well as other functions. The UPF 195 is connected to the IP Services 197. The IP Services 197 may include the Internet, an intranet, an IP Multimedia Subsystem (IMS) , a PS Streaming Service, or other IP services.

The base station may include or be referred to as a gNB, Node B, eNB, an access point, a base transceiver station, a radio base station, a radio transceiver, a transceiver function, a basic service set (BSS) , an extended service set (ESS) , a transmit reception point (TRP) , or some other suitable terminology. The base station 102 provides an access point to the EPC 160 or core network 190 for a UE 104. Examples of UEs 104 include a cellular phone, a smart phone, a session initiation protocol (SIP) phone, a laptop, a personal digital assistant (PDA) , a satellite radio, a global positioning system, a multimedia device, a video device, a digital audio player (such as a MP3 player) , a camera, a game console, a tablet, a smart device, a wearable device, a vehicle, an electric meter, a gas pump, a large or small kitchen appliance, a healthcare device, an implant, a sensor/actuator, a display, or any other similar functioning device. Some of the UEs 104 may be referred to as IoT devices (such as a parking meter, gas pump, toaster, vehicles, heart monitor, etc. ) . The UE 104 also may be referred to as a station, a mobile station, a subscriber station, a mobile unit, a subscriber unit, a wireless unit, a remote unit, a mobile device, a wireless device, a wireless communications device, a remote device, a mobile subscriber station, an access terminal, a mobile terminal, a wireless terminal, a remote terminal, a handset, a user agent, a mobile client, a client, or some other suitable terminology.

Although the following description may be focused on 5G NR, the concepts described herein may be applicable to other similar areas, such as LTE, LTE-A, CDMA, GSM, and other wireless technologies including future 6G technologies.

FIG. 2A is a diagram 200 illustrating an example of a first frame. FIG. 2B is a diagram 230 illustrating an example of DL channels within a subframe. FIG. 2C is a diagram 250 illustrating an example of a second frame. FIG. 2D is a diagram 280 illustrating an example of a subframe. The 5G NR frame structure may be FDD in which for a particular set of subcarriers (carrier system bandwidth) , subframes within the set of subcarriers are dedicated for either DL or UL, or may be TDD in which for a particular set of subcarriers (carrier system bandwidth) , subframes within the set of subcarriers are dedicated for both DL and UL. A subset of the total cell bandwidth of a cell is referred to as a Bandwidth Part (BWP) and bandwidth adaptation is achieved by configuring the UE with BWP (s) and telling the UE which of the configured BWPs is currently the active one. In an aspect, a narrow bandwidth part (NBWP) refers to a BWP having a bandwidth less than or equal to a maximum configurable bandwidth of a BWP. The bandwidth of the NBWP is less than the carrier system bandwidth.

In the examples provided by Figs. 2A, 2C, the 5G NR frame structure is assumed to be TDD, with subframe 4 being configured with slot format 28 (with mostly DL) , where D is DL, U is UL, and X is flexible for use between DL/UL, and subframe 3 being configured with slot format 34 (with mostly UL) . While subframes 3, 4 are shown with slot formats 34, 28, respectively, any particular subframe may be configured with any of the various available slot formats 0-61. Slot formats 0, 1 are all DL, UL, respectively. Other slot formats 2-61 include a mix of DL, UL, and flexible symbols. UEs are configured with the slot format (dynamically through DL control information (DCI) , or semi-statically/statically through radio resource control (RRC) signaling) through a received slot format indicator (SFI) . Note that the description infra applies also to a 5G NR frame structure that is TDD.

Other wireless communication technologies may have a different frame structure or different channels. A frame (10 milliseconds (ms) ) may be divided into 10 equally sized subframes (1 ms) . Each subframe may include one or more time slots. Subframes also may include mini-slots, which may include 7, 4, or 2 symbols. Each slot may include 7 or 14 symbols, depending on the slot configuration. For slot configuration 0, each slot may include 14 symbols, and for slot configuration 1, each slot may include 7 symbols. The symbols on DL may be cyclic prefix (CP) OFDM (CP-OFDM) symbols. The symbols on UL may be CP-OFDM symbols (for high throughput scenarios) or discrete Fourier transform (DFT) spread OFDM (DFT-s-OFDM) symbols (also referred to as single carrier frequency-division multiple access (SC-FDMA) symbols) (for power limited scenarios; limited to a single stream transmission) . The number of slots within a subframe is based on the slot configuration and the numerology. For slot configuration 0, different numerologies μ 0 to 5 allow for 1, 2, 4, 8, 16, and 32 slots, respectively, per subframe. For slot configuration 1, different numerologies 0 to 2 allow for 2, 4, and 8 slots, respectively, per subframe. Accordingly, for slot configuration 0 and numerology μ, there are 14 symbols/slot and 2^μ slots/subframe. The subcarrier spacing and symbol length/duration are a function of the numerology. The subcarrier spacing may be equal to 2^μ*15 kHz, where μ is the numerology 0 to 5. As such, the numerology μ=0 has a subcarrier spacing of 15 kHz and the numerology μ=5 has a subcarrier spacing of 480 kHz. The symbol length/duration is inversely related to the subcarrier spacing. Figs. 2A–2D provide an example of slot configuration 0 with 14 symbols per slot and numerology μ=2 with 4 slots per subframe. The slot duration is 0.25 ms, the subcarrier spacing is 60 kHz, and the symbol duration is approximately 16.67 microseconds (μs) .

A resource grid may be used to represent the frame structure. Each time slot includes a resource block (RB) (also referred to as physical RBs (PRBs) ) that extends 12 consecutive subcarriers. The resource grid is divided into multiple resource elements (REs) . The number of bits carried by each RE depends on the modulation scheme.

As illustrated in FIG. 2A, some of the REs carry reference (pilot) signals (RS) for the UE. The RS may include demodulation RS (DMRS) (indicated as R_x for one particular configuration, where 100x is the port number, but other DM-RS configurations are possible) and channel state information reference signals (CSI-RS) for channel estimation at the UE. The RS also may include beam measurement RS (BRS) , beam refinement RS (BRRS) , and phase tracking RS (PT-RS) .

