CN103297162B - 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

Signal detecting method based on compressed sensing in GSSK modulation communication system

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) a kind of signal detecting method based on compressed sensing (Compressed Sensing, CS) in modulation communication system.

Background technology

1. compressed sensing

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

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, the mainly norm solution based on protruding optimization, or greedy algorithm.Orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm in greedy algorithm, for signal reconstruction.

OMP algorithm key step is from observing matrix, to select an atom mating the most with observed result y (being certain row) at every turn, construct current sparse approaching, and calculate now approach residual error, next continue the atom that selection is mated with residual error most, iteration process, as long as algorithmic statement, just can obtain sparse solution.

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 _jthe absolute value of >, finds out the atom that meets following formula corresponding index in dictionary.

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

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

3) calculate the sparse coefficient s estimating _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 2-4 step, enters next iteration.

The sparse solution s' estimating is the vector of N × 1 size, corresponding to index Δ _tthe element value at place equals s _t, and other element is all 0.

2. spatial modulation-GSSK

SSK is as a kind of special circumstances of spatial modulation (Spatial Modulation, SM), and the bit stream sending activates antenna by selection, controls concrete which root antenna transmission, and generally on this transmitting antenna, sends fixing signal value.And the special circumstances of the corresponding GSM of GSSK send bit stream through coding, select many antennas to activate, for transmitted signal.GSSK system is simple, easily implements, and as a kind of MIMO technology, has the higher availability of frequency spectrum.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 represent respectively to receive signal, transmit and white Gaussian noise. 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 the position of the antenna that activates just of its sparse corresponding position in launching antenna array.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 and likely activates antenna combining form, || .|| ²represent 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 activating the increase of antenna number, and the increase of number of transmit antennas, it is very high that 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 the signal detecting method based on compressed sensing in a kind of GSSK modulation communication system.In OMP algorithm, each iteration is only searched for a position corresponding to sparse set, and when the norm of residual volume equals actual degree of rarefication lower than the number of certain threshold value or the sparse position found, search procedure stops.Detect performance in order to improve compressed sensing, we search at every turn and find a subset that comprises tram, and finally, by as a whole these subsets merging, the probability that comprises correct solution in this entirety is so very large.

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

Detailed technology scheme of the present invention is as follows:

Signal detecting method based on compressed sensing in GSSK modulation communication system, as shown in Figure 1, comprises the following steps:

Step 1:GSSK system model is because the signal of transmission is real signal, GSSK system model can be rewritten as wherein: the real part of y' is that real (y), imaginary part are imag (y), the real part of H' is that real (H), imaginary part are imag (H), the real part of z' is that real (z), imaginary part are imag (z), 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 normalized:

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

Wherein H'=H''C, and C is a diagonal matrix, diagonal entry C _i,ibe channel observation matrix H ' mould 2 norms of i row.Can obtain so normalized system model is:

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

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

Step 2: establishing initial searching position set is empty set T'=φ, and y' is arranged to initial residual amount r=y', calculates inner product (r ^th''), obtain auto-correlation vector, wherein a r ^tfor the transposed vector of r, then select the wherein k × n of large (being that the degree of correlation is higher) of absolute value _tthe corresponding position of transmitting antenna of item, as candidate position set, is designated as T ₁', and join in location sets T', wherein: n _tfor the number of transmit antennas being activated in a time slot in 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 candidate position set.

The transmitting antenna being activated due to GSSK modulation communication system transmits normal value " 1 ", therefore for the definite k × n of step 2 _tindividual position of transmitting antenna, carries out k × n _tinferior test: in each test, first suppose i, the data 1 that i ∈ T' transmit antennas sends, calculate corresponding residual volume r=y'-h _i, wherein h _ibe normalization channel observation matrix H ' ' i column vector; As step 2, utilize this new residual volume again to calculate inner product (r ^th ") obtains new auto-correlation vector, as k × n _tafter individual auto-correlation vector calculation, more therefrom select k × (n that wherein absolute value is larger _t-1) a corresponding position of transmitting antenna, as expanding for the first time candidate position set, is designated as T ₂', and join in location sets T'; As k × n _tinferior test off-test, the location sets T'=φ+T obtaining ₁'+T ₂'.

Step 4: for step 2 and the definite (k × n of step 3 _t) × [k × (n _t-1)+1] individual position of transmitting antenna, carries out (k × n _t) × k × (n _t-1) inferior test.In each test, first assumed position set T ₁' in wherein any two positions transmitting antenna send data be all 1, calculate corresponding residual volume r; As step 2, utilize this new residual volume again to calculate inner product (r ^th'') obtain new auto-correlation vector, as (k × n _t) × k × (n _t-1) after individual auto-correlation vector calculation, more therefrom select k × (n that wherein absolute value is larger _t-2) a corresponding position of transmitting antenna, as expanding for the second time candidate position set, is designated as T ₃', and join in 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 and likely activates antenna combining form and Ω=T ', || || ²represent mould 2 norms.

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

Brief description of the drawings

Fig. 1 is the schematic diagram of the low complex degree detection method based on 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 the signal detecting method based on compressed sensing in a kind of GSSK modulation communication system, first the method uses compressed sensing technology to obtain a credibility interval T ' who activates aerial position, then in credibility interval, carries out ML detection.Due to this candidate set less (search of relatively traditional ML entirety, still seems very little), greatly reduce computational complexity.

