A method for calculating communication decoding performance based on maximum likelihood detector

Abstract

This invention discloses a method for calculating communication decoding performance based on a maximum likelihood detector, belonging to the field of radar-communication integration technology. First, the received signal is converted to the frequency domain. Then, detection statistics are derived based on the maximum likelihood detection criterion, and a communication decoder is established. Next, a communication ambiguity function is defined based on the detection statistics matched to a specific transmitted symbol and the received signal model. The communication ambiguity function directly reflects the impact of the signal waveform on decoding accuracy and can be used for theoretical analysis of decoding performance, especially providing guidance for waveform design in the context of radar-communication integration.

Description

Technical Field

[0001] This invention belongs to the field of radar-communication integration technology, and it specifically relates to the problem of communication decoding accuracy and theoretical analysis of symbol error probability. Background Technology

[0002] With the development and popularization of wireless technology and the increasing application demands, the development of integrated radar and communication systems has become an inevitable trend, such as in automotive systems or 6G communication networks. Through cooperation between the radar and communication ends, or by adopting a dual-function integration, an integrated system can simultaneously perform radar and communication tasks. MIMO (Multiple Input Multiple Out) technology, as a multi-antenna transceiver technology, was initially applied in the field of communications. The receiver combines different received signals from the same data stream to recover the original signal, giving the communication system spatial diversity gain, reducing multipath fading, and improving channel reliability. Later, MIMO technology was applied to the radar field, known as MIMO radar. Compared to traditional radar, MIMO radar achieves multi-angle observation of targets through distributed antennas, increasing the accuracy of target detection and parameter estimation. Therefore, introducing MIMO technology into integrated radar and communication systems not only gives the communication end spatial diversity gain and increases channel capacity, but also improves the performance of the radar system, offering many advantages. In the traditional field of communication, there are already corresponding protocol specifications for waveform systems as constraints. However, for radar-communication integrated systems, since it is necessary to perform information exchange between communication and radar or to use the same waveform on the same hardware platform to complete radar and communication tasks, traditional radar or communication waveforms are often no longer applicable. Therefore, waveform design has always received widespread attention.

[0003] As one of the main tasks of the communication end of the radar-communication integrated system, the performance of communication symbol transmission can be evaluated by symbol error probability. However, since the constellation diagram of most modulation methods is irregular, the symbol error probability is an integral that cannot be calculated in a closed form. The decoding accuracy analysis of the communication system is mostly carried out through Monte Carlo simulation experiments. Reference 3 (Zhu X, Murch R D. Performance analysis of maximum likelihood detection in a MIMO antenna system[J].IEEE Transactions on Communications,2002,50(2):187-191.DOI:10.1109 / 26.983313.) derives a closed-form expression for the pairwise error probability of the MIMO system from the perspective of the upper bound of the symbol error probability.

[0004] Ambiguity functions, as one of the commonly used performance evaluation indicators for radar, can be used to measure the radar's target resolution capability. Ville first proposed the concept of ambiguity functions based on the optimal detector in reference 1 (Ville J. Theorie et application dela notion de signalanalytique[J]. Cableset Transmissions, 1948, 2.). Later, Woodward made pioneering contributions in reference 2 (Woodward PMRadar ambiguity analysis[J]. radarambiguity analysis, 1967.). He discovered that the reason why targets can be observed through echoes is because different target echoes are different. Based on this, he defined ambiguity functions, which can be used to analyze the radar system's ability to resolve targets at different positions and velocities under different waveform systems.

[0005] In conclusion, it is essential to study theoretical analysis methods for communication decoding performance and explore the direct relationship between transmitted waveforms and decoding performance. This has guiding significance for waveform design and important research value in the field of radar-communication integration. Summary of the Invention

[0006] The technical problem addressed by this invention in response to the shortcomings of the prior art is that it proposes a new communication performance index—the Communication Ambiguity Function (CAF)—for theoretical analysis of communication decoding performance.

[0007] This invention mainly includes: first, converting the received signal to the frequency domain; then, deriving the detection statistics based on the maximum likelihood detection criterion and establishing a communication decoder; and finally, defining a communication ambiguity function based on the detection statistics matched to a certain transmitted symbol and the received signal model.