FIG. 2B illustrates an example of various DL channels within a subframe of a frame. The physical downlink control channel (PDCCH) carries DCI within one or more control channel elements (CCEs) , each CCE including nine RE groups (REGs) , each REG including four consecutive REs in an OFDM symbol. A primary synchronization signal (PSS) may be within symbol 2 of particular subframes of a frame. The PSS is used by a UE 104 to determine subframe/symbol timing and a L1 identity. A secondary synchronization signal (SSS) may be within symbol 4 of particular subframes of a frame. The SSS is used by a UE to determine a L1 cell identity group number and radio frame timing. Based on the L1 identity and the L1 cell identity group number, the UE can determine a physical cell identifier (PCI) . Based on the PCI, the UE can determine the locations of the aforementioned DMRS. The physical broadcast channel (PBCH) , which carries a master information block (MIB) , may be logically grouped with the PSS and SSS to form a synchronization signal (SS) /PBCH block (SSB) . The MIB provides a number of RBs in the system bandwidth and a system frame number (SFN) . The physical downlink shared channel (PDSCH) carries user data, broadcast system information not transmitted through the PBCH such as system information blocks (SIBs) , and paging messages.

As illustrated in Figure 2C, some of the REs carry DM-RS (indicated as R for one particular configuration, but other DM-RS configurations are possible) for channel estimation at the base station. The UE may transmit DM-RS for the physical uplink control channel (PUCCH) and DM-RS for the physical uplink shared channel (PUSCH) . The PUSCH DM-RS may be transmitted in the first one or two symbols of the PUSCH. The PUCCH DM-RS may be transmitted in different configurations depending on whether short or long PUCCHs are transmitted and depending on the particular PUCCH format used. The UE may transmit sounding reference signals (SRS) . The SRS may be transmitted in the last symbol of a subframe. The SRS may have a comb structure, and a UE may transmit SRS on one of the combs. The SRS may be used by a base station for channel quality estimation to enable frequency-dependent scheduling on the UL.

Figure 2D illustrates an example of various UL channels within a subframe of a frame. The PUCCH may be located as indicated in one configuration. The PUCCH carries uplink control information (UCI) , such as scheduling requests, a channel quality indicator (CQI) , a precoding matrix indicator (PMI) , a rank indicator (RI) , and HARQ ACK/NACK feedback. The PUSCH carries data, and may additionally be used to carry a buffer status report (BSR) , a power headroom report (PHR) , or UCI.

Figure 3 is a diagram of an example of a base station 310 and a UE 350 in an access network. In the DL, IP packets from the EPC 160 may be provided to a controller/processor 375. The controller/processor 375 implements layer 3 and layer 2 functionality. Layer 3 includes a radio resource control (RRC) layer, and layer 2 includes a service data adaptation protocol (SDAP) layer, a packet data convergence protocol (PDCP) layer, a radio link control (RLC) layer, and a medium access control (MAC) layer. The controller/processor 375 provides RRC layer functionality associated with broadcasting of system information (such as MIB, SIBs) , RRC connection control (such as RRC connection paging, RRC connection establishment, RRC connection modification, and RRC connection release) , inter radio access technology (RAT) mobility, and measurement configuration for UE measurement reporting; PDCP layer functionality associated with header compression /decompression, security (ciphering, deciphering, integrity protection, integrity verification) , and handover support functions; RLC layer functionality associated with the transfer of upper layer packet data units (PDUs) , error correction through ARQ, concatenation, segmentation, and reassembly of RLC service data units (SDUs) , re-segmentation of RLC data PDUs, and reordering of RLC data PDUs; and MAC layer functionality associated with mapping between logical channels and transport channels, multiplexing of MAC SDUs onto transport blocks (TBs) , demultiplexing of MAC SDUs from TBs, scheduling information reporting, error correction through HARQ, priority handling, and logical channel prioritization.

The transmit (TX) processor 316 and the receive (RX) processor 370 implement layer 1 functionality associated with various signal processing functions. Layer 1, which includes a physical (PHY) layer, may include error detection on the transport channels, forward error correction (FEC) coding/decoding of the transport channels, interleaving, rate matching, mapping onto physical channels, modulation/demodulation of physical channels, and MIMO antenna processing. The TX processor 316 handles mapping to signal constellations based on various modulation schemes (such as binary phase-shift keying (BPSK) , quadrature phase-shift keying (QPSK) , M-phase-shift keying (M-PSK) , M-quadrature amplitude modulation (M-QAM) ) . The coded and modulated symbols may be split into parallel streams. Each stream may be mapped to an OFDM subcarrier, multiplexed with a reference signal (such as a pilot) in the time or frequency domain, and combined together using an Inverse Fast Fourier Transform (IFFT) to produce a physical channel carrying a time domain OFDM symbol stream. The OFDM stream is spatially precoded to produce multiple spatial streams. Channel estimates from a channel estimator 374 may be used to determine the coding and modulation scheme, as well as for spatial processing. The channel estimate may be derived from a reference signal or channel condition feedback transmitted by the UE 350. Each spatial stream may be provided to a different antenna 320 via a separate transmitter 318TX. Each transmitter 318TX may modulate an RF carrier with a respective spatial stream for transmission.

At the UE 350, each receiver 354RX receives a signal through its respective antenna 352. Each receiver 354RX recovers information modulated onto an RF carrier and provides the information to the receive (RX) processor 356. The TX processor 368 and the RX processor 356 implement layer 1 functionality associated with various signal processing functions. The RX processor 356 may perform spatial processing on the information to recover any spatial streams destined for the UE 350. If multiple spatial streams are destined for the UE 350, they may be combined by the RX processor 356 into a single OFDM symbol stream. The RX processor 356 converts the OFDM symbol stream from the time-domain to the frequency domain using a Fast Fourier Transform (FFT) . The frequency domain signal includes a separate OFDM symbol stream for each subcarrier of the OFDM signal. The symbols on each subcarrier, and the reference signal, are recovered and demodulated by determining the most likely signal constellation points transmitted by the base station 310. These soft decisions may be based on channel estimates computed by the channel estimator 358. The soft decisions are decoded and deinterleaved to recover the data and control signals that were originally transmitted by the base station 310 on the physical channel. The data and control signals are provided to the controller/processor 359, which implements layer 3 and layer 2 functionality.

The controller/processor 359 can be associated with a memory 360 that stores program codes and data. The memory 360 may be referred to as a computer-readable medium and may be any of the types of computer-readable mediums discussed herein (e.g., RAM, ROM, EEPROM, optical disk storage, magnetic disk storage, other magnetic storage devices, combinations of the aforementioned types of computer-readable media, or any other medium that can be used to store computer executable code in the form of instructions or data structures that can be accessed by a computer) . In the UL, the controller/processor 359 provides demultiplexing between transport and logical channels, packet reassembly, deciphering, header decompression, and control signal processing to recover IP packets from the EPC 160. The controller/processor 359 is also responsible for error detection using an ACK or NACK protocol to support HARQ operations.

