WO2008152596A2 - System and method of transmitting and receiving an ofdm signal with reduced peak -to -average power ratio using dummy sequence insertation - Google Patents
System and method of transmitting and receiving an ofdm signal with reduced peak -to -average power ratio using dummy sequence insertation Download PDFInfo
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- WO2008152596A2 WO2008152596A2 PCT/IB2008/052313 IB2008052313W WO2008152596A2 WO 2008152596 A2 WO2008152596 A2 WO 2008152596A2 IB 2008052313 W IB2008052313 W IB 2008052313W WO 2008152596 A2 WO2008152596 A2 WO 2008152596A2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2614—Peak power aspects
- H04L27/2618—Reduction thereof using auxiliary subcarriers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2614—Peak power aspects
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2614—Peak power aspects
- H04L27/2615—Reduction thereof using coding
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
Definitions
- This invention pertains to the field of data communications, and more particularly to a system and method of transmitting and receiving an orthogonal frequency division multiplexing (OFDM) signal.
- OFDM orthogonal frequency division multiplexing
- OFDM orthogonal frequency division multiplexing
- WiMAX Worldwide Interoperability for Microwave Access
- UWB WiMedia Ultra- Wideband
- OFDM is an effective transmission method for high data rate wireless communication applications due to its robustness against the frequency-selective fading, high bandwidth efficiency, and easy implementation So OFDM is an attractive technique for wireless communication applications.
- OFDM signals there are some limitations and disadvantages of OFDM signals.
- One of the major disadvantages of OFDM is the high peak-to-average power ratio (PAPR) of OFDM signals.
- PAPR peak-to-average power ratio
- OFDM signals with high PAPR impose undesirable design choices on an output power amplifier stage. If an amplifier is selected based on the average power of the transmitted OFDM signal, then the peaks in the OFDM signal may overload the power amplifier and cause in-band distortion and out-of-band radiation. The in-band distortion increases the bit error ratio (BER) and the out-band radiation results in the unacceptable adjacent channel interference.
- BER bit error ratio
- an output power amplifier can be provided with a sufficiently high compression point to handle the peaks of the OFDM signal and provide a linear response. However, in general such an amplifier would be undesirably large, inefficient, and would consume too much power.
- the schemes in the second category generate multiple modulated OFDM signals at the transmitter for a given data sequence, and then choose the OFDM signal with the lowest PAPR to be transmitted. These schemes do not cause distortion to the OFDM signal, but they come at the price of the increased complexity at the transmitter. Partial transmit sequences (PTS) and selective mapping (SLM) and are two types of schemes in this category.
- PTS Partial transmit sequences
- SLM selective mapping
- CONFERENCE, Vol. 2, pp 799-803 discloses a PAPR reduction scheme based on trellis shaping. It can efficiently reduce the PAPR of the OFDM signals. However, the spectral efficiency is decreased due to trellis shaping. Furthermore, the BER performance is worse than with a non-trellis shaping scheme due to error propagation. Meanwhile, Y. L. Lee, et al., "P eak-to-Average Power Ratio in MlMO-OFDM Systems Using Selective Mapping," IEEE COMMUNICATIONS LETTERS, Vol. 7, No. 12, pp. 575-577 (Dec. 2003) proposes a SLM -based PAPR reduction scheme for multi-input, multi-output (MIMO)- OFDM systems. The proposed scheme selects the transmitted sequence with the lowest average PAPR over all transmitted antennas.
- MIMO multi-input, multi-output
- the SLM technique generates U sufficiently different candidate OFDM signals for each input information bit sequence, and selects the one with the lowest PAPR to transmit.
- U randomized phase rotation vectors are used to randomize the frequency domain
- the index of the phase rotation vector corresponding to the transmitted OFDM signal needs to be transmitted explicitly to the receiver, typically as side information. This can increase overhead and reduce data throughput. Furthermore, errors in detecting this side information may cause error propagations due to incorrect phase de -rotator used.
- the scheme disclosed by Chen requires OFDM pilot tones which have a substantially greater power level than the normal OFDM symbols, and therefore it is unsuitable for some popular OFDM systems such as WiMAX and WiMedia UWB.
- channel coding - including interleaving - is employed before the OFDM modulator to achieve frequency diversity and to decrease BER. Accordingly, it would be desirable to provide a system and method of transmitting and receiving an OFDM signals with a reduced PAPR.
- a method for transmitting data.
- the method comprises generating a plurality of candidate orthogonal frequency division multiplex (OFDM) signals, wherein generating each of the candidate OFDM signals comprises, inserting a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, recursively convolutionally encoding the input bit sequence to generate an encoded bit sequence, interleaving the encoded bit sequence, OFDM modulating the interleaved, encoded bit sequence to generate the candidate OFDM signal, selecting one of the plurality of candidate OFDM signals having a lowest peak-to-average- power ratio; and transmitting the selected OFDM signal.
- OFDM orthogonal frequency division multiplex
- a system for transmitting data comprises: a plurality of candidate orthogonal frequency division multiplex (OFDM) signal generators, each comprising, a dummy bit inserter adapted to insert a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, a recursive convolutional encoder adapted to receive the input bit sequence and to generate an encoded bit sequence, an interleaver adapted to interleave the encoded bit sequence, an OFDM modulator adapted to receive the interleaved, encoded bit sequence and to generate a candidate OFDM signal, a signal selector adapted to select one of the plurality of candidate OFDM signals having a lowest peak-to-average-power ratio; and a transmitter adapted to transmit the selected OFDM signal/ The set of one or more dummy bits for each of the
- a data receiver comprises; an orthogonal frequency division multiplex (OFDM) demodulator adapted to receive OFDM symbols and to output an interleaved, encoded bit sequence; a deinterleaver adapted to receive the interleaved, encoded bit sequence and to output an encoded bit sequence; a convolutional decoder adapted to decode the encoded bit sequence and to output an output bit sequence; and a dummy bit remover adapted to remove a set of one or more dummy bits and to output a data bit sequence.
- OFDM orthogonal frequency division multiplex
- FIG. 1 is a functional block diagram of one embodiment of an orthogonal frequency division multiplex (OFDM) transmission system.
