CN112104520B - ZF-OSIC optimization detection sequence method and system based on channel estimation error - Google Patents

ZF-OSIC optimization detection sequence method and system based on channel estimation error Download PDF

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CN112104520B
CN112104520B CN202010838277.7A CN202010838277A CN112104520B CN 112104520 B CN112104520 B CN 112104520B CN 202010838277 A CN202010838277 A CN 202010838277A CN 112104520 B CN112104520 B CN 112104520B
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孙伟
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Nanjing Nise Electronic Technology Co ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L43/00—Arrangements for monitoring or testing data switching networks
    • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
    • H04L43/0823—Errors, e.g. transmission errors
    • H04L43/0847—Transmission error
    • 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
    • H04L1/12—Arrangements for detecting or preventing errors in the information received by using return channel
    • H04L1/16—Arrangements for detecting or preventing errors in the information received by using return channel in which the return channel carries supervisory signals, e.g. repetition request signals
    • H04L1/18—Automatic repetition systems, e.g. Van Duuren systems
    • H04L1/1812—Hybrid protocols; Hybrid automatic repeat request [HARQ]

Abstract

The invention discloses a ZF-OSIC (zero frequency offset-open circuit integrated circuit) optimization detection sequence method and system based on channel estimation errors, in particular to an algorithm for optimizing the ZF-OSIC detection sequence under the condition of channel estimation errors and related MIMO (multiple input multiple output) channels. The ZF-OSIC optimization detection sequence method based on the channel estimation error considers an effective signal detection sequence, predicts the bit error rate of each stream according to the posterior signal-to-interference-and-noise ratio of each stream by using a BER closed expression obtained by ZF performance analysis, then performs sequencing according to the bit error rate, takes a signal with a small bit error rate as a signal for preferential detection, greatly reduces the error propagation phenomenon generated by a sequencing serial interference elimination method based on ZF and MMSE, and can also achieve the purpose of improving the detection sequence through the application of a retransmission scene.

Description

ZF-OSIC (zero frequency offset-open frequency integration) optimization detection sequence method and system based on channel estimation error
Technical Field
The invention relates to a ZF-OSIC (zero frequency offset-open circuit integrated circuit) optimization detection sequence method and system based on channel estimation errors, in particular to an algorithm for optimizing the ZF-OSIC detection sequence under the existence of channel estimation errors and relevant MIMO (multiple input multiple output) channels, and belongs to the technical field of communication.
Background
The MIMO system obviously improves the spectrum efficiency of the system by sending mutually independent data streams on different antennas, and a receiving end can detect the MIMO signal in a linear or nonlinear mode. The existing performance detection mode presents the current situation that the complexity is high under the conditions of increasing the number of transmitting antennas and high-order modulation, or the complexity is still in direct proportion to the exponential power of the transmitting antennas and the modulation mode, and the complexity of MIMO detection is greatly reduced by a single MMSE receiver at the cost of sacrificing the system performance, so that the performance requirement in actual detection cannot be met.
Disclosure of Invention
The purpose of the invention is as follows: the ZF-OSIC optimization detection sequence method based on the channel estimation error is mainly an algorithm for optimizing the ZF-OSIC detection sequence under the condition of the existence of the channel estimation error and a related MIMO channel, solves the problems in the prior art, reduces the complexity, further improves the detection performance, and popularizes the algorithm to the scene with HARQ retransmission.
The technical scheme is as follows: a ZF-OSIC optimization detection sequence method based on channel estimation errors is characterized by comprising the following steps:
the method comprises the following steps: acquiring a receiving signal through a receiving antenna;
step two: according to actual requirements, modeling and estimating a channel gain matrix under a non-ideal channel;
step three: acquiring a BER closed expression by using a ZF-OSIC detection sequential receiver according to the posterior signal-to-interference-and-noise ratio of each stream and predicting the bit error rate of each stream;
step four: and sequencing according to the bit error rate, and taking the signal with the small bit error rate as a priority detection signal.