Similar to the functionality described in connection with the DL transmission by the base station 310, the controller/processor 359 provides RRC layer functionality associated with system information (such as MIB, SIBs) acquisition, RRC connections, and measurement reporting; PDCP layer functionality associated with header compression /decompression, and security (ciphering, deciphering, integrity protection, integrity verification) ; RLC layer functionality associated with the transfer of upper layer PDUs, error correction through ARQ, concatenation, segmentation, and reassembly of RLC SDUs, re-segmentation of RLC data PDUs, and reordering of RLC data PDUs; and MAC layer functionality associated with mapping between logical channels and transport channels, multiplexing of MAC SDUs onto TBs, demultiplexing of MAC SDUs from TBs, scheduling information reporting, error correction through HARQ, priority handling, and logical channel prioritization.

Channel estimates derived by a channel estimator 358 from a reference signal or feedback transmitted by the base station 310 may be used by the TX processor 368 to select the appropriate coding and modulation schemes, and to facilitate spatial processing. The spatial streams generated by the TX processor 368 may be provided to different antenna 352 via separate transmitters 354TX. Each transmitter 354TX may modulate an RF carrier with a respective spatial stream for transmission.

The UL transmission is processed at the base station 310 in a manner similar to that described in connection with the receiver function at the UE 350. Each receiver 318RX receives a signal through its respective antenna 320. Each receiver 318RX recovers information modulated onto an RF carrier and provides the information to a RX processor 370.

The controller/processor 375 can be associated with a memory 376 that stores program codes and data. The memory 376 may be referred to as a computer-readable medium and may be any of the types of computer-readable mediums discussed herein (e.g., RAM, ROM, EEPROM, optical disk storage, magnetic disk storage, other magnetic storage devices, combinations of the aforementioned types of computer-readable media, or any other medium that can be used to store computer executable code in the form of instructions or data structures that can be accessed by a computer) . In the UL, the controller/processor 375 provides demultiplexing between transport and logical channels, packet reassembly, deciphering, header decompression, control signal processing to recover IP packets from the UE 350. IP packets from the controller/processor 375 may be provided to the EPC 160. The controller/processor 375 is also responsible for error detection using an ACK or NACK protocol to support HARQ operations.

At least one of the TX processor 368, the RX processor 356, and the controller/processor 359 may be configured to perform aspects in connection with the MIMO demodulation component 140 of FIG. 1. For example, the memory 360 may include executable instructions defining the MIMO demodulation component 140. The TX processor 368, the RX processor 356, and/or the controller/processor 359 may be configured to execute the MIMO demodulation component 140. In some implementations, at least one of the TX processor 368, the RX processor 356, and the controller/processor 359 may be configured to execute the probabilistic shaping component 120 for uplink transmissions.

At least one of the TX processor 316, the RX processor 370, and the controller/processor 375 may be configured to perform aspects in connection with the MIMO demodulation component 140 of FIG. 1. For example, the memory 376 may include executable instructions defining the MIMO demodulation component 140. The TX processor 316, the RX processor 370, and/or the controller/processor 375 may be configured to execute the MIMO demodulation component 140. In some implementations, at least one of the TX processor 368, the RX processor 356, and the controller/processor 359 may be configured to execute the probabilistic shaping component 120 for downlink transmissions.

FIG. 4 is a diagram illustrating an example disaggregated base station 400 architecture. The disaggregated base station 400 architecture may include one or more central units (CUs) 410 that can communicate directly with a core network 420 via a backhaul link, or indirectly with the core network 420 through one or more disaggregated base station units (such as a Near-Real Time (Near-RT) RAN Intelligent Controller (RIC) 425 via an E2 link, or a Non-Real Time (Non-RT) RIC 415 associated with a Service Management and Orchestration (SMO) Framework 405, or both) . A CU 410 may communicate with one or more distributed units (DUs) 430 via respective midhaul links, such as an F1 interface. The DUs 430 may communicate with one or more radio units (RUs) 440 via respective fronthaul links. The RUs 440 may communicate with respective UEs 104 via one or more radio frequency (RF) access links. In some implementations, the UE 104 may be simultaneously served by multiple RUs 440.

Each of the units, i.e., the CUs 410, the DUs 430, the RUs 440, as well as the Near-RT RICs 425, the Non-RT RICs 415 and the SMO Framework 405, may include one or more interfaces or be coupled to one or more interfaces configured to receive or transmit signals, data, or information (collectively, signals) via a wired or wireless transmission medium. Each of the units, or an associated processor or controller providing instructions to the communication interfaces of the units, can be configured to communicate with one or more of the other units via the transmission medium. For example, the units can include a wired interface configured to receive or transmit signals over a wired transmission medium to one or more of the other units. Additionally, the units can include a wireless interface, which may include a receiver, a transmitter or transceiver (such as a radio frequency (RF) transceiver) , configured to receive or transmit signals, or both, over a wireless transmission medium to one or more of the other units.

In some aspects, the CU 410 may host one or more higher layer control functions. Such control functions can include radio resource control (RRC) , packet data convergence protocol (PDCP) , service data adaptation protocol (SDAP) , or the like. Each control function can be implemented with an interface configured to communicate signals with other control functions hosted by the CU 410. The CU 410 may be configured to handle user plane functionality (i.e., Central Unit –User Plane (CU-UP) ) , control plane functionality (i.e., Central Unit –Control Plane (CU-CP) ) , or a combination thereof. In some implementations, the CU 410 can be logically split into one or more CU-UP units and one or more CU-CP units. The CU-UP unit can communicate bidirectionally with the CU-CP unit via an interface, such as the E1 interface when implemented in an O-RAN configuration. The CU 410 can be implemented to communicate with the DU 430, as necessary, for network control and signaling.

The DU 430 may correspond to a logical unit that includes one or more base station functions to control the operation of one or more RUs 440. In some aspects, the DU 430 may host one or more of a radio link control (RLC) layer, a medium access control (MAC) layer, and one or more high physical (PHY) layers (such as modules for forward error correction (FEC) encoding and decoding, scrambling, modulation and demodulation, or the like) depending, at least in part, on a functional split, such as those defined by the 3^rd Generation Partnership Project (3GPP) . In some aspects, the DU 430 may further host one or more low PHY layers. Each layer (or module) can be implemented with an interface configured to communicate signals with other layers (and modules) hosted by the DU 430, or with the control functions hosted by the CU 410.

