CN106161298A - Non-linear ofdm system Iterative channel estimation based on compressed sensing - Google Patents

Abstract

The present invention relates to a kind of non-linear ofdm system Iterative channel estimation based on compressed sensing, belong to wireless communication technology field, the purpose of this algorithm is for the OFDM condition of sparse channel estimation problem existed under the influence of non-linear distortion, system is carried out channel estimation, the precision of channel estimation of raising system, reduces the complexity of system.Being technically characterized in that of the present invention utilizes the dual openness of channel and nonlinear noise, first as observing matrix, pilot frequency information is compressed channel perception to estimate, gained channel information is regarded as observing matrix again and is compressed the estimation of perception non-linear distortion, and then signal is carried out nonlinear compensation, and loop iteration.The present invention considers the non-linear impact on system, estimates channel, be effectively increased the precision of channel estimation of non-linear ofdm system, improve operation efficiency under condition of sparse channel.

Description

Non-linear ofdm system Iterative channel estimation based on compressed sensing

Technical field

The invention belongs to wireless communication technology field, particularly to a kind of non-linear ofdm system based on compressed sensing repeatedly For channel estimation method.

Background technology

OFDM (Orthogonal Frequency Division Multiplexing, OFDM) has frequency band The advantages such as utilization rate symbol high, anti-crosstalk ability is strong, mitigating frequency-selective fading ability is strong, are the core in high-speed radiocommunication field The heart.Channel estimation is one of key technology of ofdm system, and its precision directly affects the systematic function under fading channel.Channel is estimated Meter and the two big key technologies that reduction peak-to-average force ratio is ofdm system.The precision that channel is estimated directly affects the system under fading channel Performance, high peak-to-average power ratio cause signal through power amplifier produce non-linear distortion (nonlinear distortion, NLD)。

At present, the existing researchs estimated about OFDM channel in a large number, wherein channel estimation studies based on auxiliary information is For extensively, typical method has least square (least squares, LS), least mean-square error (minimum mean-squared Error, MMSE), linear minimum mean-squared error (linear minimum mean-squared error, LMMSE) estimation etc.. In recent years, along with the proposition of compressive sensing theory, a large amount of scholars start to probe into and are applied to wireless communication field, and use it OFDM channel in pilot aided is estimated to study.Compressed sensing is that a kind of Signal Compression for sparse signal is theoretical.Grind Studying carefully and show, under condition of sparse channel, pilot tone based on equal number can reach preferably to estimate performance than traditional method.

But, existing channel estimation methods does not considers the nonlinear impact of ofdm signal mostly, it is believed that signal does not exists Non-linear distortion or by reduce peak-to-average force ratio algorithm well solved.At present, the typical method reducing peak-to-average force ratio has pre-mistake True method, partial transmission sequence method, Choose for user method etc., it is implemented in transmitters and majority has higher complexity.2003 Year, a kind of alternative manner based on signal reconstruction is suggested estimate in receivers and eliminate non-linear distortion.2005, Tropp et al. proposes to be used for compressed sensing the impulsive noise of ofdm system and eliminates, and estimates impulsive noise based on pilot tone.2014 Year, A.Ghassemi et al. is it is further proposed that the non-linear distortion of ofdm signal is considered as sparse additive noise, available It is estimated and compensates by compressed sensing in receivers.Said method can be avoided implementing to reduce peak-to-average force ratio in transmitter and calculate Method, but all do not consider the impact that NLD is estimated by fading channel.

In non-linear ofdm system, cannot be carried out channel accurately based on the auxiliary information with non-linear distortion and estimate Meter, and fading channel has a strong impact on NLD and estimates performance, channel is estimated and NLD estimates to influence each other, and mutually restriction becomes the two The difficult point of Combined estimator.In recent years, the begin one's study channel of non-linear ofdm system of existing a small amount of scholar is asked with NLD Combined estimator Topic.Such as based on iteration unified algorithm, carries out channel estimation based on LS and DFT interpolation, based on decision-feedback and signal reconstruction Carry out NLD elimination.The estimated accuracy of the method is affected by pilot number and mistaken verdict, and needs known transmitter clipping operation Prior information, receiver implement signal reconstruction add system complexity.The iterative joint of compressed sensing is combined based on LMMSE Estimate also to be suggested, but LMMSE algorithm complex is higher, and need known channel prior information.Above-mentioned Combined estimator algorithm is the most not Consider the sparse characteristic that channel is had under a lot of scenes.If channel is the most sparse, and pilot number is less than channel length, then Pole is fallen sharply low by the channel estimating performance of LS, LMMSE.And under the influence of at home and abroad there is no at present about considering non-linear distortion The research of Sparse Channel Estimation Algorithm.