[0008] The technical solution of this invention is a method for calculating communication decoding performance based on a maximum likelihood detector, the method comprising:

[0009] Step 1: In the system, the signal sample values ​​received by the nth receiver from the mth transmitter are arranged in order to form the received signal vector y. nm Where n = 1, ..., N, and N represents the total number of receivers;

[0010] Step 2: Represent the received signal corresponding to the nm-th path as a vector y. nm ;

[0011] Step 3: Express the vector of the transmitted signal from the m-th transmitter in discrete time as follows:

[0012]

[0013] Step 4: Define the Discrete Fourier Transform matrix:

[0014]

[0015] Where p,q=1,2,...,K, the frequency interval is...

[0016] Step 5: Converted to the frequency domain:

[0017]

[0018] Step 6: Place w nm Converted to the frequency domain:

[0019] W nm =Dw nm

[0020] Step 7: Calculate the time shift matrix T(τ) nm ), T(τ) t,nm )

[0021]

[0022]

[0023] Step 8: Calculate the Doppler frequency shift matrix Z(f) nm )

[0024]

[0025] in

[0026]

[0027] Step 9: Convert the received signal corresponding to the nm-th path to the frequency domain Y. nm ;

[0028] Step 10: Arrange the frequency domain forms of the received signals from all receivers into a vector Y.

[0029]

[0030] Where T = diag{T(τ) 11 ),...T(τ nm ...,T(τ) NM )}, T t =diag{T(τ t,11 ),...T(τ t,nm ...,T(τ)t,NM )},X| s =[X1| s ,...X M | s ,...,X1| s ,...X M | s ] T , ζ t =diag{ζ t,11 ,ζ t,12 ,...,ζ t,NM}, ζ t,nm =ζ t,nm I K×K H = diag{H 11 H 12 ,...,H NM}, Ht=diag{Ht, 11 ,Ht, 12 ,...,Ht, NM}, H nm =h nm I K×K Ht,nm=ht,nmI K×K Z t =diag{Z(f 11 ),Z(f 12 ),...,Z(f NM )}, It follows a zero mean and a variance of Q D =BQB H The complex Gaussian distribution,

[0031] Step 11: Based on the maximum likelihood criterion, calculate the decoder match for symbol s. i Detection statistics Λ|s i ;

[0032]

[0033] Step 12: Substitute the received signal Y into the detection statistic Λ|s i And retaining quantities that are only related to the waveform, the communication ambiguity function χ(s) i The expression for |s) is:

[0034]

[0035] Where s represents the actual transmitted signal, s i This indicates the transmitted signal matched by the decoder;

[0036] Step 13: The value obtained by the communication fuzzy function is used to represent the communication decoding performance.

[0037] Furthermore, in step 1:

[0038] y nm =[y nm [1],y nm [2],…,y nm [k],…,y nm [K] T

[0039] in[·] T Indicates transpose, y nm [k] represents the nth receiver at kT. s The value of the transmitted signal received at time m from the transmitter after direct transmission and target reflection is expressed as:

[0040]

[0041] And the m-th transmitter is in kT s The transmitted signal sample value at time x m (kT s ), m=1,…,M,T s τ is the sampling interval, k is the sampling number, k = 1, ..., K, and K is the total number of samples; nm With τ t,nm h represents the corresponding direct signal delay and target reflected signal delay. nm with h t,nm ζ represents the direct channel response and the target reflection channel response. t,nm s is the target reflectance coefficient. m Indicates a communication transmission symbol; f nm ω represents the Doppler frequency shift of the corresponding signal path. nm [k] represents clutter plus noise.

[0042] Furthermore, in step 2,

[0043]

[0044] Among them, the transmitted signal with direct delay Transmitted signal delayed by target reflection For Doppler frequency shift, w nm =[w nm [1],...w nm [k]...,w nm [K] T This represents clutter plus noise, and the symbol ⊙ represents the Hadamard product.

[0045] Furthermore, in step 9,

[0046]

[0047] set up It follows a complex Gaussian distribution with zero mean and variance Q, where Q = σ. 2 I KNM×KNM ;I KNM×KNM It is a KNM×KNM identity matrix.

[0048] The above steps convert the received signal to the frequency domain, establish a communication symbol decoder based on the maximum likelihood criterion, and define a new communication decoding performance evaluation index—the communication ambiguity function—from the perspective of the decoder's output when it matches an incorrect communication symbol. The communication ambiguity function directly reflects the impact of the signal waveform on decoding accuracy and can be used for theoretical analysis of decoding performance, especially providing guidance for waveform design in the context of integrated radar and communication. Attached Figure Description

[0049] Figure 1 When the actual emitted symbol is s, when s i The communication ambiguity function graphs for different values, where the real-image plane is the constellation point plane, s i The values ​​are discretely taken on the constellation point plane, and the intersection of the CAF image and the real-image plane is the value of the real emitted symbol s.