- OFDM orthogonal frequency division multiplex
- FIG. 2 is a functional block diagram of one embodiment of a dummy bit inserter that can be used in the OFDM transmission system of FIG. 1.
- FIG. 3 is a function block diagram of one embodiment of an OFDM data receiver.
- FIG. 4 plots simulated reductions in peak-to-average power ratio of OFDM signals generated using OFDM transmission systems according to various embodiments.
- FIG. 5 illustrates the power spectral density of OFDM signals generated using OFDM transmission systems according to various embodiments.
- FIG. 6 compares bit error rate performance of OFDM systems generated using two different OFDM transmission systems.
- FIG. 1 is a functional block diagram of one embodiment of an orthogonal frequency division multiplex (OFDM) transmission system.
- OFDM orthogonal frequency division multiplex
- the various functions shown in FIG. 1 may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof.
- the functional blocks are illustrated as being segregated in FIG. 1 for explanation purposes, they may be combined in any physical implementation.
- OFDM transmission system 100 comprises a plurality of (e.g., U) candidate OFDM signal generators HO-/, a signal selector 120, and a transmitter 130.
- Each OFDM signal generator HO-/ in turn comprises: a dummy bit inserter 112, a recursive convolutional encoder 114, an interleaver 116, and an OFDM modulator 118.
- OFDM modulator 118 includes symbol mapper 140, and time domain transformer 150.
- time domain transformer 150 comprises an inverse fast Fourier transformer (IFFT), but other implementations could be employed.
- transmitter 130 includes an orthogonal space-time block coder (OSTBC) 132 and a spatial diversity transmitting system comprising antenna system 134. Other transmission arrangements may be employed which employ only a single antenna.
- OSTBC orthogonal space-time block coder
- a guard interval (cyclic prefix) insertion/removal block may be employed in OFDM transmission system 100.
- a guard interval (cyclic prefix) insertion/removal block may be employed in OFDM transmission system 100.
- PAPR peak-to-average power ration
- OFDM transmission system 100 operates as follows.
- a data bit sequence is provided to the U candidate OFDM signal generators HO-/.
- Each candidate OFDM signal generator HO-/ generates from the data bit sequence a unique candidate OFDM signal.
- Signal selector 120 selects from among the U candidate OFDM signals the one that has the lowest peak-to-average power ration (PAPR) and provides the selected OFDM signal to transmitter 130, which then transmits the selected OFDM signal having the lowest PAPR.
- PAPR peak-to-average power ration
- a channel code is used to exploit frequency diversity and improve the BER performance.
- the channel code is a recursive convolutional code and its feedback part can be thought of as a scrambler.
- a complex baseband OFDM signal can be expressed as
- OFDM transmission system 100 is a space-time coded OFDM system, and so OSTBC 132 is included in the transmission chain after OFDM modulator 118.
- the transmitted signals are generated based on two consecutive OFDM signals xj(t) and % 2 (t) using the so-called Alamouti scheme.
- xj(t) is transmitted through a first antenna of antenna system 134
- % 2 (t) is transmitted through a second antenna of antenna system 134.
- [x 2(NT-t)] is transmitted through the first antenna
- [x i(NT-t)] is transmitted through the second antenna, where (•)* denotes the complex conjugate.
- OSTBC 132 can be omitted, and antenna system 134 can employ only a single antenna.
- the PAPR of the OFDM signal in equation (1) can be defined as
- x m for 0 ⁇ m ⁇ LN are the time domain signal samples, and are defined as:
- OFDM transmitter 100 generates U sufficiently different candidate OFDM signals for each input information bit sequence, and selects the one with the lowest PAPR to transmit.
- each candidate OFDM signal generator HO-/ to set each corresponding recursive convolutional encoder 114 to a different initial state.
- U 2 n pseudo-random candidate OFDM signals can be generated.
- the channel coding can exploit the frequency diversity and improve the BER performance.
- interleaver 116 and a nonlinear symbol mapper 118 can increase the pseudo-randomness of the candidate OFDM signals.
- dummy bit inserter 112 inserts the n dummy bits directly before the data bits of a data bit sequence to produce the input bit sequence that is applied to recursive convolutional encoder 114.
- the recursive convolutional encoders 114 of the U candidate OFDM signal generators 110-/ can be set to U different initial states.
- the dummy bits which are the binary representation of /, are inserted before a data bit sequence to produce an input but sequence.
- the input bit sequence is input to recursive convolutional encoder 114 to generate a coded bit sequence.
- the coded bit sequence is provided to interleaver 116 to generate an interleaved encoded bit sequence.
- the interleaved encoded bit sequence is provided to OFDM modulator 118 to generate U different candidate OFDM signals.
- the memory length of the convolutional code should be larger than the number of dummy bits n. Otherwise, there must exist two different values of/? dummy bits that set recursive convolutional encoder 114to the same initial state, which means there are two candidate OFDM signals which are the same to each other. Thus, the PAPR reduction performance is decreased.
- FIG. 2 is a functional block diagram of another embodiment of a dummy bit inserter 200 that can be used in the OFDM transmission system of FIG. 1.
- the various functions shown in FIG. 2 may be physically implemented using a software-controlled microprocessor, hard- wired logic circuits, or a combination thereof.
- the functional blocks are illustrated as being segregated in FIG. 2 for explanation purposes, they may be combined in any physical implementation.
- Dummy bit inserter 200 includes a Hamming coder 210 and a bit flipper 220.
- Hamming encoder 210 receives a first group of (2 n - n - X) data bits of a data bit sequence of length (F - n) and produces therefrom a Hamming-coded bit sequence of length (T - X).
- Bit flipper 220 flips / bits of the Hamming-coded sequence, where 0 ⁇ i ⁇ 1, to output a first set of bits of length (T - X) of an output bit sequence.
- Bit flipper 220 deliberately introduces one bit error in the bit sequence by flipping one of the bits output by Hamming encoder 210.
- dummy bit inserter 200 receives a data bit sequence of length (F - ⁇ ) and outputs an output bit sequence comprising F bits.