Lower-layer functionality can be implemented by one or more RUs 440. In some deployments, an RU 440, controlled by a DU 430, may correspond to a logical node that hosts RF processing functions, or low-PHY layer functions (such as performing fast Fourier transform (FFT) , inverse FFT (iFFT) , digital beamforming, physical random access channel (PRACH) extraction and filtering, or the like) , or both, based at least in part on the functional split, such as a lower layer functional split. In such an architecture, the RU (s) 440 can be implemented to handle over the air (OTA) communication with one or more UEs 104. In some implementations, real-time and non-real-time aspects of control and user plane communication with the RU (s) 440 can be controlled by the corresponding DU 430. In some scenarios, this configuration can enable the DU (s) 430 and the CU 410 to be implemented in a cloud-based RAN architecture, such as a vRAN architecture.

The SMO Framework 405 may be configured to support RAN deployment and provisioning of non-virtualized and virtualized network elements. For non-virtualized network elements, the SMO Framework 405 may be configured to support the deployment of dedicated physical resources for RAN coverage requirements which may be managed via an operations and maintenance interface (such as an O1 interface) . For virtualized network elements, the SMO Framework 405 may be configured to interact with a cloud computing platform (such as an open cloud (O-Cloud) 490) to perform network element life cycle management (such as to instantiate virtualized network elements) via a cloud computing platform interface (such as an O2 interface) . Such virtualized network elements can include, but are not limited to, CUs 410, DUs 430, RUs 440 and Near-RT RICs 425. In some implementations, the SMO Framework 405 can communicate with a hardware aspect of a 4G RAN, such as an open eNB (O-eNB) 411, via an O1 interface. Additionally, in some implementations, the SMO Framework 405 can communicate directly with one or more RUs 440 via an O1 interface. The SMO Framework 405 also may include a Non-RT RIC 415 configured to support functionality of the SMO Framework 405.

The Non-RT RIC 415 may be configured to include a logical function that enables non-real-time control and optimization of RAN elements and resources, Artificial Intelligence/Machine Learning (AI/ML) workflows including model training and updates, or policy-based guidance of applications/features in the Near-RT RIC 425. The Non-RT RIC 415 may be coupled to or communicate with (such as via an A1 interface) the Near-RT RIC 425. The Near-RT RIC 425 may be configured to include a logical function that enables near-real-time control and optimization of RAN elements and resources via data collection and actions over an interface (such as via an E2 interface) connecting one or more CUs 410, one or more DUs 430, or both, as well as an O-eNB, with the Near-RT RIC 425.

In some implementations, to generate AI/ML models to be deployed in the Near-RT RIC 425, the Non-RT RIC 415 may receive parameters or external enrichment information from external servers. Such information may be utilized by the Near-RT RIC 425 and may be received at the SMO Framework 405 or the Non-RT RIC 415 from non-network data sources or from network functions. In some examples, the Non-RT RIC 415 or the Near-RT RIC 425 may be configured to tune RAN behavior or performance. For example, the Non-RT RIC 415 may monitor long-term trends and patterns for performance and employ AI/ML models to perform corrective actions through the SMO Framework 405 (such as reconfiguration via O1) or via creation of RAN management policies (such as A1 policies) .

FIG. 5 is a message diagram 500 illustrating various messages for decoding MIMO transmissions with probabilistic shaping. The UE 104 may be in communication with one or more base stations 502. The base station 502 may provide a primary cell and/or secondary cells. For illustrative purposes, the base station 502 is shown as transmitting a downlink MIMO transmission using probabilistic shaping, and the UE 104 is shown as receiving and demodulating the downlink MIMO transmission. In some implementations, a UE 104 may use probabilistic shaping for an uplink MIMO transmission, and a base station may receive and demodulate the MIMO transmission.

In an aspect, probabilistic shaping may be used by a transmitter to increase spectral efficiency of MIMO transmissions. The probabilistic shaping maximizes source entropy for a given average power. Accordingly, probabilistic shaping should improve accuracy of demodulation at a receiver. However, traditional MIMO demodulation of probabilistically shaped transmissions shows performance loss compared to MIMO demodulation of regular quadrature amplitude modulation (QAM) constellations.

A base station 502 may transmit a synchronization signal block (SSB) 505. The SSB 505 may include a primary synchronization signal (PSS) , a secondary synchronization signal (SSS) , and a physical broadcast channel (PBCH) . The PBCH may carry some information for the cell provided by the base station 502. For example, the PBCH may indicate a location for system information 510. The base station 502 may transmit the system information 510. The system information 510 may include parameters for MIMO transmissions. For example, the system information 510 may indicate a number of antenna groups and a number of layers for various channels. In some implementations, the system information 510 may indicate whether the base station 502 uses probabilistic shaping.

In some implementations, the UE 104 may transmit a capability message 515 that indicates a capability of the UE with respect to probabilistic shaping and/or lattice basis reduction. For example, the capability message 515 may indicate a capability for demodulation using lattice basis reduction.

In some implementations, the base station 502 may transmit an RRC configuration 520. The RRC configuration 520 may indicate whether MIMO transmission will utilize probabilistic shaping.

The base station 502 may perform probabilistic shaping based modulation 525. The base station 502 may generate non-uniformly distributed (QAM) constellations. For example, a Maxwell-Boltzmann (MB) distribution ofmaximizes source entropy for a given average power. One example technique for performing probabilistic shaping is constant-composition distribution matching (CCDM) with the MB distribution.

The base station 502 may perform precoding 530. For example, the base station 502 may generate a precoding matrix and apply the precoding matrix to both a data signal 542 and a DMRS 544 of a transmission 540. For instance, the transmission 540 may be one of a broadcast data transmission, a control channel, a transmission prior to radio resource control connection establishment, a fallback transmission, or a scheduled physical downlink shared channel. The base station 502 transmits the precoded transmission 540 (e.g., PDSCH) via the antenna groups.

The UE 104 receives the transmission 540 and performs channel estimation 550 based on the DMRS 544. The channel estimation 550 may generate a channel matrix H that indicates the channel for each of the pairs of antennas between the base station 502 and the UE 104. The channel estimate may have various levels of granularity. For example, the channel estimation may be per frequency domain resource unit (e.g., resource block) or per DMRS channel.

In an aspect, the UE 104 performs lattice basis reduction 560 on a translated 2N-dimensional lattice of MIMO constellation points. The lattice basis reduction 560 may be based on the channel estimate and a coefficient based on the distribution for probabilistic shaping. The lattice basis reduction results in a smaller orthogonality defect in the lattice. The UE 104 performs demodulation on a projected received point using linear demodulation with the reduced basis lattice. Further details of the lattice basis reduction 560 are described below with respect to FIG. 7 and further details of demodulation 570 are described below with respect to FIG. 8.