Summary of the invention

It is an object of the invention to, for the OFDM condition of sparse channel estimation problem existed under the influence of non-linear distortion, utilize channel Dual openness with NLD noise, proposes a kind of non-linear ofdm system Iterative channel estimation based on compressed sensing.Should Algorithm has good estimation performance, it is achieved that the high-performance channel of non-linear ofdm system is estimated.

In order to reach above effect, the present invention non-linear ofdm system Iterative channel estimation based on compressed sensing, Comprise the following steps:

Step 1: build the OFDM demodulation signal model existed when multipath channel affects with NLD；

Step 2: at receiving terminal, extracts pilot tone from the signal model of FFT and implements iterative estimate calculation based on pilot tone Method.

Use non-linear ofdm system Iterative channel estimation based on compressed sensing, under condition of sparse channel, can be effective Improve the precision of channel estimation of non-linear ofdm system, there is good estimation performance.

Accompanying drawing illustrates:

For clearer explanation inventive embodiments or technical scheme of the prior art, below will be to embodiment or existing In technology description, the required accompanying drawing used is briefly described, and the accompanying drawing in describing below is only an enforcement of the present invention Example, for those of ordinary skill in the art, do not pay creation laborious on the premise of, it is also possible to obtain it with reference to the accompanying drawings His accompanying drawing.

Fig. 1 is the present invention non-linear ofdm system iterative channel estimation theory diagram；

Fig. 2 is that the channel of distinct methods under amplitude limit thresholding 4dB estimates mean square error；

Fig. 3 is the system bit error rate of distinct methods under amplitude limit thresholding 4dB；

Fig. 4 is that the channel under signal to noise ratio 30dB difference thresholding estimates mean square error；

Fig. 5 is the system bit error rate under signal to noise ratio 30dB difference thresholding.

Detailed description of the invention:

The purport of the present invention is to propose a kind of non-linear ofdm system Iterative channel estimation based on compressed sensing, profit Estimate channel and non-linear distortion, and loop iteration by compressed sensing, can effectively reduce non-linear distortion and channel is estimated Impact, reduce system complexity.

Below in conjunction with the accompanying drawings embodiment of the present invention is described in further detail.

One, the structure of ofdm system model

In an ofdm system, frequency domain signal X=[X₀, X₁..., X_N-1]^TTime-domain signal through IDFT modulation is represented by

$x_n=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}{X}_k{e}^{j2\mathrm{\π}kn/N},n=0,1,...,N-1---\left(1\right)$

Definition vector x=[x₀, x₁..., x_N-1]^T, then (1) formula is represented by matrix form

X=QX (2)

In formula, Q is N × N-dimensional inverse Fourier transform matrix,1≤m≤N, 1≤n≤N. A length of N is added before N point data_gCyclic Prefix form complete OFDM symbol through DAC export.

Signal produces NLD through power amplifier due to the restriction of its linearity, and the signal introducing NLD is represented by

x′_n=β x_n+d_n (3)

In formula, β is for making x_nWith d_nIncoherent constant.

Definition vector d=[d₀, d₁..., d_N-1]^TFor the NLD introduced, it can regard sparse additive noise as.For analysis side Just, making β in the present invention is 1, then the signal introducing NLD is represented by

X '=x+d=QX+d (4)

For making amplifier operation in the range of linearity, at transmitting terminal, signal is carried out amplitude limiting processing, then through the time domain of amplitude limit Signal is represented by

${x_n}^{\′}=\left\{\begin{array}{cc}{x}_n,& \left|x_n\right|\≤A\\ A{x}_n/\left|x_n\right|,& \left|x_n\right|>A\end{array}\right.---\left(5\right)$

In formula, A is amplitude limitation for normalization thresholding.

Affected by multipath channel, receive signal and be represented by

$y=h\⊗x^{\′}+z=k\⊗(x+d)+z---\left(6\right)$

In formula,Represent cyclic convolution computing, z=[z₀, z₁..., z_N-1]^TRepresent additive white Gaussian noise, h=[h₀, h₁..., h_L-1, 0_1×(N-L+1)]^T, wherein h_l, l=0,1 ..., L-1 is channel impulse response (CIR).

It is represented by through DFT demodulation gained frequency-region signal

$Y_k=\underset{n=0}{\overset{N-1}{\Σ}}{y}_n{e}^{-j2\mathrm{\π}nk/N},k=0,1,...,N-1---\left(7\right)$

Definition vector Y=[Y₀, Y₁..., Y_N-1]^T, then (7) formula is written as matrix form

Y=Q^HY=HX+HQ^Hd+Z (8)

In formula, Q^HFor N × N-dimensional Fourier transform matrix, H=diag (H₀, H₁..., H_N-1) it is channel frequency domain response vector Q^HThe diagonal matrix of h deformation, Z=Q^HZ is the frequency domain form of white Gaussian noise.Formula (8) be exist simultaneously multipath channel with OFDM demodulation signal model when NLD affects.

