CN109818663B - Low-complexity differential orthogonal space modulation detection method - Google Patents
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Abstract
The application discloses a low-complexity differential orthogonal space modulation detection method (called LC-DQSM algorithm for short), which is used for estimating a transmitting antenna index sequence and transmitting symbols step by considering that the number of active antennas is one or two on the basis of splitting a receiving signal matrix into signal vectors. The first case uses the signal vector detection concept, and the second case uses the improved block ordering minimum mean square error concept detection. Simulation results show that the complexity of the LC-DQSM algorithm is greatly reduced relative to that of the maximum likelihood detection algorithm (ML) under the premise of ensuring the performance of the algorithm.
Description
Technical Field
The application relates to the technical field of communication, in particular to a signal detection method of a receiving end of a wireless communication system, and specifically relates to a low-complexity differential orthogonal space modulation detection method.
Background
Quadrature spatial modulation (QSM, quadrature spatial modulation) is a new type of multiple-input multiple-output (MIMO, multiple input multiple output) wireless communication technology that increases overall spectral efficiency by expanding the spatial constellation while retaining all of the advantages of SM. Channel state information (CSI, channel state information) is critical in QSM because a portion of the data is encoded using euclidean distance differences between different channel paths. While differential spatial modulation (DSM, differential spatial modulation) completely eliminates the need for any CSI at the receiver while also retaining the advantages of SM, the idea of DSM is therefore used for differential QSM schemes to avoid the need for CSI at the receiver.
In differential orthogonal spatial modulation (DQSM, differential quadrature spatial modulation), permutation matrices of transmit antennas are used to transmit real and imaginary parts of transmit symbols, respectively. In QSM, one or both transmit antennas may be active at a particular time, depending on the incoming data bits. Parallel transmission is not possible in DSM because differential demodulation cannot identify more than one transmit antenna at a time. However, in QSM, the in-phase and quadrature components of the transmit symbol modulate the cosine and sine portions of the carrier signal, respectively. Thus, the transmitted data are orthogonal and can be decoded separately by IQ demodulation. In this regard, a Maximum Likelihood (ML) detection algorithm of DQSM is proposed, which is excellent in performance, but requires a traversal search, and is extremely complex.
Based on the background, the application provides a novel Low-Complexity differential detection method (called LC-DQSM algorithm for short) for a differential spatial orthogonal modulation system. The method firstly splits the received signal matrix into vector forms at a receiving end, is beneficial to the application of low-complexity ML detection algorithm, and reduces the calculation complexity of the algorithm by reducing the channel matrix. Then, the transmitting antennas are considered under two different conditions, and the transmitting antenna index sequence and the transmitting symbol are estimated according to the scene by utilizing the SVD and OB-MMSE detection ideas respectively, without performing traversal search, thereby reducing the complexity.
Disclosure of Invention
The application aims to solve the problems in the prior art and provides a low-complexity differential orthogonal spatial modulation detection method.
The technical scheme of the application is as follows:
a low complexity differential orthogonal spatial modulation detection method comprising the steps of:
in a differential spatial quadrature modulation system, first, a received signal matrix is split into a received signal matrix of column vectors at a receiving end, and then a transmission antenna index sequence and a transmission symbol are estimated step by step, wherein according to the signal construction characteristics of the differential quadrature modulation system, the transmission antennas need to be considered under two different conditions. In the first case, it is assumed that only one antenna is active, which means that the real and imaginary parts of the transmitted symbols are transmitted through the same antenna. In the second case, it is assumed that the real and imaginary parts of the transmitted symbols are transmitted through two different transmit antennas.
