CN103297162B

CN103297162B - Compressed-sensing-based signal detection method for GSSK (generalized space shift keying) modulation communication system

Info

Publication number: CN103297162B
Application number: CN201310217583.9A
Authority: CN
Inventors: 范世文; 邵晋梁; 李慧蕾; 但黎琳; 李少谦
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2013-06-04
Filing date: 2013-06-04
Publication date: 2014-12-03
Anticipated expiration: 2033-06-04
Also published as: CN103297162A

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 detection method based on compressed sensing in GSSK modulation communication system

Technical Field

The invention belongs to the technical field of wireless communication, and particularly relates to a signal detection method based on Compressed Sensing (CS) in a Generalized Space Shift Keying (GSSK) modulation communication system.

Background

1. Compressed sensing

For an equation of the form y = θ s + z, the signal s is K-term sparse, contains N elements and only K elements are non-0, θ is an M × N observation matrix (M < N), M × 1 column vector y is the observation of the signal s, and z is a noise vector.

The compressed sensing technology can perfectly recover the sparse signal s with a high probability under the condition that the number of samples (observation) is far less than that required by the traditional method through a proper observation matrix. The recovery signal, i.e. signal reconstruction, is mainly based on a norm solution of convex optimization or a greedy algorithm. Orthogonal Matching Pursuit (OMP) algorithm in greedy algorithm for signal reconstruction.

The OMP algorithm mainly comprises the steps of selecting an atom (namely a certain column) which is most matched with an observation result y from an observation matrix each time, constructing the current sparse approximation, calculating the approximation residual error at the moment, continuing to select the atom which is most matched with the residual error, repeating the iteration process, and obtaining the sparse solution as long as the algorithm is converged.

OMP algorithm process:

1) initialization, index set Δ₀= phi, number of iterations t =1, residual quantity r₀= y, initial set of atoms θ₀=Δ₀And (= phi). Selecting index, calculating inner product<r_t-1,θ_j>Find the corresponding index of the atom in the dictionary that satisfies the following formula.

<math> <mrow> <msub> <mi>λ</mi> <mi>t</mi> </msub> <mo>=</mo> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>arg</mi> <mi>max</mi> </mtd> </mtr> <mtr> <mtd> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> </mtd> </mtr> </mtable> </mfenced> <mo><</mo> <msub> <mi>r</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi>j</mi> </msub> <mo>></mo> <mo>,</mo> <msub> <mi>θ</mi> <mi>j</mi> </msub> <mo>&Element;</mo> <mi>θ</mi> </mrow> </math>

2) Updating the index set Δ_t=Δ_t-1∪{λ_tH, the selected atom set θ_t=[θ_t-1,θ_j]。

3) Computing an estimated sparse coefficient s_t=(θ_t)^Ty, whereinUpdating the residue r_t=y-θ_t。

4) If t > K, the iteration is ended, otherwise, let t = t +1, repeat 2-4 steps, and enter the next iteration.

The estimated sparse solution s' is a vector of size N × 1, corresponding to the index Δ_tThe value of the element at is equal to s_tAnd other elements are allIs 0.

2. Spatial modulation-GSSK

SSK is a special case of Spatial Modulation (SM), i.e., the transmitted bit stream controls which antenna is specifically transmitting by selecting the active antenna, and generally a fixed signal value is transmitted on the transmitting antenna. And GSSK corresponds to the special case of GSM, and the transmitted bit stream is encoded and multiple antennas are selected to be activated for transmitting signals. The GSSK system is simple and easy to implement, and has a high spectrum utilization rate as a MIMO technology. It is apparent that signal detection by GSSK is the detection that those transmit antennas transmitted signals (are activated).

Consider an N_tHair, N_rThe GSSK system model received is:

wherein, andrespectively representing a received signal, a transmitted signal, and gaussian white noise.Representing a flat fading channel whose elements obey an independent identically distributed complex gaussian distribution CN (0, 1). Obviously, ρ represents the signal-to-noise ratio and x is a sparse unknown signal whose sparseness corresponds to the positive locationIs the position of the active antenna in the transmit antenna array. In addition, we assume that all active antennas are n_tAnd activates the antenna to transmit data "1".

