CN109167649B - Low-complexity detection method for GSM-MBM system - Google Patents

Low-complexity detection method for GSM-MBM system Download PDF

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CN109167649B
CN109167649B CN201811060486.2A CN201811060486A CN109167649B CN 109167649 B CN109167649 B CN 109167649B CN 201811060486 A CN201811060486 A CN 201811060486A CN 109167649 B CN109167649 B CN 109167649B
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CN109167649A (en
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金宁
宋伟婧
金小萍
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China Jiliang University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0054—Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/0048—Decoding adapted to other signal detection operation in conjunction with detection of multiuser or interfering signals, e.g. iteration between CDMA or MIMO detector and FEC decoder
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/345—Modifications of the signal space to allow the transmission of additional information
    • H04L27/3461—Modifications of the signal space to allow the transmission of additional information in order to transmit a subchannel
    • H04L27/3483—Modifications of the signal space to allow the transmission of additional information in order to transmit a subchannel using a modulation of the constellation points

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Abstract

The complexity of a Maximum Likelihood (ML) detection algorithm at a receiving end of a generalized spatial modulation-based (GSM-MBM) system based on medium modulation increases exponentially with an active antenna, a mirror active Mode (MAP) and a modulation order. Aiming at the problem, the invention provides a low-complexity detection method of a GSM-MBM system, which is a low-complexity detection method (ASVD-DOD) based on a self-adaptive signal vector and distance sorting idea, obtains an activated antenna sequence set by using the sorting method, adaptively searches an activated MAP candidate value according to a defined error probability threshold, recovers a modulation symbol corresponding to a candidate MAP by using a DOD algorithm, and realizes the joint detection of the MAP and the modulation symbol. Simulation results show that when the ASVD-DOD algorithm and the ML algorithm are applied to a GSM-MBM system with the same parameters, the error code performance of the ASVD-DOD algorithm is similar to that of the ML algorithm, but the calculation complexity is reduced by at least 90% compared with that of the ML algorithm.

Description

Low-complexity detection method for GSM-MBM system
Technical Field
The invention 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 detection method of a GSM-MBM system.
Background
Medium-based modulation (MBM) is a newly proposed antenna technology and is expected to become one of the key technologies of the 5G communication system. Unlike conventional Phase Shift Keying (PSK), Quadrature Amplitude Modulation (QAM), and the like, the core idea of medium modulation is to include transmission information in a transmission medium, i.e., to transmit different messages by utilizing the randomness and independence of channels. All transmission channels are mapped into a receiving constellation diagram, the dimension of the receiving constellation diagram can be increased on the premise of not increasing the transmitting energy consumption, and the method has great advantages in improving the frequency spectrum utilization rate and saving the energy consumption.
There is a literature reporting a single input multiple output-media based (SIMO-MBM) model using an RF mirror as a scatterer. Spectral efficiency is improved over conventional SIMO systems, but there is a limit to the number of RF mirrors that can be used for a single antenna. Researchers have proposed spatial modulation-media based modulation (SMBM), which combines Spatial Modulation (SM) with MBM to index the transmit antenna and RF mirror simultaneously, further improving spectral efficiency and transmission rate of the system. However, the multiplexing gain of the SM technique is logarithmic to the number of transmitting antennas, and the transmission efficiency is not high. Researchers have proposed generalized spatial modulation-medium based modulation based on medium modulation (GSM-MBM). The prominent feature of GSM is that the space domain concept of SM is expanded, and a combination of multiple activated antennas is used to form a space constellation point. Therefore, GSM-MBM systems tend to achieve higher spectral efficiency than SMBM systems when configured with the same number of transmit antennas. However, as the number of active antennas and the number of selectable Mirror Active Patterns (MAPs) increase, the complexity of the receiving end increases exponentially, so that the complexity and cost of the device increase. No literature has been dedicated to this problem.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a low-complexity detection method of a GSM-MBM system, which is a low-complexity detection method (ASVD-DOD) based on an adaptive signal vector and distance sorting idea. The method converts joint detection in a traditional Maximum Likelihood (ML) detection algorithm into three parts of a transmitting antenna activation sequence set, an activated MAP index value and a modulation symbol for separate detection. Firstly, an activated antenna sequence set is obtained by utilizing a sorting method, then, for each transmitting antenna in the set, a plurality of MAP are selected as candidate patterns in a self-adaptive mode according to a set error probability threshold, then, the compensation of channel attenuation is carried out on a receiving vector, and QAM/PSK symbols corresponding to each candidate MAP state are recovered based on a signal Euclidean distance. And finally, jointly detecting each candidate MAP mode and the corresponding QAM/PSK symbol. Simulation results show that the ASVD-DOD detection algorithm reduces the search space and reduces the detection complexity of a receiving end in the allowable range of system performance loss.