In a further embodiment, the first step is further: the received signal is used in MIMO system, and the transmitting antenna and the receiving antenna are respectively Nt、NrAnd when the number of the transmitting antennas is less than or equal to that of the receiving antennas, the obtained receiving signals are as follows:
y＝Hs+n
wherein the channel matrix involved is
Figure GDA0003530138350000011
RtFor transmitting the correlation matrix, HwIs N subject to independent distribution and having a mean of 0 and a variance of 1r×NtS is a symbol vector transmitted by the transmitting antenna, has a mean value of 0 and
Figure GDA0003530138350000021
n is obedient mean 0 and variance N0A complex gaussian distributed noise vector of (a);
in order to reduce noise interference, the proportion of signal to noise is divided, and the signal to noise ratio is further defined as
(SNR)γ0＝Es/N0
When the signal receiving end knows the complete channel quality information, the estimated signal detected by using ZF is as follows, wherein
Figure GDA0003530138350000022
Represents the pseudo-inverse operation:
Figure GDA0003530138350000023
in a further embodiment, the second step is further: performing channel estimation according to the pilot signals acquired in the first step, and when estimating and calculating the channel gain matrix H, the modeling estimation formula is as follows:
Figure GDA0003530138350000024
wherein e Ω is a channel estimation error irrelevant to H, Ω is a complex gaussian distribution obeying an independent distribution with a mean value of 0 and a variance of 1, and e is a real number for measuring a channel estimation preparation degree;
the estimation signal detected by ZF under the condition of channel estimation error is as follows:
Figure GDA0003530138350000025
in a further embodiment, the third step is further: the expression of the posterior signal-to-interference-and-noise ratio of the kth sending data flow ZF detection in the presence of channel estimation is as follows:
Figure GDA0003530138350000026
wherein [ (H)HH)-1]kkIs represented by (H)HH)-1The kth row and the kth column of elements of (1) will
Figure GDA0003530138350000027
Substituting the formula into the formula, the expression of the posterior signal-to-interference-and-noise ratio of the kth sending data stream under the condition of channel correlation and channel estimation error can be obtained:
Figure GDA0003530138350000028
in the above formula λkIs (R)t)-1The k-th diagonal element of (a),
Figure GDA0003530138350000029
has a value of
Figure GDA00035301383500000210
1/[(HHH)-1]kkTo comply with the degree of freedom of 2 (N)r-Nt+1) chi-square distribution, yielding compliance by combining the equations set forth above
Figure GDA00035301383500000211
Figure GDA00035301383500000212
Gamma distribution SINR ofkThe probability density function of (a) is then written as:
Figure GDA00035301383500000213
for the M-PSK modulation mode, the BER expression under AWGN channel is as follows:
Figure GDA00035301383500000214
for the M-QAM modulation mode, the BER expression under an AWGN channel is as follows:
Figure GDA0003530138350000031
wherein
Figure GDA0003530138350000032
According to SINRkCan be found by integrating the distribution of (c):
Figure GDA0003530138350000033
wherein the content of the first and second substances,
Figure GDA0003530138350000034
D＝Nr-Ntand further obtain BERMQAMThe expression of (a) is as follows:
Figure GDA0003530138350000035
the parameter mu contained thereiniIs composed of
Figure GDA0003530138350000036
M is the order of modulation;
in a retransmission scene, the retransmission mode is an HARQ-CC mode, a receiving end adopts a Maximum Ratio Combining (MRC) mode for receiving, and if the retransmission times are N-1 times, according to the property of gamma distribution, the signal-to-interference-and-noise ratio after retransmission and combination obeys
Figure GDA0003530138350000037
According to the combination of a BER expression under an AWGN channel under an M-PSK modulation mode and a BER expression under an AWGN channel under an M-QAM modulation mode, given that ZF detection performances of M-PSK and M-QAM modulation under the same conditions of a transmitting antenna and a receiving antenna are as follows:
Figure GDA0003530138350000038
Figure GDA0003530138350000039
Figure GDA0003530138350000041
and the receiver optimizing the ZF-OSIC detection sequence predicts the error rate of each stream according to the posterior signal-interference-noise ratio of each stream by using a BER closed expression obtained by ZF performance analysis, then performs sequencing according to the error rate, and reduces the phenomenon of error propagation to the maximum extent by detecting a signal with a small error rate.
