CN103297162A - Compressed-sensing-based signal detection method for GSSK (generalized space shift keying) modulation communication system - Google Patents

Abstract

The invention relates to a compressed-sensing-based signal detection method for a GSSK (generalized space shift keying) modulation communication system and belongs to the technical field of wireless communications. Compressed sensing technology is used with maximum likelihood detection; a confidence interval T' of an activated antenna position in a transmitting antenna array in the GSSK modulation communication system is obtained by the compressed sensing technology; ML (maximum likelihood) detection is performed in the confidence interval T'. Compared with overall search in ML detection, the method has the advantages that search space for ML detection is narrowed greatly so that computing complexity is reduced greatly; during the process of determining the confidence interval T' by the compressed sensing technology, detection precision is the same as that in ML detection by setting proper k constants.

Description

In the GSSK modulation communication system based on the signal detecting method of compressed sensing

Technical field

The invention belongs to wireless communication technology field, be specifically related to the strong control of generalized space displacement (generalized Space shift keying, GSSK) in the modulation communication system based on compressed sensing (Compressed Sensing, a kind of signal detecting method CS).

Background technology

1. compressed sensing

For the equation of shape such as y=θ s+z, signal s is that the K item is sparse, comprises N element and has only K item element non-0, and θ is that (M＜N), the column vector y of M * 1 is the observed result of signal s, and z is noise vector for the observing matrix of a M * N size.

The compressed sensing technology can be under the clear condition of the sample required much smaller than conventional method (observation) number, with perfect this sparse signal s that recovers of very high probability by a suitable observing matrix.Restoring signal is signal reconstruction, mainly based on the norm solution of protruding optimization, and perhaps greedy algorithm.(Orthogonal Matching Pursuit, OMP) algorithm are used for signal reconstruction to orthogonal matching pursuit in the greedy algorithm.

OMP algorithm key step is each atom that mates the most with observed result y (being certain row) of selecting from observing matrix, construct current sparse approaching, and calculate the residual error of approaching of this moment, next continue the atom that selection and residual error are mated most, the iteration process, so long as algorithmic statement just can access sparse solution.

The OMP algorithm flow:

1) initialization, index set Δ ₀=φ, iterations t=1, residual error amount r ₀=y, initial atom set θ ₀=Δ ₀=φ.Select index, calculate inner product＜r _T-1, θ _jAbsolute value, find out the atom corresponding index in dictionary that satisfies following formula.

${\mathrm{\&lambda;}}_t=\begin{array}{c}\arg \max \\ j=\mathrm{1,2},...,N\end{array}<r_{t-1},{\mathrm{\&theta;}}_j>,{\mathrm{\&theta;}}_j\&Element;\mathrm{\&theta;}$

2) upgrade index set Δ _t=Δ _T-1∪ { λ _t, the atom set θ that selects _t=[θ _T-1, θ _j].

3) calculate the sparse coefficient s that estimates _t=(θ _t) ^TY, wherein

Upgrade residual volume r _t=y-θ _t

4) if t〉K, iteration finishes, otherwise makes t=t+1, repeats the 2-4 step, enters next iteration.

The sparse solution s' that estimates is the vector of a N * 1 size, corresponding to the index Δ _tThe element value at place equals s _t, and other element is all 0.

2. spatial modulation-GSSK

(namely the bit stream of Fa Songing is by selecting to activate antenna for Spatial Modulation, a kind of special circumstances SM), and control is which root antenna emission specifically, and generally sends fixing signal value on this transmitting antenna as spatial modulation for SSK.And the special circumstances of the corresponding GSM of GSSK send bit stream through coding, select many antennas to activate, and are used for sending signal.The GSSK system is simple, implements easily, and as a kind of MIMO technology, the higher availability of frequency spectrum is arranged.Obviously, the input of GSSK is and has detected those transmission antennas transmit signal (being activated).

Consider a N _tSend out N _rThe GSSK system model of receiving is:

$y=\sqrt{\mathrm{\&rho;}}\mathrm{Hx}+z---\left(1\right)$

Wherein,

With

Expression receives signal, transmits and white Gaussian noise respectively.