[0050] Figure 2 This is a communication ambiguity function (CAF) image in a radar-communication integrated scenario when target information is incorrect. In the image, the blue hollow circles represent the ideal completion of the radar mission, while the red hollow circles represent the situation where the radar mission (such as target detection) has errors. The intersection of the CAF image and the real-image plane represents the value of the actual transmitted symbol 's'. Detailed Implementation

[0051] Suppose a transmitter is transmitting OFDM symbols. For the p-th OFDM symbol and its l-th subcarrier, we discuss the case where only the m-th antenna's transmitted symbol experiences a decoding error. For ease of description, we first define the following:

[0052] (·) T For transpose, (·) H For the conjugate transpose, E{·} denotes the expected value, det(·) denotes the determinant of a matrix, Re{·} denotes taking the real part of a complex number, and ⊙ denotes the Hadamard product. It represents the Kronecker product.

[0053] Consider a dual-power MIMO radar-communication integrated system containing M transmitters and N receivers. The m-th (m = 1, ..., M) transmitter and the n-th (n = 1, ..., N) receiver are located at known positions in a two-dimensional Cartesian coordinate system, with coordinates (a, b, c) and (n, n) respectively. m ,b m ), (a n ,b n ), the m-th transmitter at time kT s The transmitted signal is x m (kT s (m=1,...,M), where T s Let k be the sampling interval, k (k = 1, ..., K) be the sampling sequence number, and K be the total number of samples. Assume the communication decoder has already acquired the target position and velocity information through interaction with the radar mission, which are respectively (a...k ... t ,b t ), (v a ,v b ). Target reflection coefficient ζ t,nm Having already been preprocessed, the nth receiver at time kT s The received signal can be modeled as

[0054]

[0055] Where τ nm With τ t,nm τ represents the corresponding direct signal delay and target reflected signal delay. nm =d d,nm / c, τ t,nm =(d t,n +d t,m ) / c,d d,nm =[(a m -a n ) 2 +(b m -b n ) 2 ] 1 / 2 d t,n =[(a n -a t ) 2 +(b n -b t ) 2 ] 1 / 2 d t,m =[(a m -a t ) 2 +(b m -b t ) 2 ] 1 / 2h nm with h t,nm Represents the direct channel response and the target reflection channel response, s m Represents a communication transmission symbol. ω nm [k] represents clutter plus noise, f nm The Doppler frequency shift representing the corresponding signal path can be expressed as:

[0056]

[0057] The transmitted signal received by the nth (n=1,…,N) receiver from the mth transmitter is sampled and arranged in order to form the received signal vector y. nm

[0058] y nm =[y nm [1],y nm [2],…,y nm [K] T

[0059] In vector form, we have

[0060]

[0061] Among them, the transmitted signal with direct delay Transmitted signal delayed by target reflection For Doppler frequency shift, w nm =[w nm [1],...w nm [k]...,w nm [K] T This indicates clutter plus noise.

[0062] The frequency domain expression of the received signal corresponding to the nth path.

[0063]

[0064] in Y nm =Dy nm W nm =Dw nm , (p,q=1,2,...,K), frequency interval Direct and target reflection path time shift matrix Let represent the discrete-time expression of the signal vector transmitted by the m-th transmitter. p,q=1,2,...,K, where

[0065]

[0066] Arrange the received signals from all receivers into a vector Y.

[0067] Where T = diag{T(τ) 11 ),...T(τ nm ...,T(τ) NM )}, T t =diag{T(τ t,11 ),...T(τ t,nm ...,T(τ) t,NM )},X| s =[X1| s ,...X M | s ,...,X1| s ,...X M | s ] T , ζ t =diag{ζ t,11 ,ζ t,12 ,...,ζ t,NM}, ζ t,nm =ζ t,nm I K×K H = diag{H 11 H 12 ,...,H NM}, H t =diag{H t,11 H t,12 ,...,H t,NM}, H nm =h nm I K×K H t,nm =h t,nm I K×K Z t =diag{Z(f 11 ),Z(f 12 ),...,Z(f NM )}, It follows a zero mean and a variance of Q D =BQB H The complex Gaussian distribution,

[0068] The present invention employs the following steps to calculate the communication ambiguity function of a MIMO dual-power radar communication integrated system, in order to measure the decoding accuracy under a certain waveform mode.

[0069] Step 1: Arrange the (frequency domain) received signals from all receivers into a vector Y.