The method specifically comprises the following steps:
1) the GSM-MBM system has NtRoot transmitting antenna, NrRoot receiving antenna, activating N per time slotaA transmitting antenna. Each antenna has m aroundrfAnd an RF mirror which is controlled to be turned on or off by an input bit '1' or '0', respectively, thereby disturbing a transmission environment near the transmitting antenna to randomize a radio channel, thereby changing the entire transmission path. Thus, for one antenna, there may be m nearbyrfRF mirror generation
Figure BDA0001796963490000021
The channel state is different from mrfOne switching state in which an information bit controls an RF mirror is called "mirror activation pattern" (MAP). As can be seen from fig. 1, the information bits are transmitted in three ways: a) from NtSelecting N from transmitting antennasaIs used for transmission
Figure BDA0001796963490000022
Information wherein
Figure BDA0001796963490000023
Represents from NtActivating N in one transmitting antennaaNumber of combinations of units, 1. ltoreq. Na＜Nt，
Figure BDA0001796963490000024
Meaning that the rounding is done down,
Figure BDA0001796963490000025
representing a binomial coefficient; b) m in each active transmit antennarfThe on/off state of the RF mirror is defined by mrfbit information bit control, N can be transmitted altogetheramrfbits information; c) each active transmit antenna transmits a modulation symbol (M-ary QAM or PSK) for a total transmission of Nalog2Mbits information. After the transmitted vector passes through the Rayleigh channel, the information received by the receiving end is
y＝Hx+n(1)
Wherein the content of the first and second substances,
Figure BDA0001796963490000026
is the reception of the vector or vectors,
Figure BDA0001796963490000027
is a matrix of the channels and is,
Figure BDA0001796963490000028
is a Gaussian noise matrix whose elements obey a mean of 0 and a variance of σ2Complex gaussian distribution of (a);
Figure BDA0001796963490000029
the transmit vector generated for the GSM-MBM modulation end is generally in the form of
Figure BDA00017969634900000210
Wherein s isi,sjE.s denotes the MPSK modulation symbol, and Si,sjThe position m, N in the x vector is related to the position of the activated antenna, and respectively represents that the m and N antennas are activated, wherein m is more than or equal to 1 and less than or equal to Nt，1≤n≤Nt(ii) a l and k respectively represent that the m and N antennas respectively activate the l and k MAPs, and l is more than or equal to 1 and less than or equal to Nm，1≤k≤Nm(ii) a The number of non-zero symbols in the x vector is Na。
2) The channel matrix H of the GSM-MBM system is expressed as
Figure BDA00017969634900000211
Figure BDA00017969634900000212
Denotes the channel matrix from the jth transmit antenna to the receive antenna, where j e {1,2, …, Nt}. Dividing x into NtGroups of vectors x per groupjWith NmAnd (4) each element. The receive vector for the jth transmit antenna may be expressed as:
yj＝Hjxj+nj (3)
the receive vector under the GSM-MBM system can be expressed as:
Figure BDA0001796963490000031
it is assumed that at a certain time slot, the set of active transmit antenna sequences is denoted Γ1The remaining inactive transmit antenna sequences are denoted as Γ2Wherein r is1,Γ2Are all subsets of Ω, {1,2, …, Nt}. When j ∈ Γ1，yj＝Hjxj+nj(ii) a When j ∈ Γ2，yj＝nj. And then have
wj＝norm(yj) (5)
By pair yjNorm value w ofjIn descending order, first NaThe index value j corresponding to the value is the activated transmitting antenna serial number.
3) For the jth transmitting antenna, m is near each transmitting antennarfAn RF mirror capable of creating NmWith MAP mode, the channel matrix for the jth antenna can be expressed as
Figure BDA0001796963490000032
Figure BDA0001796963490000033
Represents HjThe kth column of the matrix, i.e., the kth MAP state for the jth transmit antenna. Since the jth transmit antenna is driven from N onlymIf one of the MAP patterns is selected, the formula (1) can be written as
Figure BDA0001796963490000034
Wherein
Figure BDA0001796963490000035
Means that the k-th transmitting antenna is activatedMAP transmitted modulation symbols.