Represent flat fading channel, its element is obeyed independent identically distributed multiple Gaussian Profile CN(0,1).Obviously, ρ represents signal to noise ratio, and x is a sparse unknown signaling, and its sparse the position of antenna in launching antenna array that corresponding position is activated just.In addition, we suppose that the antenna number of all activation is n _t, and activate antenna transmission data " 1 ".

Obviously its ML(maximum likelihood, maximum likelihood) detected value is:

$x_{\mathrm{ML}}^{\&prime;}=\begin{array}{c}\arg \max \\ x\&Element;\mathrm{\&Omega;}\end{array}{\left|\right|y-\sqrt{\mathrm{\&rho;}}\mathrm{Hx}\left|\right|}^2---\left(2\right)$

Wherein Ω represents the combination of antennas form that might activate, || .|| ² Expression mould 2 norms.

It is low that compressed sensing has complexity for the recovery of sparse signal, the advantage that performance is good.And GSSK is along with the increase that activates antenna number, and the increase of number of transmit antennas, and it is very high that the ML detection complexity becomes, and utilizes compressed sensing, may significantly reduce the detection complexity of GSSK system.

Summary of the invention

The present invention proposes in a kind of GSSK modulation communication system the signal detecting method based on compressed sensing.In the OMP algorithm, each iteration is only searched for a position corresponding to sparse set, and is lower than certain threshold value or the number of the sparse position found when equaling the degree of rarefication of reality when the norm of residual volume, and search procedure stops.Detect performance in order to improve compressed sensing, we search at every turn and seek a subclass that comprises the tram, and at last that these subclass merging are as a whole, the probability that comprises correct solution so in this integral body is very big.

Now, need carry out repeatedly search procedure and obtain bigger credibility interval.In new credibility interval, based on the thinking of ML, we find out most possible solution by calculating norm.Because this credibility interval is compared with maximum likelihood detection method and seemed less, carrying out ML in this minizone, to detect required complexity very low, also can obtain good performance simultaneously.

Detailed technology scheme of the present invention is as follows:

Based on the signal detecting method of compressed sensing, as shown in Figure 1, may further comprise the steps in the GSSK modulation communication system:

Step 1:GSSK system model is

Because the signal of transmission is real signal, the GSSK system model can be rewritten as

Wherein: the real part of y' is that real (y), imaginary part are imag (y), and the real part of H' is that real (H), imaginary part are imag (H), and the real part of z' is that real (z), imaginary part are imag (z), then has:

$\left[\begin{array}{c}\mathrm{real}\left(y\right)\\ \mathrm{imag}\left(y\right)\end{array}\right]=\sqrt{\mathrm{\&rho;}}\left[\begin{array}{c}\mathrm{real}\left(H\right)\\ \mathrm{imag}\left(H\right)\end{array}\right]x+\left[\begin{array}{c}\mathrm{real}\left(z\right)\\ \mathrm{imag}\left(z\right)\end{array}\right]$

Like this, the dimension of equal value of y is considered to increase.Next, H ' is carried out normalization:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;}x+z^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}\mathrm{Cx}+z^{\&prime;}$

H'=H''C wherein, and C is a diagonal matrix, diagonal entry C _{I, i}Be the channel observation matrix H ' mould 2 norms of i row.Can get normalized system model so is:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}{x}^{\&prime;}+z^{\&prime;}---\left(3\right)$ X'=Cx wherein.

Because the channel observation matrix H is obeyed multiple Gaussian Profile, the channel observation matrix H after real imaginary part is taken apart ' appoint right Gaussian distributed namely to satisfy RIP.X'=Cx does not in addition influence the sparse position of x, so is the problem (utilize the OMP algorithm to solve, but the performance that it and ML detect still being that gap is bigger) of a compressed sensing so this equation is appointed.

Step 2: establish the initial searching position set for empty set T'=φ, y' is arranged to initial residual amount r=y', calculate inner product (r ^TH''), obtain auto-correlation vector, wherein a r ^TBe the transposed vector of r, select the k * n of big (being that the degree of correlation is higher) of absolute value wherein then _tThe corresponding transmitting antenna of item position as the candidate position set, is designated as T ₁', and join among the location sets T', wherein: n _tBe the number of transmit antennas that is activated in time slot in the GSSK modulation communication system, k is a pre-determined constant (value of k is 2,3 or 4).

Step 3: upgrade residual volume and expand the candidate position set.