On the basis of adopting the technical scheme, the application can also adopt the following further technical scheme:
the differential spatial quadrature modulation system has N t Root transmit antenna and N r And M-order PSK modulation is adopted for the receiving antenna. The differential orthogonal spatial modulation process is as follows: first dividing the information bits into three parts, N of the first part t log 2 M bits pass through M ordersPSK modulation to obtain modulation symbols, the second part(/>The representation is rounded down, (. Cndot.) ]! Representing factorial) bits for selecting the antenna index of the real part, the remaining +.>The bits are used to select the antenna index of the imaginary part. Then respectively loading the real parts of the corresponding modulation symbols in the real part antenna index matrix to obtain a matrix +.>The imaginary part is loaded in the index matrix of the imaginary part antenna to obtain a matrix +.>(/> and />Any row and any column of the antenna have only one non-zero element, so that the requirement that different antennas are activated to transmit a single symbol in different time slots is met; the symbol matrix-> and />Differential transformation is performed to obtain +.> and />( wherein />For the real part differential matrix obtained after differential change at time d,/the differential matrix is the same as the real part differential matrix obtained after differential change at time d>For the imaginary part differential matrix obtained after the differential change at time d,/for the differential matrix obtained after the differential change at time d>For the real symbol matrix transmitted at time d, +.>For the imaginary symbol matrix transmitted at time d, S 0 Is a unitary matrix); finally S is arranged d Transmitting by loading on transmitting antenna, receiving matrix at d-th moment at receiving end>Is that
Y d ＝Η d S d +N d (1)
wherein ,is a transmitting matrix,/->Representing a channel matrix and a noise matrix, the elements of which follow complex Gaussian distributions CN (0, 1) and CN (0, sigma), respectively 2 )，σ 2 Is the noise power. The received signal matrix for splitting the received signal matrix into column vectors is specifically: the maximum likelihood detection algorithm formula of the receiving end can be expressed as +.> wherein ,/> and />Representing the estimated real part receiving matrix and the estimated imaginary part receiving matrix, respectively, < -> and />Representing the estimated real part transmission matrix and the estimated imaginary part transmission matrix respectively, and />Representing real and imaginary transmit matrix candidate sets, respectively,/for>Representing the form of a norm. Based on the ML detection structure, the received signal obtained at d-1 time is +.>Regarded as the channel gain matrix required for the detection of the transmitted signal at time d> Regarded as the channel gain matrix required for the detection of the transmitted signal at time d>And splits the received signal matrix into signal vector forms.
Further, in the first case, i.e. assuming the real part of the transmitted symbol sAnd imaginary part->Transmitting from the same antenna with index value of l, the algorithm specifically comprises: first, the activated transmitting antenna index sequence is obtained by using the signal vector detection concept, namely +.> wherein />G l|i 、Y d|i and Hd|l Respectively represent G l and Yd I-th column of (h) d Is the first column of (2). Then based on MPSK modulation, directly calculating modulation symbol according to angle change range of received signal by using formulas (2) and (3)> and />
Where round and mod represent rounding and modulo operations respectively,θ l|i is->Corresponding angle->Finally its Euclidean distance measure is +.>D i Column i, i e {1,2, …, N, representing D t }。
Further, in the second case, i.e. assuming the real part of the transmitted symbol sAnd imaginary part->Respectively from two index values +.> and />The antenna of the system is detected by adopting an improved block ordering minimum mean square error idea, and the algorithm specifically comprises the following steps:
first define wherein />m∈{1,2,…,N t }，(·) H Representing the conjugate transpose matrix>Representing the pseudo-inverse matrix. Then Order the />An index vector representing the alpha th transmit antenna group, wherein the number of all possible transmit antenna groups is +.> Representing a binomial coefficient, 2 representing a total of two antennas activated, 1.ltoreq.α.ltoreq.N a ，1≤k α,1 ≠k α,2 ≤N t . Then L is α Weight factor of (2)
Defining a weight vectorWill v i Arranged in descending order as wherein λ1 and />Respectively represent v i Serial numbers corresponding to the maximum value and the minimum value in the table i epsilon {1,2, …, N t }。
Suppose that it is known from lambda τ The transmission antenna groups transmit, and the estimated transmission symbols can be obtained through minimum mean square error detectionThe method comprises the following steps:
wherein τ ε {1,2, …, N a Q (·) represents the demodulation function,(·) -1 representing the inverse matrix, I 2 Representing a unit matrix of 2 x 2.