- dummy bit inserter 200 is employed in a candidate OFDM signal generator HO-/ of FIG. 1, then its output bit sequence is applied as the input bit sequence to recursive convolutional encoder 114.
- the convolutional encoding and the bit interleaving are linear operations, only a single interleaved convolutional codeword which corresponds to the dummy bit inserter UQ needs to be generated.
- the interleaved convolutional codewords corresponding to other dummy bit inserters 112 can be calculated by add a pre-calculated constant bit sequence to the interleaved convolutional codeword of UQ. This can simplify the transmitter design. Since UWFT operations need to be performed at the transmitter side, the complexity of the transmitter is increased to provide the improved PAPR performance. However, the complexity of the data receiver remains almost unchanged.
- FIG. 3 is a function block diagram of one embodiment of an OFDM data receiver.
- the various functions shown in FIG. 3 may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof.
- the functional blocks are illustrated as being segregated in FIG. 3 for explanation purposes, they may be combined in any physical implementation.
- Data receiver 300 includes an antenna system 310, an orthogonal frequency division multiplex (OFDM) demodulator 320, a deinterleaver 330, a convolutional decoder 340, and a dummy bit remover 350.
- OFDM orthogonal frequency division multiplex
- OFDM demodulator 320 includes first and second frequency domain transformers 322-1 and 322-2, an orthogonal space-time block coding (OSTBC) decoder 324, and an OFDM symbol-to-bit converter or demapper 326.
- first and second frequency domain transformers 322-1 and 322-2 are each fast Fourier transformers (FFTs).
- FFTs fast Fourier transformers
- Data receiver 300 operates to receive a space-time coded OFDM signal.
- antenna system 310 can employ only a single antenna
- OFDM demodulator 320 can include only a single frequency domain transformer 322, and OSTBC decoder 324 can be omitted.
- OFDM demodulator 310 receives an OFDM signal including OFDM symbols and outputs an interleaved, encoded bit sequence. If space-time coding is used (e.g., an MIMO-OFDM arrangement), then OSTBC decoder 324 performs space-time code decoding after the frequency domain transformation.
- Deinterleaver 330 receives the interleaved, encoded bit sequence, deinterleaves the bit sequence, and outputs an encoded bit sequence.
- Convolutional decoder 340 decodes the encoded bit sequence and outputs an output bit sequence.
- Dummy bit remover 350 removes n dummy bits form the bit sequence, and outputs a data bit sequence.
- dummy bit remover 350 includes a Hamming decoder 352 to remove one or more dummy bits inserted in the transmitted bit sequence by dummy bit inserter 200.
- FIG. 4 plots simulated reductions in peak-to-average power ratio of OFDM signals generated using OFDM transmission systems according to various embodiments.
- the number of OFDM subcarriers N is 128 and the constellation ⁇ is 16QAM.
- the industry- standard 1 A rate convolutional code [133 171] is used and the memory length of this code is 6. This code is modified to be in recursive form with the feedback polynomial of 133.
- Theoretic PAPR performance curves are also plotted as references. These theoretic results match the simulated results of Type-2 embodiments quite well. Type-2 embodiments always exhibit a better PAPR performance than Type-1 embodiments for the same number of dummy bits, but the performance gap between these two schemes decreases as n increases.
- a Type-1 scheme can achieve a reduction in PAPR of about 2.1 dB
- a Type-2 scheme can achieve a reduction in PAPR of about 2.7 dB at a probability of 10 ⁇ 4 .
- With three (3) dummy bits about a reduction ion PAPR of 3.4 dB can be achieved at the probability of 10 ⁇ 4 .
- When four (4) dummy bits are used, about a PAPR reduction of about 4 dB can be achieved. However, this improvement comes at the expense of requiring sixteen (16) 128-IFFTs be performed at the transmitter in the case of four dummy bits.
- FIG. 5 illustrates the power spectral density of OFDM signals generated using OFDM transmission systems according to various embodiments.
- the out-of-band power after a nonlinear power amplifier is evaluated by measuring the power spectral density (PSD) of the distorted transmit signal.
- PSD power spectral density
- AM/ AM conversion model is used:
- FIG. 5 also shows the simulated results for a clipping scheme with a clipping ratio (CR) of two (2).
- CR clipping ratio
- FIG. 6 compares bit error rate performance of OFDM systems generated using two different OFDM transmission systems.
- the BER performance of the scheme employed by OFDM transmission system 100, employing space-time coding is shown.
- the simulated system has two transmit antennas and one receive antenna.
- the Alamouti scheme is used to achieve space diversity.
- the channel model is a quasi- static flat fading channel.
- a hard decision demodulation is performed.
- the type-2 scheme with [7,4] Hamming code has about 1 dB performance gain over the clipping scheme, since the clipping scheme introduces in-band noise.
- an OFDM transmission system 100 can generate 2" sufficiently different candidate OFDM signals for each information bit sequence, and the one with the lowest PAPR is selected to be transmitted.
- the PAPR reduction is achieved at the price of an increase in complexity at the transmitter.
- the decoding is almost the same as the conventional coded OFDM schemes without PAPR reduction. More importantly, there is no error propagation due to any side information detection errors.
- This scheme is especially suitable for the downlink of coded OFDM systems since base stations always have more powerful digital signal processors. Furthermore, it can be easily incorporated into space-time coded OFDM systems, particularly one in which an orthogonal space-time block code is deployed to achieve space diversity, and a convolutional code is used to achieve frequency diversity and improve BER performance.
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Abstract
A method transmits data by generating (110-i) a plurality of candidate orthogonal frequency division multiplex (OFDM) signals, selecting. (120) the candidate OFDM signal that has the lowest peak- to-average-power ratio, and transmitting (130) the selected OFDM signal. Each of the candidate OFDM signals is generated by inserting (112) a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, recursively convolutionally encoding (114) the input bit sequence to generate an encoded bit sequence, interleaving- (166) the encoded. bit sequence, and OFDM modulating (118) the interleaved, encoded bit sequence to generate the candidate OFDM signal. The set of one or more dummy bits for each of the candidate OFDM signals is different than the set of one or more dummy bits for each of the other candidate OFDM signals.