It is obvious that its ML (maximum likelihood) detection value is:

<math> <mrow> <msubsup> <mi>x</mi> <mi>ML</mi> <mo>′</mo> </msubsup> <mo>=</mo> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>arg</mi> <mi>max</mi> </mtd> </mtr> <mtr> <mtd> <mi>x</mi> <mo>&Element;</mo> <mi>Ω</mi> </mtd> </mtr> </mtable> </mfenced> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <msqrt> <mi>ρ</mi> </msqrt> <mi>Hx</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein Ω represents all possible activated antenna combination forms, | | |. computation²Representing a modulo 2 norm.

The compressed sensing has the advantages of low complexity and good performance for the recovery of sparse signals. With the increase of the number of active antennas and the number of transmitting antennas of the GSSK, the ML detection complexity becomes extremely high, and the detection complexity of the GSSK system may be significantly reduced by using compressed sensing.

Disclosure of Invention

The invention provides a signal detection method based on compressed sensing in a GSSK modulation communication system. In the OMP algorithm, each iteration searches only one position corresponding to the sparse set, and the search process stops when the norm of the residual is below a certain threshold or the number of found sparse positions is equal to the actual sparsity. In order to improve the performance of compressed sensing detection, each time a subset containing the correct position is searched, and finally the subsets are combined into a whole, so that the probability of containing the correct solution in the whole is high.

Now, a plurality of search processes need to be performed to obtain a larger trusted interval. In a new credible interval, based on the ML idea, the most probable solution is found out by calculating the norm. Since the confidence interval is smaller than that of the maximum likelihood detection method, the complexity required for ML detection in the interval is low, and good performance can be obtained.

The detailed technical scheme of the invention is as follows:

a signal detection method based on compressed sensing in a GSSK modulation communication system, as shown in fig. 1, includes the following steps:

step 1: the GSSK system model isSince the transmitted signal is real signal, the GSSK system model can be rewritten intoWherein: y ' is real part (y), imaginary part (imag (y), H ' is real part (H), imaginary part (imag) (H), real part (z) and imaginary part (imag) (z), and the real part and the imaginary part of z ' are respectively as follows:

thus, the equivalent dimension of y is considered to be increased. Next, H' is normalized:

where H '= H' C, and C is a diagonal matrix, diagonal element C_i,iIs the modulo-2 norm of the ith column of the channel observation matrix H'. The system model that can be normalized is then:

where x' = Cx.

Because the channel observation matrix H obeys complex Gaussian distribution, the channel observation matrix H' with the split real and imaginary parts can meet RIP after obeying the Gaussian distribution. In addition, x' = Cx, and does not affect the sparse position of x, so the equation is a compressed sensing problem (which can be solved by the OMP algorithm, but the performance of the method is far from that of ML detection).

Step 2: assuming that the initial search position set is an empty set T ' = Φ, set y ' to the initial residual r = y ', calculate the inner product (r = y ″)^TH '') to obtain an autocorrelation vector, wherein r^TIs a transposed vector of r, and then k × n with larger absolute value (i.e., higher correlation) is selected_tThe transmitting antenna position corresponding to the item is taken as a candidate position set and is marked as T₁', and added to the location set T', wherein: n is_tK is a constant (k takes a value of 2, 3 or 4) determined in advance for the number of activated transmitting antennas in a time slot in the GSSK modulation communication system.

And step 3: the residual amount is updated and the candidate position set is expanded.

