CN109729036A - Discrete time domain window design method for inhibiting OFDMA system frequency spectrum side lobe - Google Patents

Abstract

The invention discloses a discrete time domain window design method for suppressing spectral side lobes of an OFDMA system. The invention establishes an optimization problem based on the principle of minimum spectral side lobes by quantizing the discrete time domain window, and proposes an approximate global optimal search algorithm to ensure that the designed discrete time domain window can effectively suppress the spectral side lobes of the OFDMA system, and at the same time can It can effectively reduce the computational complexity of optimization problems, and can quickly converge.

Description

A Discrete Time-Domain Window Design Method for Suppressing Spectral Sidelobes in OFDMA Systems

technical field

The invention belongs to the field of wireless communication, in particular to a discrete time-domain window design method capable of suppressing spectral sidelobes of an OFDMA system.

Background technique

OFDM is a multi-carrier modulation technology that can effectively combat frequency selective fading, and the sub-carriers are orthogonal to each other, and the carriers overlap without mutual interference, thereby saving spectrum bandwidth and maximizing the utilization of spectrum resources. OFDMA is a multiple access technology based on OFDM. OFDMA technology inherits the advantages of OFDM technology in resisting complex time-varying channel fading, but also inherits two inherent shortcomings of OFDM technology: out-of-band (OOB, Out-of- band) side lobes (out-of-band power radiation) and peak-to-average power ratio (PAPR, Peak-to-Average-Power-Ratio) is high. In an OFDMA system, out-of-band sidelobes of the spectrum represent the out-of-band power radiation of a certain user's corresponding data sub-carrier band to adjacent sub-carrier bands, resulting in multiple-access user communication interference.

In this paper, the sub-band out-of-band power radiation is defined as the sub-band out-of-band power radiation in the working frequency band (IBOSB, In-Band Out-Of-SubBand). The IBOSB conference interferes with adjacent user channels. The IBOSB problem will affect the performance of the communication system, limit or even hinder the practical application of OFDMA technology.

At this stage, the research on OOB suppression mainly includes time-domain windowing, pulse shaping, correlation coding, subcarrier weighting, suppression queue and precoding, etc., but these methods may sacrifice the bit error rate (BER, Bit error rate) performance of the communication system. At the cost, either the complexity of the OFDM system is increased, the computational complexity of the OFDM system is increased, or the decoding complexity of the receiving end is increased. The time-domain windowing method is the simplest and most effective method. At present, the raised cosine windowing method is mainly used, but the OFDMA system spectrum with raised cosine windowing is still large. Spectral sidelobes of OFDMA systems.

SUMMARY OF THE INVENTION

The purpose of the present invention is to design a new discrete time domain window function, and suppress the spectral side lobes of the OFDMA system through the time domain windowing technology.

The technical solution to achieve the purpose of the present invention is: a discrete time-domain window design method for suppressing spectral sidelobes of OFDMA system, using an optimized roll-off function to act on the OFDMA transmitting end to realize the suppression of spectral sidelobes of OFDMA system.

Compared with the prior art, the present invention has significant advantages: (1) the present invention uses a discrete time domain window function to act on the OFDMA transmitter signal, which is simple to implement; (2) an approximate global optimal search algorithm is designed, and the algorithm searches for approximate The globally optimal time domain window can effectively reduce the computational complexity of solving the optimization problem; (3) At the same time, the algorithm can converge quickly, and the convergence result has nothing to do with the selected optimization initial value.

Description of drawings

Figure 1 shows the structure of the transmitter of the windowed OFDMA system.

Detailed ways

The discrete time domain window of the present invention is mainly aimed at the problem of large spectral side lobes of the OFDMA system caused by the rectangular discrete time domain window. Based on the symmetrical function, a more reasonable roll-off discrete time domain window is designed, and the objective optimization problem of minimum out-of-band power radiation is established. . For the objective optimization problem is a multi-objective optimization problem, an approximate global optimal search algorithm is proposed, which can effectively reduce the computational complexity of the optimization problem and can quickly converge.

The present invention will be further described below in conjunction with the accompanying drawings.

The present invention designs a new and better discrete time domain window to realize the suppression of the spectral side lobes of the OFDMA system. The invention establishes an optimization problem based on the principle of minimum spectral side lobes by quantizing the discrete time domain window, and proposes an approximate global optimal search algorithm to solve it, so as to ensure that the designed discrete time domain window can effectively suppress the spectral side lobes of the OFDMA system.