FIG. 6 is a diagram 600 of uniform QAM and probabilistic shaping for constellation points 610 and 640. For the constellation points 610 and 640, the height represents the probability of transmission. In uniform QAM, each of the constellation points 610 has the same probability and is sent with the same transmission power. In contrast, probabilistic shaping, corresponding to PS-based modulation 525 (FIG. 5) , for example, applies different transmission powers based on the probability of each constellation point 640. In particular, the inner constellation points have higher probability of being transmitted (i.e., are sent more frequently) and are transmitted with lower energy, while the outer constellation points have lower probability (i.e., are sent less frequently) , and are transmitted with greater power. On average, because the higher power constellation points are sent less frequently, the average power is reduced.

For simplicity, reception of a single-input, single-output (SISO) transmission is illustrated in FIG. 6. At the receiver, for uniform QAM, the distance 620 between each of the constellation points x 622 is equal. For example, a distance metric between the constellation point x 622 and a received signal y 624 (post equalization) may be expressed as D (x) =|y-hx|²/N₀, where h is the channel estimate and N₀ is Gaussian noise. The log-likelihood logPr (y|x) is equivalent to the distance metric:

Using maximum-likelihood (ML) decoder: x^*=argmax_x∈SPr (y|x) =argmin_xD (x) . Using a log maximum a posteriori probability (MAP) decoder MAX-LOG-MAP

For probabilistic shaping, the distance 650 depends on the distance between the constellation points after probabilistic shaping. The log-likelihood function contains symbol priors 652 represented as log Pr (x) Pr (y|x) . The distance metric becomes:

Linear decoders such as ML, LOG-MAP, or MAX-LOG-MAP can generalize to PS by using the new distance metric D (x) .

For a SISO transmission using probabilistic shaping, input scaling may be used to simplify the distance computation. When the Maxwell-Boltzmann prior (log Pr (x) ∝-|x|²) is applied to the constellation points, the result 660 may be viewed as a line onto which the received signal y 664 may be projected. The distance computation simplifies to a linear distance 662. Accordingly, when input scaling is applied to H and Y, the uniform QAM demodulation (e.g., linear demodulation) may be reused. The same simplification applies for the signal layer and interference layer distance calculation.

FIG. 7 is a conceptual diagram 700 illustrating lattice basis reduction for demodulation of a MIMO transmission for transmissions with probabilistic shaping. The lattice basis reduction corresponds to lattice basis reduction 560 in FIG. 5. The whole MIMO constellation (combination of all N layers) after the effects of the channel matrix, can be seen as points from a 2N-dimensional lattice 710 (which depends on the channel matrix H) . In the case of uniform QAM, for any realization of the channel matrix H, the problem of maximum likelihood MIMO decoding is equivalent to finding the nearest point to that 2N-dimensional received MIMO constellations. Without considering the boundary of the constellation, the problem becomes finding the nearest lattice point 712 to the received MIMO point 714. Methods such as a sphere decoder can be used for exact lattice decoding. Even exact lattice decoding, without considering the effect of the constellation boundary, has some loss compared to maximum likelihood decoding (because of ignoring boundary) . But lattice decoding achieves the optimum receive diversity (unlike the layer-by-layer decoding methods such as MMSE or per stream recursive decoder (PSRD) /ePSRD) . Also, the complexity of lattice decoding scales well with the size of the constellation per dimension (which is good for larger modulation orders) .

Lattice basis reduction can be used as an efficient approximation method for lattice decoding (or finding the nearest lattice point to a given point in space) . The idea is to use lattice basis reduction to reduce the orthogonality defect of the lattice basis (which results in better linear approximation of the lattice decoding) . For example, the lattice 710 may have an original basis corresponding to the channel matrix. The reduced basis lattice 720 has a reduced basis B, which may be used for better linear demodulation of the received MIMO constellation. Lenstra-Lenstra-Lovász (LLL) lattice basis reduction is an efficient algorithm for reducing the lattice basis in polynomial time (in terms of number of dimensions) . In an aspect, lattice reduction together with linear approximation of lattice decoding achieves the optimum diversity in MIMO systems (unlike the traditional linear MIMO demods or methods based on QR decomposition) .

FIG. 8 is a diagram 800 showing a distance calculation for MIMO demodulation using lattice basis reduction. For example, the distance calculation may be used to obtain a nearest constellation point for the demodulation 570 in FIG. 5. In an aspect, lattice basis reduction may be applied to a MIMO transmission in a similar manner as input scaling is applied to a SISO transmission to simplify MIMO demodulation of probabilistically shaped transmissions to allow use of linear demodulation techniques. Assuming there are N MIMO layers, the Maxwell-Boltzmann prior (log Pr (x) ∝-|x|²) may be used for lattice basis reduction to reduce a translated 2N-dimensional lattice of MIMO constellation points in a 4N-dimensional space, which is the result of the effect of the channel matrix tilting because of the MB distribution and MAP geometry. The subspace 810 is a 2N-dimensional subspace of a 4N-dimensional space containing the lattice of received constellation points after the effects of the channel matrix. The subspace 820 is a 2N-dimensional subspace of a 4N-dimensional space containing the lattice of received constellation point after the effect of channel matrix and input scaling due to MB prior distribution.

If {x} are 2N-dimensional modulation points (e.g. from a QAM constellation) and H is the channel matrix, Hx will be a received lattice point without noise, and Hx+w is the received modulation point at the receiver after the effect of the additive noise vector. By considering the geometric effect of MAP decoding of probabilistic shaping, the demodulation problem becomes finding the nearest lattice point ofto the point in a 4N-dimensional space. The coefficient a (in ax) depends on the parameters of the MB distribution, and also the noise power (and/or SNR) . The coefficient a (in ax) may depend on other parameters of the signal transmission and/or channel (e.g. the statistics of the fading channel) .