Description
SYSTEM AND METHOD OF TRANSMITTING AND RECEIVING AN OFDM SIGNAL WITH REDUCED PEAK-TO-AVERAGE POWER RATIO
This invention pertains to the field of data communications, and more particularly to a system and method of transmitting and receiving an orthogonal frequency division multiplexing (OFDM) signal.
As new communication systems are developed, there continues to be a desire for more flexible, and efficient data communication techniques.
One popular choice for wireless communication systems is orthogonal frequency division multiplexing (OFDM). For example, both Worldwide Interoperability for Microwave Access (WiMAX) standards and the WiMedia Ultra- Wideband (UWB) Common Radio Platform employ OFDM. OFDM is an effective transmission method for high data rate wireless communication applications due to its robustness against the frequency-selective fading, high bandwidth efficiency, and easy implementation So OFDM is an attractive technique for wireless communication applications.
However, there are some limitations and disadvantages of OFDM signals. One of the major disadvantages of OFDM is the high peak-to-average power ratio (PAPR) of OFDM signals. OFDM signals with high PAPR impose undesirable design choices on an output power amplifier stage. If an amplifier is selected based on the average power of the transmitted OFDM signal, then the peaks in the OFDM signal may overload the power amplifier and cause in-band distortion and out-of-band radiation. The in-band distortion increases the bit error ratio (BER) and the out-band radiation results in the unacceptable adjacent channel interference. On the other hand, an output power amplifier can be provided with a sufficiently high compression point to handle the peaks of the OFDM signal and provide a linear response. However, in general such an amplifier would be undesirably large, inefficient, and would consume too much power.
A number of different schemes have been proposed for reducing the PAPR of an OFDM signal. Basically, these schemes can be grouped into two categories.
The schemes belonging to the first category deliberately modify the transmitted OFDM signals so that the peaks are suppressed. X. Li, et al., "Effects of Clipping and
Filtering on the Performance of OFDM," IEEE COMMUNICATIONS LETTERS, Vol. 2, No. 5, pp 131-133 (May 1998) is one example of a reference disclosing a PAPR reduction scheme in this first category. However, the deliberate modification operations themselves can introduce in-band noise, which may decrease the bit error rate (BER) performance of the
transmission. The simplest solution in this category is to deliberately clip the OFDM signal.
In contrast, the schemes in the second category generate multiple modulated OFDM signals at the transmitter for a given data sequence, and then choose the OFDM signal with the lowest PAPR to be transmitted. These schemes do not cause distortion to the OFDM signal, but they come at the price of the increased complexity at the transmitter. Partial transmit sequences (PTS) and selective mapping (SLM) and are two types of schemes in this category.
L.J. Cimini, Jr., et al. "Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences," IEEE COMMUNICATIONS LETTERS, Vol. 4, pp. 86-88 (Mar. 2000) and C. Tellambura, "Phase Optimization criterion for reducing peak-to- average power ratio in OFDM" ELECTRONIC LETTERS, Vol.43, No.2, pp. 169-170 (1998) disclose schemes that employ PTS.
Meanwhile, P.V. Eetvelt, et al. "Peak to Average Power Reduction for OFDM Schemes by Selective Scrambling " ELECTRONIC LETTERS, Vol. 32, pp. 1963-1964 (Oct. 1996); S. Muller, et al., "OFDM with Reduced Peak-to- Average Power Ratio by Multiple Signal Representation " ANNALS OF TELECOMMUNICATIONS, Vol. 52, No.1-2, pp.58-67 (1997); N. Chen, et al, "Crest Factor Reduction in OFDM U sing Blind Selected Pilot Tone Modulation," United States Patent Application Publication US2006274868A1; and M. Breiling, et al., "SLM Peak-Power Reduction Without Explicit Side Information " IEEE COMMUNICATIONS LETTERS, Vol. 5, No. 6, pp. 239-241 (June 2001) all disclose schemes that employ SLM.
Also, several approaches for reducing the PAPR of the transmitted OFDM signals in space-time coded OFDM systems have been proposed. For example, H. Reddy et al. "Space-Time Coded OFDM with Low PAPR "IEEE GLOBAL TELECOMMUNICATIONS
CONFERENCE, Vol. 2, pp 799-803 (Dec. 2003) discloses a PAPR reduction scheme based on trellis shaping. It can efficiently reduce the PAPR of the OFDM signals. However, the spectral efficiency is decreased due to trellis shaping. Furthermore, the BER performance is worse than with a non-trellis shaping scheme due to error propagation. Meanwhile, Y. L. Lee, et al., "P eak-to-Average Power Ratio in MlMO-OFDM Systems Using Selective Mapping," IEEE COMMUNICATIONS LETTERS, Vol. 7, No. 12, pp. 575-577 (Dec. 2003) proposes a SLM -based PAPR reduction scheme for multi-input, multi-output (MIMO)- OFDM systems. The proposed scheme selects the transmitted sequence with the lowest
average PAPR over all transmitted antennas.
The SLM technique generates U sufficiently different candidate OFDM signals for each input information bit sequence, and selects the one with the lowest PAPR to transmit. There are several ways to generate f/pseudo random candidate OFDM signals. In Lee et al., U randomized phase rotation vectors are used to randomize the frequency domain
OFDM symbols Xk and then generate U candidate OFDM signals. Meanwhile in Breiling et al., the authors used a scrambler to scramble the input information bits and n dummy bits are used to set the scrambler to different initial states. With different values of these n dummy bits, 2n pseudo random candidate OFDM signals can be generated. However, these existing schemes in the second category also have disadvantages.
In some cases, the index of the phase rotation vector corresponding to the transmitted OFDM signal needs to be transmitted explicitly to the receiver, typically as side information. This can increase overhead and reduce data throughput. Furthermore, errors in detecting this side information may cause error propagations due to incorrect phase de -rotator used.
In other cases, additional complexity is added to the receiver, such as the addition of a descrambler.