[0070] Y = THX | s +H t ζ t Z t T t X| s +W

[0071] T = diag{T(τ) 11 ),...T(τ nm ...,T(τ) NM )}, T t =diag{T(τ t,11 ),...T(τ t,nm ...,T(τ) t,NM )},X| s =[X1| s ,...X M | s ,...,X1| s ,...X M | s ] T , ζ t =diag{ζ t,11 ,ζ t,12 ,...,ζ t,NM}, ζ t,nm =ζ t,nm I K×K H = diag{H 11 H 12 ,...,H NM}, H t =diag{H t,11 H t,12 ,...,H t,NM}, H nm =h nm I K×K H t,nm =h t,nm I K×K Z t =diag{Z(f 11 ),Z(f 12 ),...,Z(f NM )},

[0072] Step 2: Based on the maximum likelihood criterion, calculate the decoder matching with symbol s. i Detection statistics Λ|s i

[0073]

[0074] Step 3: Substitute the received signal Y into the detection statistic Λ|si By retaining only the terms related to the waveform, the fuzzy communication function expression can be obtained.

[0075]

[0076] Where s represents the actual transmitted signal, s i This indicates the transmitted signal matched by the decoder.

[0077] Working principle of the invention

[0078] The transmitted signal from the m-th transmitter received by the n-th (n=1,…,N) receiver can be written in vector form as follows:

[0079]

[0080] Define the DFT matrix D

[0081]

[0082] Frequency interval Received signal y nm Transformed to the frequency domain via DFT

[0083]

[0084] in Y nm =Dy nm W nm =Dw nm , Let represent the discrete-time expression of the signal vector transmitted by the m-th transmitter. The time-shift matrices for the direct path and the target reflection path are respectively expressed as: Let be the discrete-time expression for the transmitted signal vector of the m-th transmitter. p,q=1,2,...,K is the Doppler frequency shift matrix, where

[0085]

[0086] Arrange the received signals from all receivers into a vector Y.

[0087]

[0088] Where T = diag{T(τ) 11 ),...T(τ nm ...,T(τ) NM )}, T t =diag{T(τ t,11 ),...T(τ t,nm ...,T(τ)t,NM )},X| s =[X1| s ,...X M | s ,...,X1| s ,...X M | s ] T , ζ t =diag{ζ t,11 ,ζ t,12 ,...,ζ t,NM}, ζ t,nm =ζ t,nm I K×K H = diag{H 11 H 12 ,...,H NM}, H t =diag{H t,11 H t,12 ,...,H t,NM}, H nm =h nm I K×K H t,nm =h t,nm I K×K Z t =diag{Z(f 11 ),Z(f 12 ),...,Z(f NM )}, Assuming It follows a complex Gaussian distribution with zero mean and variance Q, where Q = σ. 2 I KNM×KNM ,but It follows a zero mean and a variance of Q D =BQB H The complex Gaussian distribution,

[0089] The conditional probability density of the received signal can be written as:

[0090]

[0091] When the transmitted symbols are equally probable, the maximum a posteriori detector degenerates into a maximum likelihood detector, and the symbol decoding problem can be expressed as follows:

[0092]

[0093] Where Σ represents the set of communication transmission symbols. Then, when the decoder matches the symbol vector s... i At that time, the detection statistic can be denoted as:

[0094]

[0095] When the actual transmitted symbol is , the observation vector is .

[0096] Y = THX | s +H t ζ t Z t T t X| s +W

[0097] Substitute the actual observed vector into the matching symbol s i The expression for the detection statistics, after retaining the terms that are only related to the waveform, is obtained.

[0098]

[0099] The physical meaning of the above equation can be interpreted as follows: when the actual transmitted symbol vector is s and the decoder matches the symbol s... i The value of the time-of-flight detection statistic is defined as follows: when the emitted symbol vector is s, the detector determines it as s. i The "ambiguity" of the expression. Therefore, under a certain modulation scheme, in order to make the communication decision result as accurate as possible, the value of the above formula should be within the range of s≠s. i When s = s, the value should be as large as possible, while when s = s i The value should be as small as possible, and the minimum value should be obtained (otherwise it will cause misjudgment).

[0100] It is evident that the above formula is closely related to the transmitted signal and the detector structure, reflecting the communication decision performance of the dual-power MIMO radar-communication integrated system. Combining this with the definition of the radar ambiguity function, both stem from the detector structure and directly reflect the performance of the dual-power MIMO radar-communication integrated system in completing communication / radar tasks. Furthermore, this performance indicator is directly related only to the transmitted waveform and system parameters. We define the above formula as the Communication Ambiguity Function (CAF).