1. Windowed OFDMA system

It is assumed that the communication scenario of the OFDMA system is the communication uplink, which consists of a communication base station and K transmitting nodes (users), and the user indexes are k=1, 2, . . . K. Assuming that in the OFDMA system, the spectrum bandwidth is B, the spectrum bandwidth is equally divided into N sub-bandwidths (sub-carriers), and each sub-carrier index is n=0, 1...N-1; there are K users in the OFDMA system, and the Each sub-carrier is divided into K groups of sub-carrier sets according to the index order and allocated to each user, so the number of sub-carriers contained in each sub-carrier set is P=N/K, and the sub-carrier index allocated by the kth user is B _k ∈ [(k-1)P,kP-1], let the roll-off factor of the time domain window be β.

Assuming that the OFDMA symbol data period is T, the frequency interval of each subcarrier is Δf=1/T, the duration of the guard interval is T _g , and the actual OFDMA symbol period T _u is,

T _u =T+T _g (3)

If the sampling time interval is T _s =T/N=1/(NΔf), the lengths of the time-domain discrete signal sequence and the guard interval sequence are N and v respectively, and the total length of the OFDMA symbol sequence is,

L=N+v (4)

The roll-off factor of the time domain window is defined as β, so the length of the OFDMA signal after time domain windowing is (1+β)T _u ,

The length of the discrete OFDMA symbol sequence is (1+β)L.

One OFDMA symbol is synthesized by a plurality of sub-carrier signals subjected to Phase-Shift Keying (PSK, Phase-Shiftkeying) or Quadrature Amplitude Modulation (QAM, Quadrature Amplitude Modulation). Define the data to be modulated for each subcarrier of the kth user as is a column vector of size M × 1, where M≤P. Suppose the data to be modulated elements in are mutually independent and identically distributed random variables, and are the constellation mapping points of phase shift keying, satisfying the expectation E[c( ^k) ]=0 _M×1 ,

Covariance E[c ^(k) (c ^(k) ) ^H ]= _IM . where _IM represents an identity matrix of size M×M.

Figure 1 shows the structure of the transmitter of the windowed OFDMA system. The data to be modulated c ^(k) (M=P at this time) undergoes subcarrier mapping, IDFT modulation (size is N), cyclic prefix insertion (length is v), time domain windowing, and digital-to-analog conversion, and finally the output signal is The power spectrum is

in, and among them is a Fourier transform matrix of size N×N, the (m,i)th element is B ^(k) represents the subcarrier mapping matrix of the kth user of size N×P:

B ^(k) = [0 _P×[(k-1)P] I _P 0 _P×(N-kP )] ^T (6)

C represents a cyclic prefix and cyclic suffix insertion matrix of size (1+β)L×N:

2. Time domain window suppresses spectral sidelobes of OFDMA system

For the interference of the kth user in the OFDMA system to the multiple-access users in the network, the power of this data sub-carrier radiated into the adjacent sub-carriers and the interference to the communication of the multiple-access users is defined as the power outside the sub-band within the working frequency band. Radiation (IBOSB).

Define the working frequency band of OFDMA signal Ξ=[-1/2T _s , 1/2T _s ], the sub-working frequency band of the kth user is Therefore, the precoding optimization objective function to suppress the minimum out-of-subband power radiation of the kth user is:

Only the elements of the column vector matrix α(f) are functions of the frequency f, so the objective optimization problem (8) can be expressed as:

Now define three Hermitian (complex conjugate symmetric) matrices:

P ^(k) = ∫ _Ξ α(f)α ^H (f)df (11)

Under the condition of a certain signal power, the

The objective optimization problem (8) can be expressed as:

in

3. Approximate global optimal search algorithm

The discrete time domain window w ^(k) consists of two parts: a constant part with an amplitude of 1 and a symmetric roll-off part whose amplitude gradually transitions to 0. The discrete time domain window w ^(k) of the kth user is defined as follows:

Among them, n=(1+β)L-1, Represents the symmetric roll-off portion of the discrete time-domain window of size βL×1. Therefore, the matrix-vector expression of the discrete time-domain window w ^(k) is:

in, Represents the left-right symmetrical roll-off part of the discrete time domain window, and p ₁ w ₁ represents the part of the discrete time domain window whose amplitude is constant 1. p ₀ =[I _βL ; 0 _(1-β)L,βL ; J _βL ] denotes a symmetric transformation matrix of size (1+β)L×βL, J _M denotes a diagonal diagonal identity matrix of size M×M ; p ₁ =[0 _βL×(1-β)L ;I _(1-β)L ;0 _βL×(1-β)L ] means that the size is (1+β)L×(1-β)L Mapping matrix; w ₁ represents a column vector whose size is (1-β)L×1 and whose elements are all constant 1.