Because the normal value " 1 " of the transmitting antenna that the GSSK modulation communication system is activated transmission, so at the definite k * n of step 2 _tK * n is carried out in individual transmitting antenna position _tInferior test: in each test, suppose i earlier, the data 1 that i ∈ T' transmit antennas sends are calculated corresponding residual volume r=y'-h _i, h wherein _iBe normalization channel observation matrix H ' ' the i column vector; As step 2, utilize this new residual volume to calculate inner product (r again ^TH ") obtains new auto-correlation vector, as k * n _tAfter individual auto-correlation vector calculation finishes, therefrom select k * (n that wherein absolute value is bigger again _t-1) a corresponding transmitting antenna position as expanding for the first time the candidate position set, is designated as T ₂', and join among the location sets T'; As k * n _tInferior test off-test, the location sets T'=φ+T that obtains ₁'+T ₂'.

Step 4: at step 2 and the definite (k * n of step 3 _t) * [k * (n _t-1)+1] (k * n is carried out in individual transmitting antenna position _t) * k * (n _t-1) inferior test.In each test, first assumed position set T ₁' in wherein the data that send of the transmitting antenna of any two positions all be 1, calculate corresponding residual volume r; As step 2, utilize this new residual volume to calculate inner product (r again ^TH'') obtain new auto-correlation vector, as (k * n _t) * k * (n _t-1) after individual auto-correlation vector calculation finishes, therefrom selects k * (n that wherein absolute value is bigger again _t-2) a corresponding transmitting antenna position as expanding for the second time the candidate position set, is designated as T ₃', and join among the set T'.Step 2 can be calculated n altogether to step 4 _tInferior residual volume, so continuous candidate position set has finally obtained a credibility interval set T' that approximate ideal is complete.

Step 5: the maximum likelihood (ML) that receives signal y in credibility interval set T' detects, i.e. detected value

Wherein Ω represents combination of antennas form and the Ω=T ' of might activating, || || ² Expression mould 2 norms.

The present invention by the compressed sensing technology, obtains activating in the launching antenna array in the GSSK modulation communication system credibility interval T ' of aerial position in conjunction with compressed sensing technology and Maximum Likelihood Detection, carries out ML then in T ' lining, credibility interval and detects.The present invention has dwindled the search volume that ML detects greatly, thereby has greatly reduced computational complexity for the integral body search that ML detects; Simultaneously, utilizing the compressed sensing technology to determine in the process of credibility interval T ', by suitable k constant is set, can reaching with ML and detect identical accuracy of detection.

Description of drawings

Fig. 1 is based on the schematic diagram of the low complex degree detection method of compressed sensing.

Fig. 2 is n _t=2 o'clock algorithms of different complexity comparison diagrams.

Fig. 3 is n _t=1, k=4, N _tThe performance comparison figure of=256 o'clock different detection algorithms.

Fig. 4 is n _t=2, N _r=16, N _tThe performance comparison figure of=256 o'clock different detection algorithms.

Embodiment

The invention provides in a kind of GSSK modulation communication system the signal detecting method based on compressed sensing, this method at first uses the compressed sensing technology to obtain a credibility interval T ' who activates aerial position, carries out ML then and detect in the credibility interval.Because this candidate set less (the whole search of traditional relatively ML, it is very little still to seem) greatly reduces computational complexity.

Based on the signal detecting method of compressed sensing, as shown in Figure 1, may further comprise the steps in the GSSK modulation communication system:

Step 1:GSSK system model is Because the signal of transmission is real signal, the GSSK system model can be rewritten as Wherein: the real part of y' is that real (y), imaginary part are imag (y), and the real part of H' is that real (H), imaginary part are imag (H), and the real part of z' is that real (z), imaginary part are imag (z), then has:

$\left[\begin{array}{c}\mathrm{real}\left(y\right)\\ \mathrm{imag}\left(y\right)\end{array}\right]=\sqrt{\mathrm{\&rho;}}\left[\begin{array}{c}\mathrm{real}\left(H\right)\\ \mathrm{imag}\left(H\right)\end{array}\right]x+\left[\begin{array}{c}\mathrm{real}\left(z\right)\\ \mathrm{imag}\left(z\right)\end{array}\right]$

Like this, the dimension of equal value of y is considered to increase.Next, H ' is carried out normalization:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;}x+z^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}\mathrm{Cx}+z^{\&prime;}$

H'=H''C wherein, and C is a diagonal matrix, diagonal entry C _{I, i}Be the channel observation matrix H ' mould 2 norms of i row.Can get normalized system model so is:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}{x}^{\&prime;}+z^{\&prime;}---\left(3\right)$ X'=Cx wherein.