Has the advantages that: the invention relates to a ZF-OSIC (zero frequency offset-minimum interference-plus-interference) optimization detection sequence method and a system based on channel estimation errors, in particular to a method for optimizing the ZF-OSIC detection sequence under the existence of channel estimation errors and related MIMO (multiple input multiple output) channels, which considers an effective signal detection sequence, predicts the error rate of each stream according to the posterior signal-to-interference-plus-noise ratio of each stream by using a BER closed expression obtained by ZF performance analysis, sorts the streams according to the error rate, uses a signal with a small error rate as a signal for preferential detection, greatly reduces the error propagation phenomenon generated by a sorting serial interference elimination method based on ZF and MMSE (minimum error rate error) and can also achieve the purpose of improving the detection sequence by applying a retransmission scene.
Drawings
FIG. 1 is a block diagram of the steps of the present invention.
Fig. 2 is a graph of simulated and theoretical BER performance of a QPSK modulated MIMO ZF receiver of the present invention.
Fig. 3, 4 influence of channel estimation error, correlation and modulation level on the detection order.
Fig. 5 shows the effect of modulation order on ZF-OSIC detection order in the presence of both channel estimation error and correlation.
Fig. 6 is a diagram of the effect of retransmissions on the ZF-OSIC detection order.
Fig. 7 is a comparison diagram of the impact of retransmission on the ZF-OSIC detection order when the codeword transmission condition is BPSK.
Detailed Description
In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the present invention. It will be apparent, however, to one skilled in the art, that the present invention may be practiced without one or more of these specific details. In other instances, well-known features have not been described in order to avoid obscuring the invention.
Including the following explanation of characters: hw: n subject to independent distribution with mean 0 and variance 1r×NtA complex Gaussian matrix of,
Figure GDA0003530138350000043
Stands for pseudo-inverse operation, e Ω: h-uncorrelated channel estimation error, f (SINR)k): probability density function, Nt: transmitting antenna, Nr: receiving antenna, gamma0: signal-to-noise ratio, y: received signal, Rt: transmit correlation matrix, M: order of modulation,
Figure GDA0003530138350000042
Estimated signal, [ (H) detected in ZFHH)-1]kk：(HHH)-1K row and k column element of (1), lambdak：(Rt)-1The kth diagonal element of (1).
A ZF-OSIC optimization detection sequence method based on channel estimation errors comprises the following steps:
the method comprises the following steps: acquiring a receiving signal through a receiving antenna;
deducing that the transmitting antenna and the receiving antenna are respectively N in the MIMO system through a signal receiving formula of y ═ Hs + Nt、NrObtaining the value of the received signal, wherein the channel matrix involved is
Figure GDA0003530138350000051
RtFor transmitting the correlation matrix, HwIs N subject to independent distribution and having a mean of 0 and a variance of 1r×NtS is a symbol vector transmitted by the transmitting antenna, has a mean value of 0 and
Figure GDA0003530138350000052
n is obedience 0 and variance N0A complex gaussian distributed noise vector of (a); meanwhile, in order to reduce noise interference, the proportion of the signal to the generated noise is divided, and the signal to noise ratio (SNR) of the signal to noise is further defined as gamma0＝Es/N0(ii) a When the signal receiving end knows the complete channel quality information, the estimated signal detected by ZF is as follows, that is
Figure GDA0003530138350000053
Wherein
Figure GDA0003530138350000054
Representing a pseudo-inverse operation.