Is defined as
When (when)At the time, the detection is terminated, where δ=2n r σ 2 . The transmit antenna index matrix is expected->Transmitting symbol matrix->Is-> Let τ=τ+1 then continue with the above steps. If τ > N a Then->I.e.Let->Then D i '＝min{d z },i∈{1,2,…,N t }。
Finally, if D i ≤D i ',i∈{1,2,…,N t First case, the transmitted symbol is transmitted from the same antenna, and the final optimal detection value is obtainedIs->In the second case, on the other hand, the transmission symbol is transmitted from a different antenna, +.>Is->
The application has the advantages and beneficial effects that:
according to the application, the receiving signal matrix is split into vector forms at the receiving end, so that the application of a low-complexity ML detection algorithm is facilitated, and meanwhile, the calculation complexity of the algorithm is reduced by reducing the channel matrix; and then, considering the transmitting antennas under two different conditions, and estimating the transmitting antenna index sequence and the transmitting symbols according to the scene by utilizing the signal vector detection and the minimum mean square error detection ideas respectively without performing traversal search, thereby greatly reducing the complexity. The application not only approaches the performance of ML, but also has lower complexity and has excellent theoretical and practical significance.
Drawings
FIG. 1 is a diagram of N of a low complexity differential orthogonal spatial modulation detection method according to the present application t ＝2,M＝4,N r DQSM system BER performance versus plots for=2, 3, 4;
fig. 2 is a schematic diagram showing algorithm complexity comparison of the low-complexity differential orthogonal spatial modulation detection method according to the present application under different numbers of transmitting antennas, receiving antennas and modulation orders.
Table 1 is a comparison table of ML algorithm and LC-DQSM algorithm of low complexity differential orthogonal spatial modulation detection algorithm proposed according to the present application;
Detailed Description
The low-complexity differential orthogonal spatial modulation detection method adopted by the application comprises the following steps:
first, the algorithm splits the received signal matrix into a column vector received signal matrix at the receiving end, and then estimates the transmit antenna index sequence and the transmit symbols step by step. Wherein the transmit antennas need to be considered in two different cases depending on the signal construction characteristics of the differential quadrature modulation system. In the first case, it is assumed that only one antenna is active, which means that the real and imaginary parts of the transmitted symbols are transmitted through the same antenna. In the second case, it is assumed that the real and imaginary parts of the transmitted symbols are transmitted through two different transmit antennas. On the basis of adopting the technical scheme, the method of the application is described in detail:
the differential spatial quadrature modulation system has N t Root transmit antenna and N r And M-order PSK modulation is adopted for the receiving antenna. The differential orthogonal spatial modulation process is as follows: first dividing the information bits into three parts, N of the first part t log 2 M bits are subjected to M-order PSK modulation to obtain modulation symbols, and the modulation symbols are in a second part(/>The representation is rounded down, (. Cndot.) ]! Representing factorial) bits for selecting the antenna index of the real part, the remaining +.>The bits are used to select the antenna index of the imaginary part. Then respectively loading the real parts of the corresponding modulation symbols in the real part antenna index matrix to obtain a matrix +.>The imaginary part is loaded in the index matrix of the imaginary part antenna to obtain a matrix +.>(/> and />Any row and any column of the antenna have only one non-zero element, so that the requirement that different antennas are activated to transmit a single symbol in different time slots is met; the symbol matrix-> and />Respectively performing differential transformation to obtain and />( wherein />For the real part differential matrix obtained after differential change at time d,/the differential matrix is the same as the real part differential matrix obtained after differential change at time d>For the imaginary part differential matrix obtained after the differential change at time d,/for the differential matrix obtained after the differential change at time d>For the real symbol matrix transmitted at time d, +.>For the imaginary symbol matrix transmitted at time d, S 0 Is a unitary matrix); finally S is arranged d Transmitting by loading on transmitting antenna, receiving matrix at d-th moment at receiving end>Is that
Y d ＝Η d S d +N d (1)
wherein ,is a transmitting matrix,/-> and />Representing a channel matrix and a noise matrix, the elements of which follow complex Gaussian distributions CN (0, 1) and CN (0, sigma), respectively 2 )，σ 2 Is the noise power.