Because the channel observation matrix H is obeyed multiple Gaussian Profile, the channel observation matrix H after real imaginary part is taken apart ' appoint right Gaussian distributed namely to satisfy RIP.X'=Cx does not in addition influence the sparse position of x, so is the problem (utilize the OMP algorithm to solve, but the performance that it and ML detect still being that gap is bigger) of a compressed sensing so this equation is appointed.

Step 2: establish the initial searching position set for empty set T'=φ, y' is arranged to initial residual amount r=y', calculate inner product (r ^TH''), obtain auto-correlation vector, wherein a r ^TBe the transposed vector of r, select the k * n of big (being that the degree of correlation is higher) of absolute value wherein then _tThe corresponding transmitting antenna of item position as the candidate position set, is designated as T ₁', and join among the location sets T', wherein: n _tBe the number of transmit antennas that is activated in time slot in the GSSK modulation communication system, k is a pre-determined constant (value of k is 2,3 or 4).

Step 3: upgrade residual volume and expand the candidate position set.

Because the normal value " 1 " of the transmitting antenna that the GSSK modulation communication system is activated transmission, so at the definite k * n of step 2 _tK * n is carried out in individual transmitting antenna position _tInferior test: in each test, suppose i earlier, the data 1 that i ∈ T' transmit antennas sends are calculated corresponding residual volume r=y'-h _i, wherein hi be normalization channel observation matrix H ' ' the i column vector; As step 2, utilize this new residual volume to calculate inner product (r again ^TH'') obtain new auto-correlation vector, as k * n _tAfter individual auto-correlation vector calculation finishes, therefrom select k * (n that wherein absolute value is bigger again _t-1) a corresponding transmitting antenna position as expanding for the first time the candidate position set, is designated as T ₂' and join among the location sets T'; As k * n _tInferior test off-test, the location sets that obtains $T^{\&prime;}=\mathrm{\&phi;}+{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00003297786400012.png,HDA00003297786400021.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}^{\&prime;}+{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003297786400012.png,HDA00003297786400021.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}^{\&prime;}\&CenterDot;$

Step 4: at step 2 and the definite (k * n of step 3 _t) * [k * (n _t-1)+1] (k * n is carried out in individual transmitting antenna position _t) * k * (n _t-1) inferior test.In each test, first assumed position set T ₁' in wherein the data that send of the transmitting antenna of any two positions all be 1, calculate corresponding residual volume r; As step 2, utilize this new residual volume to calculate inner product (r again ^TH'') obtain new auto-correlation vector, as (k * n _t) * k * (n _t-1) after individual auto-correlation vector calculation finishes, therefrom selects k * (n that wherein absolute value is bigger again _t-2) a corresponding transmitting antenna position as expanding for the second time the candidate position set, is designated as T ₃', and join among the set T'.Step 2 can be calculated n altogether to step 4 _tInferior residual volume, so continuous candidate position set has finally obtained a credibility interval set T' that approximate ideal is complete.

Step 5: the maximum likelihood (ML) that receives signal y in credibility interval set T' detects, i.e. detected value

Wherein Ω represents combination of antennas form and the Ω=T ' of might activating, || || ² Expression mould 2 norms.

Computer Simulation shows, works as n _t=2, reception antenna N _r=16, transmitting antenna N _t=256 algorithms of different complexity contrast as shown in Figure 2.ML represents maximum likelihood detection method among Fig. 2, OMP represents the orthogonal matching pursuit method in the conventional compression cognition technology, i-OMP represents in the GSSK modulation communication system provided by the invention that based on the signal detecting method of compressed sensing, wherein the k constant is got 2,3 and 4 respectively and represented three kinds of specific embodiments.As can be seen from Figure 2, signal detecting method based on compressed sensing greatly reduces complexity compared to the ML detection method in the GSSK modulation communication system provided by the invention.

Work as n _tParameter k=4 among=1, the I-OMP.The number of transmit antennas of SSK is the performance that the performance of the new detection algorithm of 256, k=4 detects near ML, as shown in Figure 3.