Step two: modeling and estimating a channel gain matrix according to actual requirements;
by using
Figure GDA0003530138350000055
Performing channel estimation on the pilot signal acquired in the first step, wherein e Ω is a channel estimation error irrelevant to H, Ω is a complex Gaussian distribution obeying independent distribution with a mean value of 0 and a variance of 1, and e is a real number for measuring the preparation degree of channel estimation; the estimation signal detected by ZF under the condition of channel estimation error is as follows:
Figure GDA0003530138350000056
step three: analyzing and verifying detection performance, predicting the bit error rate of each stream by using a BER closed expression obtained by ZF performance analysis according to the posterior signal-to-interference-and-noise ratio of each stream, and then sequencing according to the bit error rate, thereby optimizing the detection sequence;
the expression of the posterior signal-to-interference-and-noise ratio of the kth sending data flow ZF detection in the presence of channel estimation is as follows:
Figure GDA0003530138350000057
wherein [ (H)HH)-1]kkIs represented by (H)HH)-1The kth row and the kth column of elements of (1) will
Figure GDA0003530138350000058
Substituting the formula into the formula, the expression of the posterior signal-to-interference-and-noise ratio of the kth sending data stream under the condition of channel correlation and channel estimation error can be obtained:
Figure GDA0003530138350000059
in the above formula λkIs (R)t)-1The k-th diagonal element of (a),
Figure GDA00035301383500000510
has a value of
Figure GDA00035301383500000511
1/[(HHH)-1]kkTo comply with the degree of freedom of 2 (N)r-Nt+1) and the following equation is obtained by combining the above-mentioned formulas
Figure GDA00035301383500000512
Figure GDA00035301383500000513
Gamma distribution SINR ofkThe probability density function of (d) is then written as:
Figure GDA0003530138350000061
for the M-PSK modulation mode, the BER expression under AWGN channel is as follows:
Figure GDA0003530138350000062
for the M-QAM modulation mode, the BER expression under an AWGN channel is as follows:
Figure GDA0003530138350000063
wherein
Figure GDA0003530138350000064
According to SINRkCan be found by integrating the distribution of (c):
Figure GDA0003530138350000065
wherein the content of the first and second substances,
Figure GDA0003530138350000066
D＝Nr-Ntm is the order of modulation, thereby obtaining BERMQAMThe expression of (a) is as follows:
Figure GDA0003530138350000067
the parameter mu contained thereiniIs composed of
Figure GDA0003530138350000068
M is the order of modulation;
and the receiver optimizing the ZF-OSIC detection sequence predicts the error rate of each stream by using a BER closed expression obtained by ZF performance analysis according to the posterior signal-to-interference-and-noise ratio of each stream, then performs sequencing according to the error rate, and reduces the phenomenon of error propagation to the maximum extent by detecting a signal with a small error rate.
As shown in fig. 1, the BER performance simulated by using monte carlo under different channel estimation error coefficients and correlation coefficients is compared with the BER performance analyzed theoretically, and it can be seen from the figure that although the channel correlation may affect the BER performance, the effect is not as serious as the effect caused by channel estimation errors, and the channel estimation errors may cause the BER performance to be leveled incorrectly. System performance is further degraded when both channel estimation errors and channel correlation are present. It can also be seen from the figure that the theoretical value of BER performance analysis given by us is consistent with MC simulation, which proves the correctness of the closed expression of BER given by the present invention.
In a retransmission scene, the retransmission mode is an HARQ-CC mode, a receiving end adopts a Maximum Ratio Combining (MRC) mode for receiving, and if the retransmission times are N-1 times, according to the property of gamma distribution, the signal-to-interference-and-noise ratio after retransmission and combination obeys
Figure GDA0003530138350000071
According to the combination of the BER expression under AWGN channel under M-PSK modulation mode and the BER expression under AWGN channel under M-QAM modulation mode, given that M-PSK and receiving antenna are identicalThe ZF detection performance of M-QAM modulation is as follows:
Figure GDA0003530138350000072
Figure GDA0003530138350000073
fig. 2 and 3 are performance simulation curves of a conventional MIMO receiver with 4 × 4 antennas and a receiver according to the present invention. The modulation modes of the four streams are QPSK, 16QAM and ZF-OSIC detection of BPSK, 16QAM and 16 QAM. The BER performance curves of the traditional ZF-OSIC detection which does not contain the line representation of the five-star pattern under different channel estimation errors and different channel correlation coefficients and the proposed ZF-OSIC detection which contains the line representation of the five-star pattern are shown in the figure. It can be seen from the figure that both channel information imperfections and channel imperfections, which affect the ZF-OSIC detection performance more than the channel imperfections, and which may suffer from false floor. The performance of the algorithm for optimizing the ZF-OSIC detection sequence by predicting the performance of ZF detection is obviously superior to that of the traditional ZF-OSIC detection, particularly under the condition that a channel estimation error coefficient or a channel correlation coefficient is small.