In an aspect, a first step of the demodulation process is to project the received 4N-dimensional point 812 to the 2N-dimensional subspace 820 spanned by PS-demod-equivalent receive constellation pointsand obtain x*814. The second step is to do lattice basis reduction B (where B=UH’ with an appropriate unimodular matrix U, which changes the basis of the lattice resulting a smaller orthogonality defect) for the lattice corresponding toin the subspace 820. In some implementations, LLL algorithms may be used for performing lattice basis reduction. Lattice basis reduction (in terms of finding the unimodular matrix U that does the change of basis) can be done once for a group of resource elements (in time and frequency domain) that see relatively similar channel conditions. That is, even though channel matrix H’₁ and H’₂ can be different for two different resource elements, as long as the there is no large deviation in channel coefficients (i.e. H’₁ and H’₂ are relatively similar) , the same unimodular matrix U may be used for obtaining their corresponding reduced basis, i.e. B₁=UH’₁ and B₂=UH’₂. The third step is to obtain the approximated nearest lattice point 822, by using zero forcing or MMSE or other linear methods using matrix B. For example, zero forcing can be done by multiplying the pseudo-inverse of B with the projected received point x*814. The nearest lattice point 822 may be output as the result of demodulation for the symbol.

FIG. 9 is a conceptual data flow diagram 900 illustrating the data flow between different means/components in an example UE 104, which may be an example of the UE 104 (FIG. 1) and include the MIMO demodulation component 140. The MIMO demodulation component 140 may be implemented by the memory 360 and the TX processor 368, the RX processor 356, and/or the controller/processor 359. For example, the memory 360 may store executable instructions defining the MIMO demodulation component 140and the TX processor 368, the RX processor 356, and/or the controller/processor 359 may execute the instructions.

The UE 104 may include a receiver component 970, which may include, for example, a RF receiver for receiving the signals described herein via antennas 974. The UE 104 may include a transmitter component 972, which may include, for example, an RF transmitter for transmitting the signals described herein. In an aspect, the receiver component 970 and the transmitter component 972 may co-located in a transceiver such as the TX/RX 354 in FIG. 3.

As discussed with respect to FIG. 1, the MIMO demodulation component 140 includes the projection component 142, the reduction component 144, and the linear demod component 146. In some implementations, the MIMO demodulation component 140 may optionally include a channel estimation component 910.

The receiver component 970 may receive DL signals described herein such as the SSB 505, system information 510, RRC configuration 520, and transmission 540. The receiver component 970 may output the SSB 505, system information 510, or RRC configuration 520 to the MIMO demodulation component 140 as control signaling (e.g., indicating probabilistic shaping) . The receiver component 970 may output the transmission 540 to the projection component 142 as a received signal including received constellation points.

The optional channel estimation component 910 may be configured to generate a channel estimate matrix H. For example, the channel estimation component 910 may receive the DMRS from the receiver component 970. The channel estimation component 910 may generate the channel estimate matrix H based on the DMRS as known in the art. The channel estimation component 910 may provide the channel estimate matrix H to the projection component 142 and/or the reduction component 144.

The projection component 142 is configured to project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point. The received 4N-dimensional point is due to two dimensions of the QAM constellation, two dimensions of channel matrix tilting, and N layers. Projecting the received 4N-dimensional point may include projecting a received point (Hx+w) to a pointwhere H is the estimated channel and w is additive noise. The 2N-dimensional subspace 820 spanned by probabilistic shaping demod-equivalent receive constellation points may be represented by a matrixwhere a is a coefficient based at least in part on a distribution for probabilistic shaping (e.g., the Maxwell-Boltzmann distribution) , H is the estimated channel, and x is a matrix of 2N-dimensional modulation points. The projection into the 2N-dimensional subspace 820 spanned by probabilistic shaping demod-equivalent receive constellation points removes the two dimensions of channel matrix tilting. The projection component 142 may output the projected received point to the linear demod component 146.

The reduction component 144 is configured to perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. The reduction component 144 may receive a channel estimate H from the channel estimation component 910. The reduction component 144 may use a generator (H’) based on an estimated channel (H) and a coefficient (a) based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace. For example, the generator (H’) may be represented asThe reduction component 144 may include a unimodular matrix component 920 configured to determine a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect. A reduced basis lattice B may be expressed as B=UH’. In some implementations, the unimodular matrix is applicable to multiple resource elements. A number of the resource elements is based on a rate of change of the channel. For example, resource elements that are within a threshold distance metric of the channel estimate corresponding to a computed unimodular matrix may utilize the same computed unimodular matrix. In some implementations, the reduction component 144 includes a LLL component 922 configured to determine the unimodular matrix using Lenstra-Lenstra-Lovász (LLL) basis reduction. The reduction component 144 may output the reduced basis lattice B to the linear demod component 146.

The linear demod component 146 is configured to obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice. The linear demod component 146 receive the reduced basis lattice from the reduction component 144. The linear demodulation may include techniques such as zero forcing or minimum mean squared error (MMSE) . In some implementations, the linear demod component 146 may include a zero forcing demodulator 930 configured to perform zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice. In some implementations, the linear demod component 146 may include a MMSE demodulator 932 configured to perform MMSE estimation. The linear demod component 146 may output the nearest point (e.g., as log likelihood ratios) to other receive chain components such as a decoder 940.

FIG. 10 is a flowchart of an example method 1000 demodulating a multiple-input multiple-output (MIMO) transmission with N layers. The method 1000 may be performed by a UE (such as the UE 104, which may include the memory 360 and which may be the entire UE 104 or a component of the UE 104 such as the MIMO demodulation component 140, TX processor 368, the RX processor 356, or the controller/processor 359) . The method 1000 may be performed by MIMO demodulation component 140 in communication with a probabilistic shaping component 120 of the base station 102. In some implementations, the base station 102 may include the MIMO demodulation component 140 and perform the method 1000, and a UE 104 may include a probabilistic shaping component 120. Optional blocks are shown with dashed lines.

At block 1010, the method 1000 includes projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point. In some implementations, for example, the UE 104, the RX processor 356 or the controller/processor 359 may execute the MIMO demodulation component 140 or the projection component 142 to project the received 4N-dimensional point 812 to a 2N-dimensional subspace 820 spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point 814. In some implementations, at sub-block 1012, the block 1010 may optionally include projecting a received point (Hx+w) to a pointwhere H is an estimated channel and w is additive noise. In some implementations, the 2N-dimensional subspace 820 spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrixwhere a is a coefficient based at least in part on a distribution for probabilistic shaping, H is the estimated channel, and x is a matrix of 2N-dimensional modulation points. Accordingly, the UE 104, the RX processor 356, or the controller/processor 359 executing the MIMO demodulation component 140 or projection component 142 may provide means for projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point.