Therefore, the time-domain windowed objective optimization problem can be expressed as a symmetric roll-off vector function, that is

in

Design an approximate global search optimization (AGSO, Approximation Global SearchOptimization) algorithm to find the optimal symmetric roll-off vector of the target optimization problem (2)

The approximate global optimal search algorithm (AGSO) is described as in Algorithm 1: first find one by one The optimal value of each sample point of the column vector, that is, the value of all other sample points is fixed, and only the value of a sample point is adjusted according to the fixed step size delta, the objective function Record it once it drops. When the sample traverses the [0,1] interval with a fixed step size, the optimized sample value is recorded. Refine all samples to get a new column vector. The sample-by-sample optimization process is then repeated for this new column vector until the value of the objective function no longer decreases. Through this repeated iteration, finding column vector such that keep going Approximation, the algorithm gradually converges, and finally the discrete window function column vector is output

Figure 1 shows the transmitter block diagram of a time-domain windowed OFDMA system. As can be seen from the figure, the initial data is subjected to subcarrier mapping, IDFT modulation, cyclic prefix insertion, and windowing processing, and then the OFDMA time-domain discrete signal is output.

The following pseudocode depicts the implementation steps of the approximate global optimal search algorithm. The algorithm first finds the symmetric roll-off vector The best solution element at each position element, obtain the optimal symmetrical roll-off vector of each element position Subsequently, through multiple iterations, the algorithm gradually converges to the approximately globally optimal symmetric roll-off vector Approximate Global Optimum Search Algorithm

Algorithm starts

Step 1: Program initialization: initialization is any real number between [0,1[;

Step 2: Calculate the discrete window w ^{(k) using formula (1)} , calculate

Step 3:

Adjust a certain sample point of the window function each time value, add a small value delta,

And make the value not exceed the interval [0,1];

Then use formula (1) to recalculate the discrete window w ^(k) ;

recalculate

If S<S ₀ , then record this new discrete window function and side lobe power value;

Repeat this step until the values of all samples are optimized.

Step 4: If the value of the objective function Compared with the value of the last loop output, repeat step 3; otherwise, the value of the objective function does not change any more and has converged, and the recorded optimal discrete window function w ^(k) is output.

The algorithm ends.

Claims (2)

1. A design method of a discrete time domain window for inhibiting the spectrum sidelobe of an OFDMA system is characterized in that: and the optimized roll-off function is adopted to act on an OFDMA transmitting end, so that the suppression of the frequency spectrum side lobe of the OFDMA system is realized.

2. The discrete time domain window design method of claim 1, comprising the specific implementation steps of:

firstly, constructing a discrete time domain window w of a k user^(k)Expressed as follows:

wherein β is the roll-off factor of the time domain window, L is the total length of the OFDMA symbol sequence, n is (1+ β) L-1,representing a symmetrical roll-off portion of discrete time-domain window size β L × 1, discrete time-domain window w^(k)The matrix vector expression of (a) is:

wherein,representing a roll-off portion, p, of a discrete time-domain window that is bilaterally symmetric₁w₁Representing a portion of the discrete time domain window having a constant magnitude of 1; p is a radical of₀＝[I_βL；0_(1-β)L,βL；J_βL]Representing a symmetric transform matrix of size (1+ β) Lx β L, p₁＝[0_βL×(1-β)L；I_(1-β)L；0_βL×(1-β)L]Representing a mapping matrix of size (1+ β) Lx (1- β) L, w₁The column vector with the size of (1- β) Lx 1 and all the values of the elements being constant 1 is represented;

the time-domain windowing target optimization problem can be represented as a symmetric roll-off vectorA function of, i.e.

Wherein Is a Fourier transform matrix of size NxN, B^(k)A subcarrier mapping matrix representing the k-th user of size nxp:

B^(k)＝[0_P×[(k-1)P]I_P0_P×(N-kP)]^T

c denotes a cyclic prefix and cyclic suffix insertion matrix of size (1+ β) lxn:

；

then using approximate global optimum search algorithm to find the optimum symmetrical roll-off vector of the target optimization problem (2)I.e. each time the time-domain window function w is adjusted stepwise^(k)And such that the value does not exceed 0,1]In the interval, a side lobe power value of the optimized objective function is calculated; if the side lobe power value is reduced, recording a new discrete window function; optimizing all sample point values once; after one time, obtaining a new vector and an objective function value, and if the objective function value is improved, repeatedly optimizing all sample point values once again; if the objective function value is not improved, the algorithm converges and a new discrete window function is output.