Based on the scheme, a system with a channel estimation error optimization detection sequence can be constructed, and the system comprises the following modules:
first module for acquiring a received signal, in which module the number of transmit and receive antennas, respectively N, in a MIMO system is taken into accountt、NrAnd N ist≤NrWhen the receiving end knows the complete channel quality information, the estimated signal detected by ZF is Hs + n
Figure GDA0003530138350000074
A second module for modeling estimation of the channel gain matrix according to the actual demand, forFor channel estimation in a real system, the estimated value is modeled as
Figure GDA0003530138350000081
The estimated signal detected by ZF in the presence of channel estimation error is:
Figure GDA0003530138350000082
a third module for analyzing and verifying the detection performance, which passes the posterior SINR of the kth sending data stream under the condition of channel correlation and channel estimation errork、SINRkProbability density function f (SINR)k) Analyzing the detection performance of ZF aiming at the M-PSK modulation mode and the error rate under an AWGN channel; optimizing the ZF-OSIC detection sequence, namely predicting the bit error rate of each stream by using a BER closed expression obtained by ZF performance analysis according to the posterior signal-to-interference-and-noise ratio of each stream, then sequencing according to the bit error rate, detecting a signal with a small bit error rate, and reducing the error propagation phenomenon.
The fourth module is used for popularizing the application to a scene with HARQ retransmission, the module adopts a maximum ratio combining mode to receive at a receiving end under an HARQ-CC mode, when the retransmission times are N-1 times, and the quantity of transmitting antennas and receiving antennas is the same, the ZF detection performance of M-PSK and M-QAM modulation is as follows:
Figure GDA0003530138350000083
Figure GDA0003530138350000084
the invention discloses a ZF-OSIC (zero frequency offset-minimum interference-plus-minimum) optimization detection sequence method based on channel estimation errors, and further relates to an algorithm for optimizing the ZF-OSIC detection sequence under the existence of channel estimation errors and related MIMO (multiple input multiple output) channels.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A ZF-OSIC optimization detection sequence method based on channel estimation errors is characterized by comprising the following steps:
the method comprises the following steps: acquiring a receiving signal through a receiving antenna;
step two: according to actual requirements, modeling and estimating a channel gain matrix under a non-ideal channel;
step three: acquiring a BER closed expression by using a ZF-OSIC detection sequential receiver according to the posterior signal-to-interference-and-noise ratio of each stream and predicting the bit error rate of each stream;
step four: sorting according to the bit error rate, and taking the signal with the small bit error rate as a priority detection signal;
the second step is further as follows: in the presence of non-ideal channel factors, channel estimation is performed on the acquired pilot signal in an actual system, and an estimation calculation is performed on a channel gain matrix H, namely, an error matrix is added to a channel gain matrix under an ideal channel, that is:
Figure FDA0003530138340000011
wherein e Ω is a channel estimation error irrelevant to the channel gain matrix H, Ω is a complex gaussian distribution obeying an independent distribution with a mean value of 0 and a variance of 1, and e is a real number for measuring a channel estimation preparation degree;
the third step is further as follows:
will transmit a signal-to-noise ratio gamma0Defined as the ratio of signal to noise, the dataIn the transmission process, the posterior signal-to-interference-and-noise ratio of the kth transmission data stream under the conditions of channel correlation and channel estimation error is as follows:
Figure FDA0003530138340000012