The received signal matrix for splitting the received signal matrix into column vectors is specifically: the maximum likelihood detection algorithm formula of the receiving end can be expressed as wherein ,/> and />Representing the estimated real part receiving matrix and the estimated imaginary part receiving matrix, respectively, < -> and />Representing the estimated real part transmission matrix and the estimated imaginary part transmission matrix, respectively, < -> and />Representing real and imaginary transmit matrix candidate sets, respectively,/for>Representing the form of a norm. Based on the ML detection structure, the received signal obtained at d-1 time is +.>Regarded as the channel gain matrix required for the detection of the transmitted signal at time d> Regarded as the channel gain matrix required for the detection of the transmitted signal at time d>And splits the received signal matrix into signal vector forms.
Further, in the first case, i.e. assuming the real part of the transmitted symbol sAnd imaginary part->Transmitting from the same antenna with index value of l, specifically comprising: first, the activated transmitting antenna index sequence is obtained by using the signal vector detection concept, namely +.> wherein />G l|i 、Y d|i and Hd|l Respectively represent G l and Yd I-th column of (h) d Is the first column of (2). Then based on MPSK modulation, directly calculating modulation symbol ++using formula (2) according to angle change range of received signal> and />
Where round and mod represent rounding and modulo operations respectively,θ l|i is->Corresponding angle->Finally its Euclidean distance measure is +.>D i Column i, i e {1,2, …, N, representing D t }。
Further, in the second case, i.e. assuming the real part of the transmitted symbol sAnd imaginary part->Respectively from two index values +.> and />The antenna of the system adopts the improved block ordering minimum mean square error idea to detect, and specifically comprises the following steps:
first define wherein />(·) H Representing the conjugate transpose matrix>Representing the pseudo-inverse matrix. Then let L α ＝[k α,1 ,k α,2 ]An index vector representing the alpha th transmit antenna group, wherein the number of all possible transmit antenna groups is +.> Representing a binomial coefficient, 2 representing a total of two antennas activated, 1.ltoreq.α.ltoreq.N a ，1≤k α,1 ≠k α,2 ≤N t。 Then L is α Weight factor of (2)
Defining a weight vectorWill v i Arranged in descending order as wherein λ1 and λNa Respectively represent v i Serial numbers corresponding to the maximum value and the minimum value in the table i epsilon {1,2, …, N t }。
Suppose that it is known from lambda τ The transmission antenna groups transmit, and the estimated transmission symbols can be obtained through minimum mean square error detectionThe method comprises the following steps:
wherein τ ε {1,2, …, N a Q (·) represents the demodulation function,(·) -1 representing the inverse matrix, I2 represents the identity matrix of 2 x 2.
Is defined as
When (when)At the time, the detection is terminated, where δ=2n r σ 2 . The transmit antenna index matrix is expected->Transmitting symbol matrix->Is->Let τ=τ+1 then continue with the above steps. If τ > N a Then->I.e.Let->Then D i '＝min{d z },i∈{1,2,…,N t }。
Finally, if D i ≤D i ',i∈{1,2,…,N t First case, the transmitted symbol is transmitted from the same antenna, and the final optimal detection value is obtainedIs->In the second case, on the other hand, the transmission symbol is transmitted from a different antenna, +.>Is->
Specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.
From fig. 1, it can be observed that the BER performance of the LC-DQSM algorithm is similar to that of the ML algorithm, the loss is not more than 3dB, and the system performance of both algorithms is improved with the increase of the number of receiving antennas. The ML algorithm uses classical block-wise detection to jointly detect the activated antenna index and modulation symbols to obtain the best performance. The LC-DQSM algorithm is designed based on splitting the received signal matrix into signal vectors, which results in performance loss of the algorithm due to erroneous decisions in the previous detection. However, the computational complexity of the LC-DQSM algorithm is much less than that of the ML algorithm.