Two, receiving terminal extracts pilot tone and implements Iterative Method based on pilot tone

Specifically comprise the following steps that

Just estimate:

Nonlinear properties model (8) formula is deformed, vector X is rewritten as diagonal matrix form, and chooses pilot tone institute Row, can obtain

$Y_P={X_p}^{\′}{Q}_P^H{h}^i+H_P^i{Q}_P^H{d}^i+Z_P---\left(9\right)$

In formula, i is iterations, Y_p、Z_pFor P × 1 dimensional vector, X_p'=diag (X₁, X₂..., X_P) it is that P × P dimension is right Angular moment battle array, P is pilot number.

Initialize i=0, and non-linear distortion now is regarded as noise, thus be integrated in noise item, then (9) formula can It is written as

$Y_P={X_P}^{\′}{Q}_P^H{h}^i+{Z_p}^{\′}---\left(10\right)$

Based on compressed sensing principle, by known pilot information X_p' regard observing matrix as, willRegard orthogonal basis as, then can profit With compressed sensing algorithm to the channel h in (10) formulaⁱSolve,

$\begin{array}{ccc}{\hat{h}}^i=\arg min\left|\right|h^i|{|}_1& s.t.& \left|\right|{X_p}^{\′}{Q}_P^H{h}^i-Y_P|{|}_2\≤\mathrm{\ϵ}\end{array}---\left(11\right)$

Algorithm completes the first estimation of channel.

Iterative estimate:

To the h estimatedⁱCarry out Fourier transformation, obtain its frequency domain response Hⁱ, by Hⁱ(8) formula of substitution also chooses pilot tone row, Can obtain

$V_P=Y_P-H_P^i{X}_P=H_P^i{Q}_P^H{d}^{i+1}+Z_P---\left(12\right)$

In formula, V_pFor P × 1 dimensional vector.

Based on compressed sensing principle, willRegard observing matrix as, willRegard orthogonal basis as, utilize compressed sensing algorithm To non-linear distortion d in (18) formulaⁱ⁺¹Solve, can obtain

$\begin{array}{ccc}{\hat{d}}^{i+1}=\arg min\left|\right|d^{i+1}|{|}_1& s.t.& \left|\right|H_P^i{Q}_P^H{d}^{i+1}-V_P|{|}_2\≤\mathrm{\ϵ}\end{array}---\left(13\right)$

The d that will try to achieveⁱ⁺¹(9) formula of substitution carries out nonlinear distortion compensation to signal, can obtain

$U_P=Y_P-H_P^i{Q}_P^H{d}^{i+1}={X_p}^{\′}{Q}_P^H{h}^{i+1}+Z_P---\left(14\right)$

In formula, U_pFor p × 1 dimensional vector.

Recycling compressed sensing algorithm is to the h in (14) formulaⁱ⁺¹Solve,

$\begin{array}{ccc}{\hat{h}}^{i+1}=\arg min\left|\right|h^{i+1}|{|}_1& s.t.& \left|\right|X_P{Q}_P^H{h}^{i+1}-U_P|{|}_2\≤\mathrm{\ϵ}\end{array}---\left(15\right)$

Algorithm completes interative computation for the first time.Circulation repetition (12), to the process of (15) formula, can carry out successive ignition fortune Calculate, thus improve precision of channel estimation.The channel response utilizing iterative estimate to go out can be to carrying out nonlinear distortion compensation Signal implements channel equalization.

Three, instance analysis

Build ofdm system for checking inventive algorithm performance, comprise 512 subcarriers, including 336 information Carrier wave, 80 pilot sub-carriers, 96 null subcarrier, circulating prefix-length is 128, and 64QAM modulates, and 5/8LDPC encodes.Set up Sparse multi-path channel model, channel length is 90, and wherein active path number is 12.

For embodying the performance of inventive algorithm, carrying out Performance comparision with existing algorithm in same system, wherein algorithm 1 is A kind of Iterative Method, estimates channel based on LMMSE, estimates NLD noise based on compressed sensing；Algorithm 2 combines judgement for LS The Joint iteration algorithm of feedback.