wherein N istFor the number of transmit antennas, e is a real number that measures how well the channel estimates are prepared, [ (H)HH)-1]kkIs represented by (H)HH)-1K row and k column element of (1), lambdakIs (R)t)-1The kth diagonal element of (1), HwRepresenting a complex gaussian matrix subject to independent distribution,
Figure FDA0003530138340000013
has a value of
Figure FDA0003530138340000014
1/[(HHH)-1]kkTo comply with the degree of freedom of 2 (N)r-Nt+1) chi-square distribution, synthesizing the proposed formula to obtain obedience
Figure FDA0003530138340000015
The probability density function f (SINR) of the gamma distribution SINRk of (1)k) (ii) a In the formula, NrIndicating the number of receiving antennas;
and predicting the bit error rate of each stream by using ZF performance detection to obtain a BER closed expression according to the signal to interference plus noise ratio, wherein for an M-PSK modulation mode, the BER is p in an AWGN channelb(SINRk) For M-QAM modulation mode, BER is p under AWGN channelb(SINRk) According to SINRkThe distribution integration obtains the closed expression BER under two modulation modesMPSKAnd BERMQAMWherein
Figure FDA0003530138340000016
Figure FDA0003530138340000021
For M-PSK modulation mode, closed expression BERMPSKContains muiIs composed of
Figure FDA0003530138340000022
D＝Nr-NtAnd M is the order of modulation,
Figure FDA0003530138340000023
has a value of
Figure FDA0003530138340000024
γ0Representing the transmitted signal-to-noise ratio, λkIs (R)t)-1The kth diagonal element of (1), RtIs a transmit correlation matrix; in M-QAM modulation mode, closed expression BERMQAMContains muiIs composed of
Figure FDA0003530138340000025
μ0Represents muiWherein i is a value when 0 is taken; m is the order of the modulation,
Figure FDA0003530138340000026
has a value of
Figure FDA0003530138340000027
γ0Representing the transmitted signal-to-noise ratio, λkIs (R)t)-1The kth diagonal element of (1), RtIs a transmit correlation matrix;
in the retransmission scene, when the retransmission mode is HARQ-CC mode, the receiving end adopts the Maximum Ratio Combining (MRC) mode for receiving, and when the retransmission times is N-1 times, according to the property of gamma distribution, the signal-to-interference-and-noise ratio after retransmission and combination obeys
Figure FDA0003530138340000028
According to the combination of the BER expression under the AWGN channel under the M-PSK modulation mode and the BER expression under the AWGN channel under the M-QAM modulation mode, given that the ZF detection performance of M-PSK and M-QAM modulation under the same condition of a transmitting antenna and a receiving antenna is as follows:
Figure FDA0003530138340000029
Figure FDA00035301383400000210
in the formula (I), the compound is shown in the specification,
Figure FDA00035301383400000211
has a value of
Figure FDA00035301383400000212
γ0Representing the transmitted signal-to-noise ratio, λkIs (R)t)-1The kth diagonal element of (1), RtIs a transmit correlation matrix.
2. The ZF-OSIC optimized detection order method based on channel estimation error as claimed in claim 1, wherein said step one is further:
in MIMO system, the transmitting antenna and the receiving antenna are respectively Nt、NrWhen the number of the transmitting antennas is less than or equal to the number of the receiving antennas, obtaining a receiving signal y containing a transmitting correlation matrix, a symbol vector, a complex Gaussian matrix and a noise vector sent by the transmitting antennas; wherein the complex Gaussian matrix is subjected to independent distribution, the mean value is 0, and the variance is 1; the noise vector obeys a mean value of 0 and a variance of N0Complex gaussian distribution.
3. The ZF-OSIC optimized detection order method based on channel estimation error as claimed in claim 1, wherein said step four further comprises:
sorting the bit error rate predicted by a BER closed expression obtained by ZF performance detection according to the value size, and taking the signal with small bit error rate as a signal for preferential detection.
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