Also, for example, the scheme disclosed by Chen requires OFDM pilot tones which have a substantially greater power level than the normal OFDM symbols, and therefore it is unsuitable for some popular OFDM systems such as WiMAX and WiMedia UWB.
Furthermore, in some of these schemes, no channel coding is taken into consideration, while in most real OFDM systems, channel coding - including interleaving - is employed before the OFDM modulator to achieve frequency diversity and to decrease BER. Accordingly, it would be desirable to provide a system and method of transmitting and receiving an OFDM signals with a reduced PAPR.
In one aspect of the invention, a method is provided for transmitting data. The method comprises generating a plurality of candidate orthogonal frequency division multiplex (OFDM) signals, wherein generating each of the candidate OFDM signals comprises, inserting a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, recursively convolutionally encoding the input bit sequence to generate an encoded bit sequence, interleaving the encoded bit sequence, OFDM modulating the interleaved, encoded bit sequence to generate the candidate OFDM signal,
selecting one of the plurality of candidate OFDM signals having a lowest peak-to-average- power ratio; and transmitting the selected OFDM signal. The set of one or more dummy bits for each of the candidate OFDM signals is different than the set of one or more dummy bits for each of the other candidate OFDM signals. In another aspect of the invention, a system for transmitting data comprises: a plurality of candidate orthogonal frequency division multiplex (OFDM) signal generators, each comprising, a dummy bit inserter adapted to insert a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, a recursive convolutional encoder adapted to receive the input bit sequence and to generate an encoded bit sequence, an interleaver adapted to interleave the encoded bit sequence, an OFDM modulator adapted to receive the interleaved, encoded bit sequence and to generate a candidate OFDM signal, a signal selector adapted to select one of the plurality of candidate OFDM signals having a lowest peak-to-average-power ratio; and a transmitter adapted to transmit the selected OFDM signal/ The set of one or more dummy bits for each of the candidate OFDM signal generators is different than the set of one or more dummy bits for each of the other candidate OFDM signal generators.
In yet another aspect of the invention, a data receiver comprises; an orthogonal frequency division multiplex (OFDM) demodulator adapted to receive OFDM symbols and to output an interleaved, encoded bit sequence; a deinterleaver adapted to receive the interleaved, encoded bit sequence and to output an encoded bit sequence; a convolutional decoder adapted to decode the encoded bit sequence and to output an output bit sequence; and a dummy bit remover adapted to remove a set of one or more dummy bits and to output a data bit sequence.
FIG. 1 is a functional block diagram of one embodiment of an orthogonal frequency division multiplex (OFDM) transmission system.
FIG. 2 is a functional block diagram of one embodiment of a dummy bit inserter that can be used in the OFDM transmission system of FIG. 1.
FIG. 3 is a function block diagram of one embodiment of an OFDM data receiver.
FIG. 4 plots simulated reductions in peak-to-average power ratio of OFDM signals generated using OFDM transmission systems according to various embodiments.
FIG. 5 illustrates the power spectral density of OFDM signals generated using OFDM transmission systems according to various embodiments.
FIG. 6 compares bit error rate performance of OFDM systems generated using two
different OFDM transmission systems.
In the following detailed description, for purposes of explanation and not limitation, example embodiments disclosing specific details are set forth in order to provide a thorough understanding of an embodiment according to the present teachings. However, it will be apparent to one having ordinary skill in the art having had the benefit of the present disclosure that other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known devices and methods may be omitted so as to not obscure the description of the example embodiments. Such methods and devices are clearly within the scope of the present teachings.
FIG. 1 is a functional block diagram of one embodiment of an orthogonal frequency division multiplex (OFDM) transmission system. As will be appreciated by those skilled in the art, the various functions shown in FIG. 1 may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Also, while the functional blocks are illustrated as being segregated in FIG. 1 for explanation purposes, they may be combined in any physical implementation.
OFDM transmission system 100 comprises a plurality of (e.g., U) candidate OFDM signal generators HO-/, a signal selector 120, and a transmitter 130. Each OFDM signal generator HO-/ in turn comprises: a dummy bit inserter 112, a recursive convolutional encoder 114, an interleaver 116, and an OFDM modulator 118. OFDM modulator 118 includes symbol mapper 140, and time domain transformer 150. In OFDM transmission system 100, time domain transformer 150 comprises an inverse fast Fourier transformer (IFFT), but other implementations could be employed. In OFDM transmission system 100, transmitter 130 includes an orthogonal space-time block coder (OSTBC) 132 and a spatial diversity transmitting system comprising antenna system 134. Other transmission arrangements may be employed which employ only a single antenna.
Although not shown in FIG. 1, a guard interval (cyclic prefix) insertion/removal block may be employed in OFDM transmission system 100. However, as such a block does not affect the peak-to-average power ration (PAPR) of the OFDM signal, it is omitted from FIG. 1 to simplify the drawing and the discussion to follow.
OFDM transmission system 100 operates as follows.
A data bit sequence is provided to the U candidate OFDM signal generators HO-/. Each candidate OFDM signal generator HO-/ generates from the data bit sequence a
unique candidate OFDM signal. Signal selector 120 selects from among the U candidate OFDM signals the one that has the lowest peak-to-average power ration (PAPR) and provides the selected OFDM signal to transmitter 130, which then transmits the selected OFDM signal having the lowest PAPR. In each candidate OFDM signal generator HO-/, a channel code is used to exploit frequency diversity and improve the BER performance. Beneficially, the channel code is a recursive convolutional code and its feedback part can be thought of as a scrambler.
An input bit sequence is input to recursive convolutional encoder 114. Then, the encoded bits are passed through bit interleaver 116 and mapped by symbol mapper 140 to symbols Xk, k = (1 . . . N), which are from a symbol constellation Ω, where N is the number of subcarriers in the OFDM signal. The resulting symbols are grouped together and delivered to IFFT 150 to output a candidate OFDM signal.
A complex baseband OFDM signal can be expressed as
N-I
1 ? 2πf(k)t
(1) , 0 < t < NT
where f(k) = k*Δf, Δf = 1/(NT), and NT is the OFDM symbol interval length.