[0101] To analyze the characteristics and physical meaning of the communication ambiguity function more clearly and intuitively, we only consider the signal along the nm path, i.e., the case where the number of transmit and receive antennas degenerates to 1, ignoring the coefficient terms introduced by the DFT matrix. In this case, the time-domain expression of the communication ambiguity function is as follows:

[0102]

[0103] Transform to the time domain using Paswald's theorem

Claims

1. A method for computing the performance of a communication decoder based on a maximum likelihood detector, characterized in that, The method comprises: Step 1: In the system, the signal sample values received by the nth receiver from the mth transmitter are arranged in order to form a received signal vector y nm , where n = 1, …, N, N represents the total number of receivers; y nm = [y nm [1], y nm [2], …, y nm [k], …, y nm [K]] T where [·] T denotes the transpose, y nm [k] is the value of the signal received by the nth receiver at the time instant kT s from the mth transmitter after direct and target reflection, and is expressed as and the mth transmitter's signal sample at time instant kT is xm(kT) = x s (kT m + mh s ), m = 1,..., M, where M denotes the total number of transmitters, T s is the sampling interval, k is the sample index, k = 1,..., K, and K is the total number of samples; τ nm and τ t,nm denote the corresponding direct signal delay and target reflected signal delay, h nm and h t,nm denote the direct channel response and target reflected channel response, ζ t,nm is the target reflection coefficient, s m denotes the transmitted communication symbol; f nm denotes the Doppler shift of the corresponding signal path, ω nm [k] is the clutter plus noise. Step 2: Represent the received signal corresponding to the nth path pair as a vector y nm ; Step 3: Discrete-time representation of the mth transmitter signal vector is given as: Step 4: Discrete Fourier transform matrix is defined as: where p, q = 1, 2,..., K, the frequency interval Step 5: The conversion to the frequency domain is: to the frequency domain is: Step 6: w nm Transforming to the frequency domain gives: W nm = Dw nm Step 7: Compute the time shift matrix T(τ nm ), T(τ t,nm ) Step 8: Compute the Doppler shift matrix Z(f nm ); Step 9: convert the received signal corresponding to the nth path to the frequency domain Y nm ; Step 10: The frequency domain form of the received signals of all receivers is arranged into a vector Y, where T = diag{T(τ 11 ),...T(τ nm )...,T(τ NM )}, T t = diag{T(τ t,11 ),...T(τ t,nm )...,T(τ t,NM )}, X| s = [X1| s ,...X M | s ,...,X1| s ,...X M | s ] T , ζ t = diag{ζ t,11 ,ζ t,12 ,...,ζ t,NM}, ζ t,nm = ζ t,nm I K×K , H = diag{H 11 ,H 12 ,...,H NM}, H t = diag{H t,11 ,H t,12 ,...,H t,NM}, H nm = h nm I K×K , H t,nm = h t,nm I K×K , Z t = diag{Z(f 11 ),Z(f 12 ),...,Z(f NM )}, is subject to a complex Gaussian distribution with zero mean and variance Q D = BQB H , Step 11: Based on the maximum likelihood criterion, compute the detector's match to the symbol s i Λ|s i ; The conditional probability density of the received signal is written as In the case of equiprobable transmitted symbols, the maximum a posteriori detector degenerates into a maximum likelihood detector, and the symbol decoding problem is expressed as Thus the decoder needs to compute the detection statistic Λ|s i for each symbol s i ; Step 12: Substitute the received signal Y into the detection statistic Λ|s i and retain only the waveform-dependent quantity, the communication ambiguity function χ(s i |s) is given by: where s represents the actual transmitted signal, s i represents the transmitted signal matched by the decoder; Step 13: The value calculated by using the communication ambiguity function represents the communication decoding performance.

2. A method of computing the performance of a communication decoder based on a maximum likelihood detector as defined in claim 1, wherein, In the step 2, where the direct path delayed transmit signal target-reflected delayed transmit signal for Doppler shift, w nm = [w nm [1],...w nm [k]...,w nm [K]] T denotes clutter plus noise, and the symbol denotes Hadamard product.

3. A method of computing the performance of a communication decoder based on a maximum likelihood detector as recited in claim 1, wherein, In the step 9, set up It follows a complex Gaussian distribution with zero mean and variance Q, where Q = σ. 2 I KNM×KNM ;I KNM×KNM It is a KNM×KNM identity matrix.

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