At block 1020, the method 1000 includes performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. In some implementations, for example, the UE 104, the RX processor 356 or the controller/processor 359 may execute the MIMO demodulation component 140 or the reduction component 144 to performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice. In some implementations, at sub-block 1022, the block 1020 may optionally include using a generator (H’) based on an estimated channel (H) and a coefficient (a) based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace. At sub-block 1024, the block 1020 may further optionally include determining a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect. In some implementations, the unimodular matrix is applicable to multiple resource elements. In some implementations, a number of the multiple resource elements is based on a rate of change of the channel. In some implementations, at sub-block 1026, the block 1020 may optionally include utilizing Lenstra-Lenstra-Lovász (LLL) basis reduction to perform the lattice basis reduction. Accordingly, the UE 104, the RX processor 356, or the controller/processor 359 executing the MIMO demodulation component 140 or the reduction component 144 may provide means for performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice.

At block 1030, the method 1000 includes obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice. In some implementations, for example, the UE 104, the RX processor 356 or the controller/processor 359 may execute the MIMO demodulation component 140 or the linear demod component 146 to obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice. In some implementations, at sub-block 1032, the block 1030 may optionally include performing zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice. In some implementations, at sub-block 1034, the block 1030 may optionally include performing MMSE estimation. In some implementations, the nearest point may be output as the result of the demodulation for the received point. Accordingly, the UE 104, the RX processor 356, or the controller/processor 359 executing the MIMO demodulation component 140 or the linear demod component 146 may provide means for obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

The following numbered clauses provide an overview of aspects of the present disclosure:

Clause 1. A method of demodulating a multiple-input multiple-output (MIMO) transmission with N layers, the method comprising: projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

Clause 2. The method of clause 1, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.

Clause 3. The method of clause 1, wherein the projecting the received 4N-dimensional point comprises projecting a received point (Hx+w) to a point , where is an estimated channel and w is additive noise.

Clause 4. The method of clause 3, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrix , where is a coefficient based at least in part on a distribution for probabilistic shaping, is an estimated channel, and x is a matrix of 2N-dimensional modulation points.

Clause 5. The method of clause 1, wherein performing the lattice basis reduction comprises: using a generator (H') based on an estimated channel (H) and a coefficient () based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and determining a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.

Clause 6. The method of clause 5, wherein the unimodular matrix is applicable to multiple resource elements.

Clause 7. The method of clause 6, wherein a number of the multiple resource elements is based on a rate of change of the channel.

Clause 8. The method of clause 1, wherein performing the lattice basis reduction utilizes Lenstra-Lenstra-Lovász (LLL) basis reduction.

Clause 9. The method of clause 1, wherein obtaining the nearest lattice point using the reduced basis lattice comprises performing zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice.

Clause 10. The method of clause 1, wherein obtaining the nearest lattice point using the reduced basis lattice comprises performing minimum mean squared error (MMSE) estimation.

Clause 11. An apparatus for wireless communication, comprising: one or more memories storing computer-executable instructions; and one or more processors coupled with the one or more memories and configured to execute the computer-executable instructions, individually or in combination, to cause the apparatus to: project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

Clause 12. The apparatus of clause 11, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.

Clause 13. The apparatus of clause 11, wherein to project the received 4N-dimensional point, the one or more processors, individually or in combination, are configured to project a received point (Hx+w) to a point , where is an estimated channel and w is additive noise.

Clause 14. The apparatus of clause 13, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrix , where is a coefficient based at least in part on a distribution for probabilistic shaping, is an estimated channel, and x is a matrix of 2N-dimensional modulation points.

Clause 15. The apparatus of clause 11, wherein to perform the lattice basis reduction, the one or more processors, individually or in combination, are configured to: use a generator (H') based on an estimated channel (H) and a coefficient () based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and determine a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.

Clause 16. The apparatus of clause 15, wherein the unimodular matrix is applicable to multiple resource elements.

Clause 17. The apparatus of clause 16, wherein a number of resource elements is based on a rate of change of the channel.

Clause 18. The apparatus of clause 11, wherein to perform the lattice basis reduction, the one or more processors, individually or in combination, are configured to perform Lenstra-Lenstra-Lovász (LLL) basis reduction.

Clause 19. The apparatus of clause 11, wherein to obtain the nearest lattice point using the reduced basis lattice, the one or more processors, individually or in combination, are configured to perform zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice.

Clause 20. The apparatus of clause 11, wherein the one or more processors, individually or in combination, are configured to perform minimum mean squared error (MMSE) estimation.

Clause 21. An apparatus for wireless communication, comprising: means for projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; means for performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and means for obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

Clause 22. The apparatus of clause 21, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.

Clause 23. The apparatus of clause 21, the means for projecting the received 4N-dimensional point, is configured to project a received point (Hx+w) to a point , where is an estimated channel and w is additive noise.

Clause 24. The apparatus of clause 23, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrix , where is a coefficient based at least in part on a distribution for probabilistic shaping, is an estimated channel, and x is a matrix of 2N-dimensional modulation points.

Clause 25. The apparatus of clause 21, the means for performing the lattice basis reduction is configured to: use a generator (H') based on an estimated channel (H) and a coefficient () based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and determine a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.

Clause 26. The apparatus of clause 25, wherein the unimodular matrix is applicable to multiple resource elements.

Clause 27. The apparatus of clause 26, wherein a number of resource elements is based on a rate of change of the channel.

Clause 28. The apparatus of clause 21, the means for performing the lattice basis reduction is configured to perform Lenstra-Lenstra-Lovász (LLL) basis reduction.

Clause 29. The apparatus of clause 21, wherein the means for obtaining the nearest lattice point using the reduced basis lattice is configured to perform zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice or to o perform minimum mean squared error (MMSE) estimation.

Clause 30. A non-transitory computer-readable medium storing computer-executable code that when executed by one or more processors of a receiving device causes the receiving device to: project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point; perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.

As used herein, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c.

The various illustrative logics, logical blocks, modules, circuits and algorithm processes described in connection with the implementations disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. The interchangeability of hardware and software has been described generally, in terms of functionality, and illustrated in the various illustrative components, blocks, modules, circuits and processes described above. Whether such functionality is implemented in hardware or software depends upon the particular application and design constraints imposed on the overall system.

The hardware and data processing apparatus used to implement the various illustrative logics, logical blocks, modules and circuits described in connection with the aspects disclosed herein may be implemented or performed with a general purpose single-or multi-chip processor, a digital signal processor (DSP) , an application specific integrated circuit (ASIC) , a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, or any conventional processor, controller, microcontroller, or state machine. A processor also may be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, particular processes and methods may be performed by circuitry that is specific to a given function.