For each active transmit antenna, a corresponding MAP index value is detected using the SVD algorithm. The basic idea is that under noise neglect conditions the received vector has the property of coinciding with the direction of the active channel vector, whereas under noise considerations the direction of the received vector is also in the vicinity of the direction of the active channel vector. For this, the following formula can be used
msvd＝arg maxG(k),k∈{1,2,…,Nm} (7)
Wherein
Figure BDA0001796963490000036
To represent
Figure BDA0001796963490000037
And yjCorrelation between msvdNamely, the activated MAP state index value detected by the SVD algorithm.
However, when the channel condition is poor and the signal-to-noise ratio is low, the performance of the detection algorithm is poor, and therefore an improved SVD (singular value decomposition) detection algorithm, namely an ASVD (automatic sequence decomposition) algorithm, is provided.
Assuming that the kth MAP is activated, for any k ≠ msvdDefinition of
Figure BDA0001796963490000038
Then
Figure BDA0001796963490000039
Has a probability of occurrence of
Figure BDA00017969634900000310
Wherein the content of the first and second substances,
Figure BDA00017969634900000311
p is the signal-to-noise ratio,
Figure BDA00017969634900000312
Figure BDA00017969634900000313
description of the invention
Figure BDA00017969634900000314
And
Figure BDA00017969634900000315
the square of the correlation coefficient between. Setting a probability threshold value P for PthFor any k ≠ msvdWhen is coming into contact with
Figure BDA0001796963490000041
Not less than PthWhen we regard the kth MAP as a candidate MAP, then
Figure BDA0001796963490000042
Therein, ζth＝Q-1(Pth) The above formula can be obtained by finishing
Figure BDA0001796963490000043
Can be obtained from the above formula
Figure BDA0001796963490000044
Figure BDA0001796963490000045
Then the MAP candidate set LasvdComprising msvdAnd an index value of the MAP state satisfying equations (11) and (12).
The modulation symbols are detected by using a DOD detection algorithm, which is a sequence detection method based on the Euclidean distance of signals. First, the received vector is compensated for channel attenuation, i.e. the received signal yjLeft ride
Figure BDA0001796963490000046
Obtaining an estimated value of a modulation symbol corresponding to the candidate MAP, and then demodulating the estimated symbol obtained by calculation, i.e. finding a modulation constellation point closest to the actual transmission symbol, as shown in the following formula
Figure BDA0001796963490000047
Wherein the content of the first and second substances,
Figure BDA0001796963490000048
d (-) denotes demodulation; then from LasvdThe candidate MAP pattern finds the optimal MAP index value using equation (14)
Figure BDA0001796963490000049
Wherein the content of the first and second substances,
Figure BDA00017969634900000410
MAP index activated for jth transmit antenna.
The invention has the advantages and beneficial effects that:
the invention provides a new detection method based on a GSM-MBM system, the error code performance of the method is similar to that of an ML algorithm, but the calculation complexity of the method is at least reduced by 90 percent compared with that of the ML algorithm, and the method has excellent theoretical and practical significance.
Drawings
FIG. 1 is a block diagram of a transmitting end of a GSM-MBM system;
FIG. 2 is a schematic diagram showing comparison of BER performance of the ASVD-DOD detection method proposed by the present invention with conventional ML algorithm and SVD-DOD algorithm under different modulation orders, wherein the SVD-DOD algorithm refers to a combination of SVD algorithm (corresponding to equation (7)) and DOD algorithm;
FIG. 3 is Nt＝4,Nr＝4,Na＝2,NmThe complexity contrast diagram of an ASVD-DOD algorithm, an ML algorithm and an SVD-DOD algorithm under different modulation orders is 8;
FIG. 4 is Nt＝4,Nr＝4,NaAnd when M is 16, the complexity of the ASVD-DOD algorithm, the ML algorithm and the SVD-DOD algorithm under different MAP numbers is shown in a schematic diagram.
Detailed Description
The invention adopts a low-complexity detection method (ASVD-DOD) of a GSM-MBM system, which comprises the following steps: firstly, an activated antenna sequence set is obtained by utilizing a sorting method, then, for each transmitting antenna in the set, a plurality of MAP are selected as candidate patterns in a self-adaptive mode according to a set error probability threshold, then, the compensation of channel attenuation is carried out on a receiving vector, and QAM/PSK symbols corresponding to each candidate MAP state are recovered based on a signal Euclidean distance. And finally, jointly detecting each candidate MAP mode and the corresponding QAM/PSK symbol.