Fig. 2 compares the complexity of the ML algorithm and the LC-DQSM algorithm at different transmit antenna numbers, receive antenna numbers, and modulation orders. As can be seen from FIG. 2, the complexity of the LC-DQSM algorithm is reduced by about 99% compared with that of the ML algorithm, specifically, the (4, 4) and (4,4,64) conditions in the figure are the same, the number of transmitting antennas and receiving antennas is unchanged, the modulation order is increased, the complexity of the ML algorithm is greatly increased, and the LC-DQSM algorithm is only slightly increased; compared with the (16,4,4) condition, the (4, 4) has the advantages that the modulation order and the number of the receiving antennas are unchanged, the transmitting antennas are increased, the complexity of the ML algorithm is larger than that of the ML algorithm which only increases the modulation order, and the LC-DQSM algorithm still has only a small increase in amplitude; (16,4,4) the number of transmit antennas and modulation order are unchanged, the number of receive antennas are increased, the complexity of the ML algorithm is greatly increased, and the LC-DQSM algorithm is only slightly increased compared to the (16,16,4) condition.
The complexity calculation is based on the number of real numbers multiplied, and the calculation complexity when the differential spatial modulation system adopts different detection algorithms is shown in table 1. As can be seen from the table, the computation complexity of the ML algorithm is a function of the modulation order M and the number of transmit antennas N, as compared to the LC-DQSM algorithm t Exponentially growing, M, N t The higher the ML complexity is. Thus, in a large-scale NCSM system, the computational complexity of the LC-DQSM algorithm is much less than that of the ML algorithm.
Table 1 complexity analysis table
The specific embodiments of the present application have been described in detail hereinabove with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, and various modifications and changes may be made by one skilled in the art without departing from the spirit and scope of the appended claims.
Claims (6)
1. The low-complexity differential orthogonal spatial modulation detection method is characterized by comprising the following steps of:
1) Under a differential quadrature modulation system, a receiving end splits a receiving signal matrix into a receiving signal matrix of column vectors; 2) Step-wise estimating a transmit antenna index sequence and a transmit symbol, wherein the transmit antenna is considered in two different cases according to the signal construction characteristics of the differential orthogonal modulation system: in the first case, it is assumed that only one antenna is active, which means that the real and imaginary parts of the transmitted symbols are transmitted through the same antenna, detected using the signal vector idea; in the second case, the real part and the imaginary part of the transmission symbol are assumed to be transmitted through two different transmission antennas, the improved block ordering minimum mean square error concept detection is adopted, the Euclidean distance in the two cases is finally compared, and the transmission antennas are the corresponding cases of smaller transmission antennas.
2. The method for detecting low-complexity differential orthogonal spatial modulation according to claim 1, wherein the differential spatial orthogonal modulation system has N t Root transmit antenna and N r The M-order PSK modulation is adopted for the root receiving antenna, and the differential quadrature spatial modulation process is as follows: first dividing the information bits into three parts, N of the first part t log 2 M bits are subjected to M-order PSK modulation to obtain modulation symbols, and the modulation symbols are in a second partBits are used to select the antenna index of the real part, the remaining +.>Bits are used to select the antenna index of the imaginary part; then respectively loading the real parts of the corresponding modulation symbols in the real part antenna index matrix to obtain a matrix +.>The imaginary part is loaded in the index matrix of the imaginary part antenna to obtain a matrix +.> and />Any row and any column of the antenna have only one non-zero element, so that the requirement that different antennas are activated to transmit a single symbol in different time slots is met; the symbol matrix-> and />Differential transformation is performed to obtain +.> and /> wherein />For the real part differential matrix obtained after differential change at time d,/the differential matrix is the same as the real part differential matrix obtained after differential change at time d>For the imaginary part differential matrix obtained after the differential change at time d,/for the differential matrix obtained after the differential change at time d>For the real symbol matrix transmitted at time d, +.>For the imaginary symbol matrix transmitted at time d, S is finally applied d Transmitting by loading on transmitting antenna, receiving matrix at d-th moment at receiving end>Is that
Y d ＝Η d S d +N d (1)
wherein ,is a transmitting matrix,/-> and />Representing a channel matrix and a noise matrix, the elements of which follow complex Gaussian distributions CN (0, 1) and CN (0, sigma), respectively 2 )，σ 2 Is the noise power.