OFDM transmission system 100 is a space-time coded OFDM system, and so OSTBC 132 is included in the transmission chain after OFDM modulator 118. For example, in one, the transmitted signals are generated based on two consecutive OFDM signals xj(t) and %2(t) using the so-called Alamouti scheme. In the first OFDM symbol interval, xj(t) is transmitted through a first antenna of antenna system 134, and %2(t) is transmitted through a second antenna of antenna system 134. In the second OFDM symbol interval, [x 2(NT-t)] is transmitted through the first antenna and [x i(NT-t)] is transmitted through the second antenna, where (•)* denotes the complex conjugate. However, it should be understood that in other embodiments of an OFDM transmission system where spatial diversity is not employed, OSTBC 132 can be omitted, and antenna system 134 can employ only a single antenna.
The PAPR of the OFDM signal in equation (1) can be defined as
where E{»} denotes the expectation operation. It can be shown that when the oversampling rate L is large, the PAPR defined in (2) can be accurately approximated as:
where xm for 0 < m < LN are the time domain signal samples, and are defined as:
OFDM transmitter 100 generates U sufficiently different candidate OFDM signals for each input information bit sequence, and selects the one with the lowest PAPR to transmit.
In particular a different pattern of/? dummy bits is used in each candidate OFDM signal generator HO-/ to set each corresponding recursive convolutional encoder 114 to a different initial state. With different values of these n dummy bits, U= 2n pseudo-random candidate OFDM signals can be generated. The channel coding can exploit the frequency diversity and improve the BER performance. Also, interleaver 116 and a nonlinear symbol mapper 118 can increase the pseudo-randomness of the candidate OFDM signals.
As will be seen below, at the data receiver, no descrambler is required, and only a Viterbi decoder is required for decoding the recursive convolutional code. Compared with receiving a similar OFDM signal without PAPR, the complexity of the Viterbi decoder does not change, provided the feedback polynomial of the convolutional code employed by recursive convolutional encoder 114 does not increase the memory length. Moreover, there is no BER performance loss due to PAPR reduction since no error propagation exists.
In a first embodiment, dummy bit inserter 112 inserts the n dummy bits directly before the data bits of a data bit sequence to produce the input bit sequence that is applied to recursive convolutional encoder 114. With U= T different values of the n dummy bits, the recursive convolutional encoders 114 of the U candidate OFDM signal generators 110-/ can be set to U different initial states. For dummy bit inserter D1, i = (0 . . . U-I) in FIG.1 , the dummy bits, which are the binary representation of /, are inserted before a data bit sequence to produce an input but sequence. Then the input bit sequence is input to recursive convolutional encoder 114 to generate a coded bit sequence. The coded bit sequence is provided to interleaver 116 to generate an interleaved encoded bit sequence. Finally, the interleaved encoded bit sequence is provided to OFDM modulator 118 to generate U different candidate OFDM signals.
However, with this embodiment, there is a constraint that the memory length of the convolutional code should be larger than the number of dummy bits n. Otherwise, there must exist two different values of/? dummy bits that set recursive convolutional encoder 114to the same initial state, which means there are two candidate OFDM signals which are the same to each other. Thus, the PAPR reduction performance is decreased.
FIG. 2 is a functional block diagram of another embodiment of a dummy bit inserter 200 that can be used in the OFDM transmission system of FIG. 1. As will be appreciated by those skilled in the art, the various functions shown in FIG. 2 may be physically implemented using a software-controlled microprocessor, hard- wired logic circuits, or a combination thereof. Also, while the functional blocks are illustrated as being segregated in FIG. 2 for explanation purposes, they may be combined in any physical implementation.
Dummy bit inserter 200 includes a Hamming coder 210 and a bit flipper 220. Hamming encoder 210 receives a first group of (2n- n - X) data bits of a data bit sequence of length (F - n) and produces therefrom a Hamming-coded bit sequence of length (T - X). Bit flipper 220 flips / bits of the Hamming-coded sequence, where 0 < i < 1, to output a first set of bits of length (T - X) of an output bit sequence. Bit flipper 220 deliberately introduces one bit error in the bit sequence by flipping one of the bits output by Hamming encoder 210. Dummy bit inserter then outputs a second group of (F - n - \T - n - I]) = (F - 2n + 1) bits of the data bit sequence as a second set of bits of the output bit sequence. Thus, dummy bit inserter 200 receives a data bit sequence of length (F - ή) and outputs an output bit sequence comprising F bits. When dummy bit inserter 200 is
employed in a candidate OFDM signal generator HO-/ of FIG. 1, then its output bit sequence is applied as the input bit sequence to recursive convolutional encoder 114.
For each of the candidate OFDM signal generators HO-/, a different bit of the Hamming-coded sequence is flipped (including not flipping any bits for one of the OFDM signal generators 110-/).
Thus:
• the Hamming coded bits dl5 1 < / < (2n - 1), and
• the other data bits d, = b(l_n), 2n < i <F are fed into recursive convolutional encoder 114 to do the channel coding. Since Hamming codes can correct one bit error, the deliberately introduced one bit error can be corrected by a Hamming decoder at the receiver side provided all the Hamming encoded bits are correctly detected. Recursive convolutional coder 114, bit interleaver 114, and the nonlinear mapper 140 can guarantee that 2" candidate OFDM signals are sufficiently different so that a good PAPR reduction performance can be achieved. In this embodiment, there is no constraint on the memory length of the convolutional code.
In the above two embodiments, since the dummy bit insertion operation, the convolutional encoding and the bit interleaving are linear operations, only a single interleaved convolutional codeword which corresponds to the dummy bit inserter UQ needs to be generated. The interleaved convolutional codewords corresponding to other dummy bit inserters 112 can be calculated by add a pre-calculated constant bit sequence to the interleaved convolutional codeword of UQ. This can simplify the transmitter design. Since UWFT operations need to be performed at the transmitter side, the complexity of the transmitter is increased to provide the improved PAPR performance. However, the complexity of the data receiver remains almost unchanged.