1) The GSM-MBM system has NtRoot transmitting antenna, NrA plurality of receiving antennas each having m aroundrfAn RF mirror, each time slot activating NaAnd the root transmitting antenna adopts M-ary PSK modulation. The receiving matrix is
y＝Hx+n (1)
Wherein the content of the first and second substances,
Figure BDA0001796963490000051
is the reception of the vector or vectors,
Figure BDA0001796963490000052
is a matrix of the channels and is,
Figure BDA0001796963490000053
is a Gaussian noise matrix whose elements obey a mean of 0 and a variance of σ2Complex gaussian distribution.
Figure BDA0001796963490000054
The transmit vector generated for the GSM-MBM modulation end is generally in the form of
Figure BDA0001796963490000055
Wherein s isi,sjE.s denotes the MPSK modulation symbol, and Si,sjThe position m, N in the x vector is related to the position of the activated antenna, and respectively represents that the m and N antennas are activated, wherein m is more than or equal to 1 and less than or equal to Nt，1≤n≤Nt(ii) a l and k respectively represent that the m and N antennas respectively activate the l and k MAPs, and l is more than or equal to 1 and less than or equal to Nm，1≤k≤Nm(ii) a The number of non-zero symbols in the x vector is Na。
2) The channel matrix H of the GSM-MBM system can be expressed as
Figure BDA0001796963490000056
Figure BDA0001796963490000057
Denotes the channel matrix from the jth transmit antenna to the receive antenna, where j e {1,2, …, Nt}. Dividing x into NtGroups of vectors x per groupjWith NmAnd (4) each element. The receive vector for the jth transmit antenna may be expressed as:
yj＝Hjxj+nj (3)
the receive vector under the GSM-MBM system can be expressed as:
Figure BDA0001796963490000058
it is assumed that at a certain time slot, the set of active transmit antenna sequences is denoted Γ1The remaining inactive transmit antenna sequences are denoted as Γ2Wherein r is1,Γ2Are all subsets of Ω, {1,2, …, Nt}. When j ∈ Γ1，yj＝Hjxj+nj(ii) a When j ∈ Γ2，yj＝nj. And then have
wj＝norm(yj) (5)
By pair yjNorm value w ofjIn descending order, first NaThe index value j corresponding to the value is the activated transmitting antenna serial number.
3) For the jth transmitting antenna, m is near each transmitting antennarfAn RF mirror capable of creating NmWith MAP mode, the channel matrix for the jth antenna can be expressed as
Figure BDA0001796963490000061
Figure BDA0001796963490000062
Represents HjThe kth column of the matrix, i.e., the kth MAP state for the jth transmit antenna. Since the jth transmit antenna is driven from N onlymIf one of the MAP patterns is selected, the formula (1) can be written as
Figure BDA0001796963490000063
Wherein
Figure BDA0001796963490000064
Indicating the modulation symbol transmitted by the kth MAP activated via the jth transmit antenna.
For each active transmit antenna, a corresponding MAP index value is detected using the SVD algorithm. The basic idea is that under noise neglect conditions the received vector has the property of coinciding with the direction of the active channel vector, whereas under noise considerations the direction of the received vector is also in the vicinity of the direction of the active channel vector. For this, the following formula can be used
msvd＝arg maxG(k),k∈{1,2,…,Nm} (7)
Wherein
Figure BDA0001796963490000065
To represent
Figure BDA0001796963490000066
And yjCorrelation between msvdI.e. detected by SVD algorithmThe MAP state index value is activated.
However, when the channel condition is poor and the signal-to-noise ratio is low, the performance of the detection algorithm is poor, and therefore an improved SVD (singular value decomposition) detection algorithm, namely an ASVD (automatic sequence decomposition) algorithm, is provided.
Assuming that the kth MAP is activated, for any k ≠ msvdDefinition of
Figure BDA0001796963490000067
Then
Figure BDA0001796963490000068
Has a probability of occurrence of
Figure BDA0001796963490000069
Wherein the content of the first and second substances,
Figure BDA00017969634900000610
p is the signal-to-noise ratio,
Figure BDA00017969634900000611
Figure BDA00017969634900000612
description of the invention
Figure BDA00017969634900000613
And
Figure BDA00017969634900000614
the square of the correlation coefficient between. Setting a probability threshold value P for PthFor any k ≠ msvdWhen is coming into contact with
Figure BDA00017969634900000615
Not less than PthWhen we regard the kth MAP as a candidate MAP, then
Figure BDA0001796963490000071
Therein, ζth＝Q-1(Pth) The above formula can be obtained by finishing
Figure BDA0001796963490000072
Can be obtained from the above formula
Figure BDA0001796963490000073
Figure BDA0001796963490000074
Then the MAP candidate set LasvdComprising msvdAnd an index value of the MAP state satisfying equations (11) and (12).