Fig. 2 is amplitude limit thresholding when being 4dB, and distinct methods channel under different signal to noise ratios estimates that mean square error (MSE) is bent Line.It can be seen that along with the increase of signal to noise ratio, the estimated accuracy of each method is more and more higher.When signal to noise ratio is relatively low, the present invention calculates The impact of method iterations is inconspicuous；And when signal to noise ratio is higher (>=17dB), along with the increase of iterations, precision of channel estimation It is substantially better than the first estimation of not iteration, illustrates to consider necessity and the inventive algorithm that channel is estimated impact by non-linear distortion For improving the superiority of nonlinear system channel estimating performance.Inventive algorithm and algorithm 1, algorithm 2 are in the feelings of equal iteration 3 times Under condition, compared with assuming not consider the perfect channel estimation performance curve of NLD, inventive algorithm performance closest to.Due to letter Road is condition of sparse channel, and channel length is more than pilot number, and the channel estimating performance of LS with LMMSE is poor.Simultaneously as son carries Wave number is not the integral multiple of pilot number, and LS performance is inferior to LMMSE.

Fig. 3 is amplitude limit thresholding when being 4dB, distinct methods system bit error rate (BER) curve under different signal to noise ratios.Can To find out, the channel estimating performance of nonlinear system all has certain gap with ideal linearity system, but inventive algorithm performance is For close to ideal situation, and along with the increase of iterations, algorithm performance is significantly better than the first estimation of not iteration.In signal to noise ratio it is During 30dB, the BER just estimated is 1 × 10^-3, the BER that iteration is 3 times is 1 × 10^-4。

Fig. 4 is signal to noise ratio when being 30dB, and distinct methods channel under different amplitude limit thresholdings estimates (MSE) curve.Permissible Finding out, along with increasing of amplitude limit thresholding, the channel estimating performance of each method is become better and better.Under identical amplitude limit thresholding, this At the beginning of bright algorithm, the performance of estimation, 2 iteration and 3 iteration gradually steps up.In three kinds of methods that 3 iteration are corresponding, the present invention calculates Method best performance.

Fig. 5 is signal to noise ratio when being 30dB, distinct methods system (BER) curve under different amplitude limit thresholdings.Can from figure To find out, along with the rising of threshold value, the systematic function performance that distinct methods is corresponding gradually steps up, and the property between various method Can have same conclusion.When threshold value is 4dB, at the beginning of inventive algorithm, estimation, 2 iteration, the bit error rates of 3 iteration are divided It is not 1 × 10^-3、2×10^-4、1×10^-4, and it is significantly better than that algorithm 1, algorithm 2.

Sample result shows, this algorithm has good estimation performance, and under condition of sparse channel, the method can be effectively improved non- The precision of channel estimation of linear ofdm system, good value estimated to ofdm system channel.

The foregoing is only presently preferred embodiments of the present invention, be not limiting as the present invention, all in the spirit and principles in the present invention Within, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (3)

1. non-linear ofdm system Iterative channel estimation based on compressed sensing, comprises the following steps:

Step 1: build the OFDM demodulation signal model that there is multipath channel with non-linear distortion impact；

Step 2: at receiving terminal, extracts pilot tone from the signal model of FFT and implements Iterative Method based on pilot tone.

2. according to based on compressed sensing the non-linear ofdm system Iterative channel estimation described in right 1, it is characterised in that: , there is OFDM demodulation signal model when multipath channel affects with non-linear distortion in step 1 simultaneously

Y=Q^HY=HX+HQ^Hd+Z (1)

In formula, Y=[Y₀, Y₁..., Y_N-1]^TFor the frequency domain response of receiving end signal, X=[X₀, X₁..., X_N-1]^TBelieve for transmitting terminal Number frequency domain response, Q^HFor N × N-dimensional Fourier transform matrix, H=diag (H₀, H₁..., H_N-1) it is channel frequency domain response vector Q^HThe diagonal matrix of h deformation, h=[h₀, h₁..., h_L-1, 0_1×(N-L+1)]^T, wherein h_l, l=0,1 ..., L-1 is channel Shock response (CIR), Z=Q^HZ is the frequency domain form of white Gaussian noise.

3. according to based on compressed sensing the non-linear ofdm system Iterative channel estimation described in right 1, it is characterised in that: Step 2, chooses the pilot tone row of transmitting terminal and receiving end signal,

$Y_P={X_p}^{\′}{Q}_P^H{h}^i+H_P^i{Q}_P^H{d}^i+Z_P---\left(2\right)$

In formula, i is iterations, Y_p、Z_pFor P × 1 dimensional vector, X_p'=diag (X₁, X₂..., X_P) it is that P × P ties up angular moment Battle array, P is pilot number.First by nonlinear noise merger noise item, compressed sensing is utilized to estimate the h of each iterationⁱ, will estimate HⁱBring formula (2) into, utilize compressed sensing to estimate dⁱ, by dⁱBring formula (2) into and estimate the h of next iterationⁱ⁺¹, according to this Plant the continuous iteration of mode to algorithmic statement.