FIG. 3 is a function block diagram of one embodiment of an OFDM data receiver. As will be appreciated by those skilled in the art, the various functions shown in FIG. 3 may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Also, while the functional blocks are illustrated as being segregated in FIG. 3 for explanation purposes, they may be combined in any physical implementation.
Data receiver 300 includes an antenna system 310, an orthogonal frequency division multiplex (OFDM) demodulator 320, a deinterleaver 330, a convolutional decoder
340, and a dummy bit remover 350.
OFDM demodulator 320 includes first and second frequency domain transformers 322-1 and 322-2, an orthogonal space-time block coding (OSTBC) decoder 324, and an OFDM symbol-to-bit converter or demapper 326. In one embodiment, first and second frequency domain transformers 322-1 and 322-2 are each fast Fourier transformers (FFTs). Data receiver 300 operates to receive a space-time coded OFDM signal. However, it should be understood that in other embodiments of an OFDM receiver, spatial diversity is not employed, antenna system 310 can employ only a single antenna, OFDM demodulator 320 can include only a single frequency domain transformer 322, and OSTBC decoder 324 can be omitted.
OFDM demodulator 310 receives an OFDM signal including OFDM symbols and outputs an interleaved, encoded bit sequence. If space-time coding is used (e.g., an MIMO-OFDM arrangement), then OSTBC decoder 324 performs space-time code decoding after the frequency domain transformation. Deinterleaver 330 receives the interleaved, encoded bit sequence, deinterleaves the bit sequence, and outputs an encoded bit sequence. Convolutional decoder 340 decodes the encoded bit sequence and outputs an output bit sequence. Dummy bit remover 350 removes n dummy bits form the bit sequence, and outputs a data bit sequence. In one embodiment, dummy bit remover 350 includes a Hamming decoder 352 to remove one or more dummy bits inserted in the transmitted bit sequence by dummy bit inserter 200.
In FIGs. 4-6 to follow, the curves denoted as "Type-1" correspond to the first embodiment dummy bit inserter 112 described above with respect to FIG. 1, and the curves denoted as "Type-3" correspond to the second embodiment dummy bit inserter, an example of which is dummy bit inserter 200 shown in FIG. 2. FIG. 4 plots simulated reductions in peak-to-average power ratio of OFDM signals generated using OFDM transmission systems according to various embodiments. In the simulations, the number of OFDM subcarriers N is 128 and the constellation Ω is 16QAM. The industry- standard 1A rate convolutional code [133 171] is used and the memory length of this code is 6. This code is modified to be in recursive form with the feedback polynomial of 133.
Theoretic PAPR performance curves are also plotted as references. These theoretic results match the simulated results of Type-2 embodiments quite well. Type-2 embodiments always exhibit a better PAPR performance than Type-1 embodiments for the
same number of dummy bits, but the performance gap between these two schemes decreases as n increases. With two (2) dummy bits, a Type-1 scheme can achieve a reduction in PAPR of about 2.1 dB, and a Type-2 scheme can achieve a reduction in PAPR of about 2.7 dB at a probability of 10~4. With three (3) dummy bits, about a reduction ion PAPR of 3.4 dB can be achieved at the probability of 10~4. When four (4) dummy bits are used, about a PAPR reduction of about 4 dB can be achieved. However, this improvement comes at the expense of requiring sixteen (16) 128-IFFTs be performed at the transmitter in the case of four dummy bits.
FIG. 5 illustrates the power spectral density of OFDM signals generated using OFDM transmission systems according to various embodiments. In FIG. 5, the out-of-band power after a nonlinear power amplifier is evaluated by measuring the power spectral density (PSD) of the distorted transmit signal. To simulate a nonlinear power amplifier, the following AM/ AM conversion model is used:
where xm is the input signal, and A is the maximum output signal amplitude of the power amplifier. In these simulations,/? =3. With an input back-off (IBO) of 6 dB, the proposed Type-2 scheme with n =3 can decrease the out-of-band radiation by about 5 dB. For comparison, FIG. 5 also shows the simulated results for a clipping scheme with a clipping ratio (CR) of two (2). One can see clipping without post- filtering increases the out-of-band radiation greatly. For the same adjacent channel interference requirement, the PAPR scheme employed by OFDM transmission system 100 puts a less stringent requirement on the IBO of the power amplifier, which means a greater power efficiency is achieved. FIG. 6 compares bit error rate performance of OFDM systems generated using two different OFDM transmission systems. In FIG. 6, the BER performance of the scheme employed by OFDM transmission system 100, employing space-time coding is shown. The simulated system has two transmit antennas and one receive antenna. The Alamouti scheme is used to achieve space diversity. In this simulation, the channel model is a quasi- static flat fading channel. A nonlinear power amplifier with IBO = 6 dB is employed after
the OFDM modulator. At the receiver side, a hard decision demodulation is performed. The BER performance of a system employing a clipping scheme with CR =1.9 is also given for comparison. As can be seen, the type-2 scheme with [7,4] Hamming code has about 1 dB performance gain over the clipping scheme, since the clipping scheme introduces in-band noise.
In summary, with n dummy bits, an OFDM transmission system 100 can generate 2" sufficiently different candidate OFDM signals for each information bit sequence, and the one with the lowest PAPR is selected to be transmitted. The PAPR reduction is achieved at the price of an increase in complexity at the transmitter. At the receiver side, the decoding is almost the same as the conventional coded OFDM schemes without PAPR reduction. More importantly, there is no error propagation due to any side information detection errors. This scheme is especially suitable for the downlink of coded OFDM systems since base stations always have more powerful digital signal processors. Furthermore, it can be easily incorporated into space-time coded OFDM systems, particularly one in which an orthogonal space-time block code is deployed to achieve space diversity, and a convolutional code is used to achieve frequency diversity and improve BER performance. It should be understood that this scheme can be naturally extended to systems with other channel codes and space-time coded schemes, such as turbo codes and space-time trellis codes. While preferred embodiments are disclosed herein, many variations are possible which remain within the concept and scope of the invention. Such variations would become clear to one of ordinary skill in the art after inspection of the specification, drawings and claims herein. The invention therefore is not to be restricted except within the spirit and scope of the appended claims.