The modulation symbols are detected by using a DOD detection algorithm, which is a sequence detection method based on the Euclidean distance of signals. First, the received vector is compensated for channel attenuation, i.e. the received signal yjLeft ride
Figure BDA0001796963490000075
Obtaining an estimated value of a modulation symbol corresponding to the candidate MAP, and then demodulating the estimated symbol obtained by calculation, i.e. finding a modulation constellation point closest to the actual transmission symbol, as shown in the following formula
Figure BDA0001796963490000076
Wherein the content of the first and second substances,
Figure BDA0001796963490000077
d (-) denotes demodulation; then from LasvdThe candidate MAP pattern finds the optimal MAP index value using equation (14)
Figure BDA0001796963490000078
Wherein the content of the first and second substances,
Figure BDA0001796963490000079
MAP index activated for jth transmit antenna.
Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As can be seen from fig. 2, the error rate performance of the ASVD-DOD algorithm is better than that of the SVD-DOD algorithm and is similar to the ML algorithm, and the performance of the low-order modulation mode is better than that of the high-order modulation mode. The ASVD-DOD algorithm can self-adaptively select candidate MAP activation state index values according to the change of a channel environment, so that the performance of the ASVD-DOD algorithm is close to that of the ML algorithm, the SVD-DOD algorithm can only select one MAP activation state value, the performance is lost in detection, and the anti-interference capability of a low-order modulation mode is due to high-order modulation.
Fig. 3 shows the computational complexity of three detection algorithms, when 4 transmitting antennas, 4 receiving antennas, 2 active antennas, and 8 mirror activation modes are used. As can be seen from the figure, the computational complexity of maximum likelihood detection is higher with the modulation order. The ASVD algorithm and the SVD algorithm adopt estimation detection of modulation symbols, so that the complexity is irrelevant to the modulation order.
Fig. 4 shows the computation complexity of three detection algorithms when there are 4 transmitting antennas, 4 receiving antennas, 2 active antennas, and a modulation scheme of 16 PSK. As is clear from the figure, the complexity of the ML algorithm increases from 10 as the number of MAPs increases5Sharply increased to 3 x 107This is because the search space of the ML algorithm grows exponentially with the number of MAPs. And the complexity of the ASVD-DOD and SVD-DOD algorithms is linearly increased along with the number of the MAP.
Table 1 shows a comparison table of the low complexity detection method ASVD-DOD algorithm of the GSM-MSB system, the ML algorithm and the SVD-DOD algorithm;
TABLE 1 complexity analysis Table
Figure BDA0001796963490000081
While the present invention has been described in detail with reference to the specific embodiments thereof, the present invention is not limited to the above-described embodiments, and various modifications or alterations can be made by those skilled in the art without departing from the spirit and scope of the claims of the present application.

Claims (1)

1. A low-complexity detection method of a GSM-MBM system is characterized by comprising the following steps:
firstly, an activated antenna sequence set is obtained by using a sorting method, then, for each transmitting antenna in the set, a plurality of MAPs are selected as candidate patterns in a self-adaptive manner according to a set error probability threshold, then, compensation of channel attenuation is carried out on a receiving vector, QAM/PSK symbols corresponding to each candidate MAP state are recovered based on a signal Euclidean distance, and finally, each candidate MAP pattern and the corresponding QAM/PSK symbols are jointly detected;
the method comprises the following specific steps:
1) the GSM-MBM system has NtRoot transmitting antenna, NrA plurality of receiving antennas each having m aroundrfAn RF mirror for generating
Figure FDA0002939359950000011
Channel state, N is activated per time slotaRoot transmitting antenna, adopting M-ary PSK modulation;
the receiving matrix is
y＝Hx+n (1)
Wherein the content of the first and second substances,
Figure FDA0002939359950000012
is the reception of the vector or vectors,
Figure FDA0002939359950000013
is a matrix of the channels and is,
Figure FDA0002939359950000014
is a Gaussian noise matrix whose elements obey a mean of 0 and a variance of σ2Complex gaussian distribution of (a);