In one or more aspects, the functions described may be implemented in hardware, digital electronic circuitry, computer software, firmware, including the structures disclosed in this specification and their structural equivalents thereof, or in any combination thereof. Implementations of the subject matter described in this specification also can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on a computer storage media for execution by, or to control the operation of, data processing apparatus.

If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. The processes of a method or algorithm disclosed herein may be implemented in a processor-executable software module which may reside on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that can be enabled to transfer a computer program from one place to another. A storage media may be any available media that may be accessed by a computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that may be used to store desired program code in the form of instructions or data structures and that may be accessed by a computer. Also, any connection can be properly termed a computer-readable medium. Disk and disc, as used herein, includes compact disc (CD) , laser disc, optical disc, digital versatile disc (DVD) , floppy disk, and Blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. Additionally, the operations of a method or algorithm may reside as one or any combination or set of codes and instructions on a machine readable medium and computer-readable medium, which may be incorporated into a computer program product.

Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. Thus, the claims are not intended to be limited to the implementations shown herein, but are to be accorded the widest scope consistent with this disclosure, the principles and the novel features disclosed herein.

Additionally, a person having ordinary skill in the art will readily appreciate, the terms “upper” and “lower” are sometimes used for ease of describing the figures, and indicate relative positions corresponding to the orientation of the figure on a properly oriented page, and may not reflect the proper orientation of any device as implemented.

Certain features that are described in this specification in the context of separate implementations also can be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation also can be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Further, the drawings may schematically depict one more example processes in the form of a flow diagram. However, other operations that are not depicted can be incorporated in the example processes that are schematically illustrated. For example, one or more additional operations can be performed before, after, simultaneously, or between any of the illustrated operations. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.

Claims

A method of demodulating a multiple-input multiple-output (MIMO) transmission with N layers, the method comprising:

projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point;

performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and

obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.
The method of claim 1, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.
The method of claim 1, wherein the projecting the received 4N-dimensional point comprises projecting a received point (Hx+w) to a pointwhere H is an estimated channel and w is additive noise.
The method of claim 3, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrixwhere a is a coefficient based at least in part on a distribution for probabilistic shaping, H is an estimated channel, and x is a matrix of 2N-dimensional modulation points.
The method of claim 1, wherein performing the lattice basis reduction comprises:

using a generator (H’) based on an estimated channel (H) and a coefficient (a) based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and

determining a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.
The method of claim 5, wherein the unimodular matrix is applicable to multiple resource elements.
The method of claim 6, wherein a number of the multiple resource elements is based on a rate of change of the channel.
The method of claim 1, wherein performing the lattice basis reduction utilizes Lenstra-Lenstra-Lovász (LLL) basis reduction.
The method of claim 1, wherein obtaining the nearest lattice point using the reduced basis lattice comprises performing zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice.
The method of claim 1, wherein obtaining the nearest lattice point using the reduced basis lattice comprises performing minimum mean squared error (MMSE) estimation.
An apparatus for wireless communication, comprising:

one or more memories storing computer-executable instructions; and

one or more processors coupled with the one or more memories and configured to execute the computer-executable instructions, individually or in combination, to cause the apparatus to:

project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point;

perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and

obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.
The apparatus of claim 11, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.
The apparatus of claim 11, wherein to project the received 4N-dimensional point, the one or more processors, individually or in combination, are configured to project a received point (Hx+w) to a pointwhere H is an estimated channel and w is additive noise.
The apparatus of claim 13, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrixwhere a is a coefficient based at least in part on a distribution for probabilistic shaping, H is an estimated channel, and x is a matrix of 2N-dimensional modulation points.
The apparatus of claim 11, wherein to perform the lattice basis reduction, the one or more processors, individually or in combination, are configured to:

use a generator (H’) based on an estimated channel (H) and a coefficient (a) based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and

determine a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.
The apparatus of claim 15, wherein the unimodular matrix is applicable to multiple resource elements.
The apparatus of claim 16, wherein a number of resource elements is based on a rate of change of the channel.
The apparatus of claim 11, wherein to perform the lattice basis reduction, the one or more processors, individually or in combination, are configured to perform Lenstra-Lenstra-Lovász (LLL) basis reduction.
The apparatus of claim 11, wherein to obtain the nearest lattice point using the reduced basis lattice, the one or more processors, individually or in combination, are configured to perform zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice.
The apparatus of claim 11, wherein the one or more processors, individually or in combination, are configured to perform minimum mean squared error (MMSE) estimation.
An apparatus for wireless communication, comprising:

means for projecting a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point;

means for performing lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and

means for obtaining a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.
The apparatus of claim 21, wherein the probabilistic shaping is based on scaling for a Maxwell-Boltzmann distribution with a log-likelihood of a prior being proportional to an opposite of an absolute value of the 4N-dimensional point squared.
The apparatus of claim 21, the means for projecting the received 4N-dimensional point, is configured to project a received point (Hx+w) to a point where H is an estimated channel and w is additive noise.
The apparatus of claim 23, wherein the 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points is represented by a matrixwhere a is a coefficient based at least in part on a distribution for probabilistic shaping, H is an estimated channel, and x is a matrix of 2N-dimensional modulation points.
The apparatus of claim 21, the means for performing the lattice basis reduction is configured to:

use a generator (H’) based on an estimated channel (H) and a coefficient (a) based at least in part on a distribution for probabilistic shaping as a matrix representing a lattice in the 2N-dimensional subspace; and

determine a unimodular matrix (U) that changes a basis of the generator resulting in a smaller orthogonality defect.
The apparatus of claim 25, wherein the unimodular matrix is applicable to multiple resource elements.
The apparatus of claim 26, wherein a number of resource elements is based on a rate of change of the channel.
The apparatus of claim 21, the means for performing the lattice basis reduction is configured to perform Lenstra-Lenstra-Lovász (LLL) basis reduction.
The apparatus of claim 21, wherein the means for obtaining the nearest lattice point using the reduced basis lattice is configured to perform zero forcing by multiplying the projected received point by a pseudo-inverse of the reduced basis lattice or to o perform minimum mean squared error (MMSE) estimation.
A non-transitory computer-readable medium storing computer-executable code that when executed by one or more processors of a receiving device causes the receiving device to:

project a received 4N-dimensional point to a 2N-dimensional subspace spanned by probabilistic shaping demod-equivalent receive constellation points to obtain a projected received point;

perform lattice basis reduction for a 2N-dimensional lattice to obtain a reduced basis lattice; and

obtain a nearest point of the reduced basis lattice to the projected received point using linear demodulation with the reduced basis lattice.