Since the activated transmitting antenna of the GSSK modulation communication system transmits a constant value of '1', the k × n determined in step 2_tOne transmitting antenna position, k × n_tAnd (4) secondary test: in each test, data 1 sent by the ith, i ∈ T 'transmitting antenna is assumed, and the corresponding residual r = y' -h is calculated_iWherein h is_iIs the ith column vector of the normalized channel observation matrix H'; as in step 2, the inner product (r) is again calculated using this new residual amount^TH') to obtain a new autocorrelation vector when k × n_tAfter the autocorrelation vectors are calculated, k x (n) with larger absolute value is selected from the autocorrelation vectors_t-1) the transmitting antenna position corresponding to the item as the first extended candidate position set, denoted as T₂', and added to the location set T'; when k × n_tAfter the test is finished, the obtained position set T' = phi + T₁'+T₂'。

And 4, step 4: (k × n) determined for step 2 and step 3_t)×[k×(n_t-1)+1]One transmitting antenna position, proceed by (k × n)_t)×k×(n_t-1) trials. In each test, a set of positions T is assumed first₁In' where the data sent by the transmitting antennas at any two positions are both 1, calculating the corresponding residual r; as in step 2, the inner product (r) is again calculated using this new residual amount^TH') obtaining a new autocorrelation vector when (k × n)_t)×k×(n_tAfter-1) autocorrelation vectors are calculated, k x (n) with larger absolute value is selected from the autocorrelation vectors_t-2) the transmitting antenna position corresponding to the item as the second candidate position set of expansion, denoted as T₃', and added to the set T'. Step 2 to step 4 total meeting calculation n_tAnd the residual quantity is reduced, so that the candidate position set is continuously obtained, and finally, an approximately ideal and complete credible interval set T' is obtained.

And 5: maximum Likelihood (ML) detection of the received signal y in a set of confidence intervals T', i.e. detection valuesWhere Ω represents all possible combinations of active antennas and Ω ═ T', | · | | computationally idle²Representing a modulo 2 norm.

The invention combines the compressed sensing technology and the maximum likelihood detection, obtains the credible interval T 'of the position of the activated antenna in the transmitting antenna array in the GSSK modulation communication system through the compressed sensing technology, and then carries out ML detection in the credible interval T'. Compared with the whole search of ML detection, the method greatly reduces the search space of ML detection, thereby greatly reducing the operation complexity; meanwhile, in the process of determining the credible interval T' by using a compressed sensing technology, the detection precision same as that of ML detection can be achieved by setting a proper k constant.

Drawings

Fig. 1 is a schematic diagram of a low complexity detection method based on compressed sensing.

FIG. 2 is n_tDifferent algorithm complexity contrast maps when = 2.

FIG. 3 is n_t=1，k=4,N_tPerformance of different detection algorithms is compared in case of = 256.

FIG. 4 is n_t=2，N_r=16,N_tPerformance of different detection algorithms is compared in case of = 256.

Detailed Description

The invention provides a signal detection method based on compressed sensing in a GSSK modulation communication system. Since this candidate set is small (still appears small compared to the conventional ML whole search), the computational complexity is greatly reduced.

where x' = Cx.

Since the activated transmitting antenna of the GSSK modulation communication system transmits a constant value of '1', the k × n determined in step 2_tOne transmitting antenna position, k × n_tAnd (4) secondary test: in each test, data 1 sent by the ith, i ∈ T 'transmitting antenna is assumed, and the corresponding residual r = y' -h is calculated_iWhere hi is the ith column vector of the normalized channel observation matrix H "; as in step 2, the inner product (r) is again calculated using this new residual amount^TH') to obtain a new autocorrelation vector when k × n_tAfter the autocorrelation vectors are calculated, k x (n) with larger absolute value is selected from the autocorrelation vectors_t-1) the transmitting antenna position corresponding to the item as the first extended candidate position set, denoted as T₂'and added to the location set T'; when k × n_tSub-testThe position set obtained after the experiment is finished

Computer simulation shows that when n_t=2, receiving antenna N_r=16, transmitting antenna N_tThe different algorithm complexity comparisons of =256 are shown in fig. 2. ML in FIG. 2 denotes the maximum likelihood detection methodThe method is characterized in that OMP represents an orthogonal matching tracking method in the traditional compressed sensing technology, i-OMP represents a signal detection method based on compressed sensing in the GSSK modulation communication system provided by the invention, and k constants respectively take 2, 3 and 4 to represent three specific implementation schemes. As can be seen from fig. 2, compared with the ML detection method, the compressed sensing-based signal detection method in the GSSK modulation communication system provided by the present invention greatly reduces the complexity.