Figure FDA0002939359950000015
the transmit vector generated for the GSM-MBM modulation end is generally in the form of
Figure FDA0002939359950000016
Wherein s isi,sjE.s denotes the MPSK modulation symbol, and Si,sjThe position m, N in the x vector is related to the position of the activated antenna, and respectively represents that the m and N antennas are activated, wherein m is more than or equal to 1 and less than or equal to Nt，1≤n≤Nt(ii) a l and k respectively represent that the m and N antennas respectively activate the l and k MAPs, and l is more than or equal to 1 and less than or equal to Nm，1≤k≤Nm(ii) a The number of non-zero symbols in the x vector is Na；
2) The channel matrix H of the GSM-MBM system is expressed as
Figure FDA0002939359950000017
Figure FDA0002939359950000018
Denotes the channel matrix from the jth transmit antenna to the receive antenna, where j e {1,2, …, NtDivide x into NtGroups of vectors x per groupjWith NmThe element, the receive vector for the jth transmit antenna, may be expressed as:
yj＝Hjxj+nj (3)
the receive vector under the GSM-MBM system can be expressed as:
Figure FDA0002939359950000019
it is assumed that at a certain time slot, the set of active transmit antenna sequences is denoted Γ1The remaining inactive transmit antenna sequences are denoted as Γ2Wherein r is1,Γ2Are all subsets of Ω, {1,2, …, NtWhen j is equal to gamma1，yj＝Hjxj+nj(ii) a When j ∈ Γ2，yj＝njAnd then have
wj＝norm(yj) (5)
By pair yjNorm value w ofjIn descending order, first NaThe index value j corresponding to the value is the activated transmitting antenna serial number;
3) for the jth transmitting antenna, m is near each transmitting antennarfAn RF mirror capable of creating NmWith MAP mode, the channel matrix for the jth antenna can be expressed as
Figure FDA0002939359950000021
Figure FDA0002939359950000022
Represents HjKth column of matrix, kth MAP state for jth transmit antenna, since jth transmit antenna is from N onlymIf one of the MAP patterns is selected, the formula (1) can be written as
Figure FDA0002939359950000023
Wherein
Figure FDA0002939359950000024
Represents a modulation symbol transmitted by activating the kth MAP via the jth transmit antenna;
for each active transmit antenna, the corresponding MAP index value is detected by the SVD algorithm, which is expressed by the following formula
msvd＝argmaxG(k),k∈{1,2,…,Nm} (7)
Wherein
Figure FDA0002939359950000025
To represent
Figure FDA0002939359950000026
And yjCorrelation between msvdThe index value is the activated MAP state index value detected by adopting SVD algorithm;
assuming that the kth MAP is activated, for any k ≠ msvdDefinition of
Figure FDA0002939359950000027
Then
Figure FDA0002939359950000028
Has a probability of occurrence of
Figure FDA0002939359950000029
Wherein the content of the first and second substances,
Figure FDA00029393599500000210
p is the signal-to-noise ratio,
Figure FDA00029393599500000211
Figure FDA00029393599500000212
description of the invention
Figure FDA00029393599500000213
And
Figure FDA00029393599500000214
the square of the correlation coefficient between the two is set as a probability threshold value PthFor any k ≠ msvdWhen is coming into contact with
Figure FDA00029393599500000215
Not less than PthWhen the kth MAP is considered as a candidate MAP, the kth MAP is considered as a candidate MAP
Figure FDA00029393599500000216
Therein, ζth＝Q-1(Pth) The above formula can be obtained by finishing
Figure FDA00029393599500000217
Can be obtained from the above formula
Figure FDA00029393599500000218
Figure FDA0002939359950000031
Then the MAP candidate set LasvdComprising msvdAnd an index value of the MAP state satisfying equations (11) and (12);
4) the modulation symbols are detected by using a DOD detection algorithm, and firstly, the received vector is compensated for channel attenuation, namely, the received signal yjLeft ride
Figure FDA0002939359950000032
Obtaining an estimated value of a modulation symbol corresponding to the candidate MAP, and then demodulating the estimated symbol obtained by calculation, i.e. finding a modulation constellation point closest to the actual transmission symbol, as shown in the following formula
Figure FDA0002939359950000033
Wherein the content of the first and second substances,
Figure FDA0002939359950000034
d (-) denotes demodulation; then from LasvdThe candidate MAP pattern finds the optimal MAP index value using equation (14)
Figure FDA0002939359950000035
Wherein the content of the first and second substances,
Figure FDA0002939359950000036
MAP index activated for jth transmit antenna.
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