Claims
1. A method of transmitting data, comprising: generating (110-/) a plurality of candidate orthogonal frequency division multiplex (OFDM) signals, wherein generating each of the candidate OFDM signals comprises, inserting (112, 200) a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, recursively convolutionally encoding (114) the input bit sequence to generate an encoded bit sequence, interleaving (116) the encoded bit sequence,
OFDM modulating (118) the interleaved, encoded bit sequence to generate the candidate OFDM signal, selecting (120) one of the plurality of candidate OFDM signals having a lowest peak-to-average-power ratio; and transmitting (130) the selected OFDM signal, wherein the set of one or more dummy bits for each of the candidate OFDM signals is different than the set of one or more dummy bits for each of the other candidate OFDM signals.
2. The method of claim 1, wherein the data bit sequence comprises z bits, and wherein inserting (200) the set of one or more dummy bits before the data bit sequence to produce the input bit sequence comprises: applying a first group of x bits of the data bit sequence to a Hamming coder (210) to produce a Hamming-coded bit sequence; flipping (220) i bits of the Hamming-coded sequence, where 0 < i < 1, to output a first set of bits of the input bit sequence; and outputting a second group of z-x bits of the data bit sequence as a second set of bits of the input bit sequence, wherein for each of the candidate OFDM signals a bit of the Hamming-coded sequence that is flipped is different than for each of the other candidate OFDM signals.
3. The method of claim 1, wherein OFDM modulating (118) the interleaved, encoded bit sequence to generate the candidate OFDM signal comprises: mapping (140) the interleaved, encoded bit sequence to a plurality of OFDM symbols; and transforming (150) the OFDM symbols into the time domain to produce the OFDM signal.
4. The method of claim 1, wherein transmitting (130) the selected OFDM signal comprises orthogonal space-time block coding (OSTBC) (132) the OFDM signal and applying the OSBTC signal to a spatial diversity transmitting system (134).
5. A system (100) for transmitting data, comprising: a plurality of candidate orthogonal frequency division multiplex (OFDM) signal generators (110-/), each comprising, a dummy bit inserter (112, 200) adapted to insert a set of one or more dummy bits before a data bit sequence to produce an input bit sequence, a recursive convolutional encoder (114) adapted to receive the input bit sequence and to generate an encoded bit sequence, an interleaver (116) adapted to interleave the encoded bit sequence, an OFDM modulator (118) adapted to receive the interleaved, encoded bit sequence and to generate a candidate OFDM signal, a signal selector (120) adapted to select one of the plurality of candidate OFDM signals having a lowest peak-to-average-power ratio; and a transmitter (130) adapted to transmit the selected OFDM signal, wherein the set of one or more dummy bits for each of the candidate OFDM signal generators (110-/) is different than the set of one or more dummy bits for each of the other candidate OFDM signal generators (110-/).
6. The system (100) of claim 5, wherein each dummy bit inserter (200) comprises: a Hamming coder (210) adapted to receive a first group of bits of the data bit sequence and to produce a Hamming-coded bit sequence; and a bit flipper (220) adapted to flip i bits of the Hamming-coded sequence, where 0 < i < 1, to output a first set of bits of the input bit sequence; wherein for each of the candidate OFDM signals a bit of the Hamming-coded sequence that is flipped is different than for each of the other candidate OFDM signals.
7. The system (100) of claim 5, wherein the OFDM modulator (118) comprises: an OFDM symbol mapper (140) adapted to map the interleaved, encoded bit sequence to a plurality of OFDM symbols; and a transformer (150)adapted to transform the OFDM symbols into the time domain to produce the OFDM signal.
8. The system (100) of claim 5, wherein the transmitter (130) comprises an orthogonal space-time block coder (OSTBC) (132) and a spatial diversity transmitting system (134).
9. A data receiver (300), comprising: an orthogonal frequency division multiplex (OFDM) demodulator (320) adapted to receive OFDM symbols and to output an interleaved, encoded bit sequence; a deinterleaver (330) adapted to receive the interleaved, encoded bit sequence and to output an encoded bit sequence; a convolutional decoder (340) adapted to decode the encoded bit sequence and to output an output bit sequence; and a dummy bit remover (350) adapted to remove a set of one or more dummy bits from the output bit sequence and to output a data bit sequence.
10. The data receiver (300) of claim 9, wherein the dummy bit remover (300) includes a Hamming decoder (352) to determine values of the set of one or more dummy bits to be removed.
11. The data receiver (300) of claim 9, wherein the OFDM demodulator includes a frequency domain transformer (322) and a demapper (326) for demapping the output of the frequency domain transformer.
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| US60/984,766 | 2007-11-02 |
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| US8737911B2 (en) | 2009-05-11 | 2014-05-27 | Qualcomm Incorporated | Dual-stage echo cancellation in a wireless repeater using an inserted pilot |
| TWI501596B (en) * | 2010-03-08 | 2015-09-21 | Sony Corp | Communications system using adaptive orthogonal frequency division multiplexing |
| CN102137055A (en) * | 2010-09-06 | 2011-07-27 | 华为技术有限公司 | Method, device and system for reducing peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) system |
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| DONG WANG; XIANG-GEN XIA; JINYUN ZHANG: "A novel peak-to-average power ratio reduction method for coded OFDM systems" 2008 IEEE INTERNATIONAL SYMPOSIUM ON BROADBAND MULTIMEDIA SYSTEMS AND BROADCASTING, [Online] 31 March 2008 (2008-03-31), - 2 April 2008 (2008-04-02) pages 1-5, XP002500605 Las Vegas, NV, USA ISBN: 978-1-4244-1649-3 Retrieved from the Internet: URL:http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04536673> [retrieved on 2008-10-21] * |
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| CN114747259A (en) * | 2019-12-13 | 2022-07-12 | 中兴通讯股份有限公司 | Time-domain modulation scheme for low peak-to-average power ratio |
| US12149393B2 (en) | 2019-12-13 | 2024-11-19 | Zte Corporation | Time-domain modulation scheme for low peak average power ratio |
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| WO2008152596A3 (en) | 2009-02-05 |
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