Signal detecting method based on compressed sensing in GSSK modulation communication system, as shown in Figure 1, comprises the following steps:

Step 1:GSSK system model is because the signal of transmission is real signal, GSSK system model can be rewritten as wherein: the real part of y' is that real (y), imaginary part are imag (y), the real part of H' is that real (H), imaginary part are imag (H), the real part of z' is that real (z), imaginary part are imag (z), 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 normalized:

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

Wherein H'=H''C, and C is a diagonal matrix, diagonal entry C _i,ibe channel observation matrix H ' mould 2 norms of i row.Can obtain so normalized system model is:

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

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

Step 2: establishing initial searching position set is empty set T'=φ, and y' is arranged to initial residual amount r=y', calculates inner product (r ^th''), obtain auto-correlation vector, wherein a r ^tfor the transposed vector of r, then select the wherein k × n of large (being that the degree of correlation is higher) of absolute value _tthe corresponding position of transmitting antenna of item, as candidate position set, is designated as T ₁', and join in location sets T', wherein: n _tfor the number of transmit antennas being activated in a time slot in 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 candidate position set.

The transmitting antenna being activated due to GSSK modulation communication system transmits normal value " 1 ", therefore for the definite k × n of step 2 _tindividual position of transmitting antenna, carries out k × n _tinferior test: in each test, first suppose i, the data 1 that i ∈ T' transmit antennas sends, calculate corresponding residual volume r=y'-h _i, wherein hi be normalization channel observation matrix H ' ' i column vector; As step 2, utilize this new residual volume again to calculate inner product (r ^th'') obtain new auto-correlation vector, as k × n _tafter individual auto-correlation vector calculation, more therefrom select k × (n that wherein absolute value is larger _t-1) a corresponding position of transmitting antenna, as expanding for the first time candidate position set, is designated as T ₂' and join in location sets T'; As k × n _tinferior test off-test, the location sets obtaining $T^{\&prime;}=\mathrm{\&phi;}+{T_1}^{\&prime;}+{T_2}^{\&prime;}\&CenterDot;$

Step 4: for step 2 and the definite (k × n of step 3 _t) × [k × (n _t-1)+1] individual position of transmitting antenna, carries out (k × n _t) × k × (n _t-1) inferior test.In each test, first assumed position set T ₁' in wherein any two positions transmitting antenna send data be all 1, calculate corresponding residual volume r; As step 2, utilize this new residual volume again to calculate inner product (r ^th'') obtain new auto-correlation vector, as (k × n _t) × k × (n _t-1) after individual auto-correlation vector calculation, more therefrom select k × (n that wherein absolute value is larger _t-2) a corresponding position of transmitting antenna, as expanding for the second time candidate position set, is designated as T ₃', and join in 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 and likely activates antenna combining form and Ω=T ', || || ²represent 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 contrasts as shown in Figure 2.In Fig. 2, ML represents maximum likelihood detection method, OMP represents the orthogonal matching pursuit method in conventional compression cognition technology, i-OMP represents the signal detecting method based on compressed sensing in GSSK modulation communication system provided by the invention, and wherein k constant is got respectively 2,3 and 4 and represented three kinds of specific embodiments.As can be seen from Figure 2, in GSSK modulation communication system provided by the invention, the signal detecting method based on compressed sensing greatly reduces complexity compared to ML detection method.

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

Work as n _t=2 GSSK system, gets 256 and penetrates antenna, and reception antenna is 16, and the performance of the stylish detection method of k=4 approaches the performance that ML detects, 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 be understood to 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 depart 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. Signal detecting method based on compressed sensing in 1.GSSK modulation communication system, comprises the following steps:

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

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

   Wherein H'=H " C, and C is a diagonal matrix, diagonal entry C _i,ibe channel observation matrix H ' mould 2 norms of i row; Can obtain so normalized system model is:

   Wherein x'=Cx;

   Step 2: establishing initial searching position set is empty set T'=φ, and y' is arranged to initial residual amount r=y', calculates inner product (r ^th "), obtains auto-correlation vector, wherein a r ^tfor the transposed vector of r, then select the wherein larger k × n of absolute value _tthe corresponding position of transmitting antenna of item, as candidate position set, is designated as T ₁', and join in location sets T', wherein: n _tfor the number of transmit antennas being activated in a time slot in GSSK modulation communication system, k is a pre-determined constant;

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

   The transmitting antenna being activated due to GSSK modulation communication system transmits normal value " 1 ", therefore for the definite k × n of step 2 _tindividual position of transmitting antenna, carries out k × n _tinferior test: in each test, first suppose i, the data 1 that i ∈ T' transmit antennas sends, calculate corresponding residual volume r=y'-h _i, wherein h _inormalization channel observation matrix H " i column vector; As step 2, utilize this new residual volume again to calculate inner product (r ^th ") obtains new auto-correlation vector, as k × n _tafter individual auto-correlation vector calculation, more therefrom select k × (n that wherein absolute value is larger _t-1) a corresponding position of transmitting antenna, as expanding for the first time candidate position set, is designated as T ₂', and join in location sets T'; As k × n _tinferior test off-test, the location sets T'=φ+T obtaining ₁'+T ₂';

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

   Step 5: receive the Maximum Likelihood Detection of signal y in credibility interval set T', i.e. detected value wherein Ω represents and likely activates antenna combining form and Ω=T', || || ²represent mould 2 norms.
2. 2. the signal detecting method based on compressed sensing in GSSK modulation communication system according to claim 1, is characterized in that, the value of k described in step 2 is 2,3 or 4.