Work as n _t=2 GSSK system gets 256 and penetrates antenna, and reception antenna is 16, the performance that the performance of the stylish detection method of k=4 detects near ML, as shown in Figure 4.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's implementation method of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these technology enlightenments disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (2)

1.GSSK based on the signal detecting method of compressed sensing, may further comprise the steps in the modulation communication system:

Step 1:GSSK system model is

Because the signal of transmission is real signal, the GSSK system model can be rewritten as

Wherein: the real part of y' is that real (y), imaginary part are imag (y), and the real part of H' is that real (H), imaginary part are imag (H), and the real part of z' is that real (z), imaginary part are imag (z), then has:

$\left[\begin{array}{c}\mathrm{real}\left(y\right)\\ \mathrm{imag}\left(y\right)\end{array}\right]=\sqrt{\mathrm{\&rho;}}\left[\begin{array}{c}\mathrm{real}\left(H\right)\\ \mathrm{imag}\left(H\right)\end{array}\right]x+\left[\begin{array}{c}\mathrm{real}\left(z\right)\\ \mathrm{imag}\left(z\right)\end{array}\right]$

Like this, the dimension of equal value of y is considered to increase; Next, H ' is carried out normalization:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;}x+z^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}\mathrm{Cx}+z^{\&prime;}$

H'=H''C wherein, and C is a diagonal matrix, diagonal entry C _{I, i}Be the channel observation matrix H ' mould 2 norms of i row.Can get normalized system model so is:

$y^{\&prime;}=\sqrt{\mathrm{\&rho;}}{H}^{\&prime;\&prime;}{x}^{\&prime;}+z^{\&prime;}---\left(3\right)$ X'=Cx wherein;

Step 2: establish the initial searching position set for empty set T'=φ, y' is arranged to initial residual amount r=y', calculate inner product (r ^TH''), obtain auto-correlation vector, wherein a r ^TBe the transposed vector of r, select the k * n of big (being that the degree of correlation is higher) of absolute value wherein then _tThe corresponding transmitting antenna of item position as the candidate position set, is designated as T ₁', and join among the location sets T', wherein: n _tBe the number of transmit antennas that is activated in time slot in the GSSK modulation communication system, k is a pre-determined constant;

Step 3: upgrade residual volume and expand the candidate position set;

Because the normal value " 1 " of the transmitting antenna that the GSSK modulation communication system is activated transmission, so at the definite k * n of step 2 _tK * n is carried out in individual transmitting antenna position _tInferior test: in each test, suppose i earlier, the data 1 that i ∈ T' transmit antennas sends are calculated corresponding residual volume r=y'-h _i, h wherein _iBe normalization channel observation matrix H ' ' the i column vector; As step 2, utilize this new residual volume to calculate inner product (r again ^TH'') obtain new auto-correlation vector, as k * n _tAfter individual auto-correlation vector calculation finishes, therefrom select k * (n that wherein absolute value is bigger again _t-1) a corresponding transmitting antenna position as expanding for the first time the candidate position set, is designated as T ₂', and join among the location sets T'; As k * n _tInferior test off-test, the location sets T'=φ+T that obtains ₁'+T ₂';

Step 4: at step 2 and the definite (k * n of step 3 _t) * [k * (n _t-1)+1] (k * n is carried out in individual transmitting antenna position _t) * k * (n _t-1) inferior test.In each test, first assumed position set T ₁' in wherein the data that send of the transmitting antenna of any two positions all be 1, calculate corresponding residual volume r; As step 2, utilize this new residual volume to calculate inner product (r again ^TH'') obtain new auto-correlation vector, as (k * n _t) * k * (n _t-1) after individual auto-correlation vector calculation finishes, therefrom selects k * (n that wherein absolute value is bigger again _t-2) a corresponding transmitting antenna position as expanding for the second time the candidate position set, is designated as T ₃', and join among the set T';

Step 5: in credibility interval set T', receive the Maximum Likelihood Detection of signal y, i.e. detected value

Wherein Ω represents combination of antennas form and the Ω=T ' of might activating, || || ²Expression mould 2 norms.

In the GSSK modulation communication system according to claim 1 based on the signal detecting method of compressed sensing, it is characterized in that the value of k described in the step 2 is 2,3 or 4.

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