3. The low-complexity differential orthogonal spatial modulation detection method according to claim 2, wherein the splitting the received signal matrix into column vectors is specifically: the maximum likelihood detection algorithm formula of the receiving end can be expressed as wherein ,/> and />Representing the estimated real part receiving matrix and the estimated imaginary part receiving matrix, respectively, < -> and />Representing the estimated real part transmission matrix and the estimated imaginary part transmission matrix respectively, and />Representing real and imaginary transmit matrix candidate sets, respectively,/for>Representing the form of a norm, based on the detection structure of the ML algorithm, the received signal obtained at time d-1 is +.>Regarded as the channel gain matrix required for the detection of the transmitted signal at time d>Regarded as the channel gain matrix required for the detection of the transmitted signal at time d>The received signal matrix is split into signal vector forms.
4. A low complexity differential orthogonal spatial modulation detection method according to claim 3 wherein in step 2) in the first case, the real part of the transmitted symbol s is assumedAnd imaginary part->Transmitting from the same antenna with index value of l, then: first, the activated transmitting antenna index sequence is obtained by using the signal vector detection concept, namely +.> wherein />G l|i 、Y d|i and Hd|l Respectively represent G l Ith row, Y of (2) d I-th column of (h) d Based on MPSK modulation, directly calculating modulation symbols according to angle change range of received signal by using formulas (2) and (3)> and />
Where round and mod represent rounding and modulo operations respectively,m represents modulation order, θ l|i Is->Corresponding angle->(·) H Representing a conjugate transpose matrix;
finally, the Euclidean distance is measured asD i Column i, i e {1,2, …, N, representing D t }。
5. A low complexity differential orthogonal spatial modulation detection method according to claim 3 wherein in step 2) in the second case, the real part of the transmitted symbol s is assumedAnd imaginary part->Respectively from two index values +.> and />The antenna of the system adopts the improved block ordering minimum mean square error idea to detect, and specifically comprises the following steps:
first define wherein />m∈{1,2,…,N t }，(·) H Representing the conjugate transpose matrix>Representing the pseudo-inverse matrix and then let L α ＝[k α,1 ,k α,2 ]An index vector representing the alpha th transmit antenna group, wherein the number of all possible transmit antenna groups is +.>The binomial coefficient is represented by 2, wherein 2 represents that a total of two antennas are activated, and 1.ltoreq.alpha.ltoreq.N a ，1≤k α,1 ≠k α,2 ≤N t L is then α Weight factor of->
Defining a weight vectorWill v i Arranged in descending order as wherein λ1 and />Respectively represent v i Serial numbers corresponding to the maximum value and the minimum value in the table i epsilon {1,2, …, N t }；
Suppose that it is known from lambda τ The transmission antenna groups transmit, and the estimated transmission symbols can be obtained through minimum mean square error detectionThe method comprises the following steps:
wherein τ ε {1,2, …, N a Q (·) represents the demodulation function,(·) -1 representing the inverse matrix, I 2 Representing a unit matrix of 2 x 2;
is defined as
When (when)At the time, the detection is terminated, where δ=2n r σ 2 Then the transmit antenna index matrix is expected>Transmitting symbol matrix->Is->Then let τ=τ+1 continue the above steps; if τ > N a Then->I.e.Let->Then D i '＝min{d z },i∈{1,2,…,N t }。
6. The method of claim 3, wherein if the euclidean distance in the first case is not greater than the second case, the transmitting antenna is the first case, the transmitting symbol is transmitted from the same antenna, and otherwise, the transmitting symbol is transmitted from a different antenna.
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