When n is_t=1, parameter k =4 in I-OMP. The number of transmit antennas for SSK is 256 and the performance of the new detection algorithm with k =4 approaches the performance of ML detection, as shown in fig. 3.

When n is_tIn the GSSK system of =2, 256 antennas are used, 16 receiving antennas are used, and the performance of the new detection method approaches the performance of ML detection when k =4, as shown in fig. 4.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the manner of practicing the invention, and it is to be understood that the scope of the invention is not limited to such specifically recited and practiced embodiments. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims

The signal detection method based on compressed sensing in the GSSK modulation communication system comprises the following steps:

step 1: the GSSK system model isSince the transmitted signal is real signal, the GSSK system model can be rewritten intoWherein: the real part of y' is real (y),Imaginary part is imag (y), real part of H 'is real (H), imaginary part is imag (H), real part of z' is real (z), imaginary part is imag (z), and the following components are provided:

thus, the equivalent dimension of y is considered to be increased; next, H' is normalized:

where H 'is H' C and C is a diagonal matrix, diagonal elements C_i,iIs the modulo-2 norm of the ith column of the channel observation matrix H'; the system model that can be normalized is then:

wherein x ═ Cx;

step 2: setting the initial search position set as an empty set T '═ phi, setting y' as an initial residual amount r '═ y', and calculating an inner product (r^TH') to obtain an autocorrelation vector, wherein r^TIs a transposed vector of r, and then k × n where the absolute value is larger is selected_tThe transmitting antenna position corresponding to the item is taken as a candidate position set and is marked as T₁', and added to the location set T', wherein: n is_tThe number of activated transmitting antennas in a time slot in the GSSK modulation communication system is determined, and k is a constant determined in advance;

and step 3: updating the residual amount and expanding the candidate position set;

since the activated transmitting antenna of the GSSK modulation communication system transmits a constant value of '1', the k × n determined in step 2_tOne transmitting antenna position, k × n_tAnd (4) secondary test: in each test, data 1 sent by the ith, i ∈ T' transmitting antenna is assumed, and the corresponding residual quantity is calculatedr＝y'-h_iWherein h is_iIs the ith column vector of the normalized channel observation matrix H'; as in step 2, the inner product (r) is again calculated using this new residual amount^TH') to obtain a new autocorrelation vector when k × n_tAfter the autocorrelation vectors are calculated, k x (n) with larger absolute value is selected from the autocorrelation vectors_t-1) the transmitting antenna position corresponding to the item as the first extended candidate position set, denoted as T₂', and added to the location set T'; when k × n_tAfter the test is finished, the position set T' ═ phi + T is obtained₁'+T₂'；

And 4, step 4: (k × n) determined for step 2 and step 3_t)×[k×(n_t-1)+1]One transmitting antenna position, proceed by (k × n)_t)×k×(n_t-1) trials, in each of which a set of positions T is assumed first₁In' where the data sent by the transmitting antennas at any two positions are both 1, calculating the corresponding residual r; as in step 2, the inner product (r) is again calculated using this new residual amount^TH') to obtain a new autocorrelation vector when (k × n)_t)×k×(n_tAfter-1) autocorrelation vectors are calculated, k x (n) with larger absolute value is selected from the autocorrelation vectors_t-2) the transmitting antenna position corresponding to the item as the second candidate position set of expansion, denoted as T₃', and added to the set T';

and 5: maximum likelihood detection of received signal y in set of confidence intervals T', i.e. detection valuesWhere Ω represents all possible combinations of active antennas and Ω ═ T', | · | | computationally idle²Representing a modulo 2 norm.
2. The method for detecting a signal based on compressed sensing in a GSSK modulation communication system according to claim 1, wherein the value of k in step 2 is 2, 3 or 4.