CN104104629A - Rapid signal detection method based on echo state network - Google Patents
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Abstract
The invention relates to a rapid signal detection method based on an echo state network. Firstly construction of an echo state network structure suitable for a rapid signal detection problem is given, and then concrete forms of corresponding echo state network reading functions are designed according to constellation diagram characteristics of different transmitting signals; and then a reserve pool weight matrix form of the echo state network of the rapid signal detection problem is designed, the number of conditions of a weight matrix is reduced by adopting a method of cutting undersized singular values, and reading weight confirmation and updating criteria of the network are designed. With application of the technical schemes, the invention provides the rapid signal detection method based on the echo state network so that severe dependence of existing signal detection methods on data amount is overcome, and the situation that characteristics of being abrupt and short in data frames of signals of a modern communication system are not considered is also overcome, and thus detection is accurate.
Description
Technical Field
The invention relates to the technical field of signal processing of wireless communication, in particular to a method for realizing direct detection of short frame signals of a wireless communication system by adopting an echo state network under the conditions that a channel between communication emission and a receiver has deep fading, signals at a receiving end have serious intersymbol interference, transmitted data has certain burstiness and the length of a data frame at the receiving end is short.
Background
Burst signals are widely applied in modern communication, in a non-cooperative or antagonistic communication system, the burst signals are sent in a burst mode by randomly selecting time, the signals are transmitted at a continuous time point instantly, and a receiving party or an intercepting party cannot obtain the prior knowledge of a burst signal synchronization head and a signal detection sequence, so that a detection link needs to be added for processing the burst signals to determine whether the signals and the start and the end of the signals exist at present. Fast detection of burst signals is a prerequisite for subsequent signal processing. Due to the fact that the signal length is too short, the traditional blind signal processing method is not applicable, especially blind processing methods based on a statistical method are not applicable any more, and therefore a rapid detection method which only depends on small data volume for rapid convergence is needed. On one hand, along with the increasingly rapid development of wireless communication technologies, the requirements of battery energy conservation, short-time burstiness of data, incomplete collaboration of a transmitting party and a receiving party and the emergency communication system need to be considered in more and more communication occasions. For example: the wireless sensor network and meteor burst communication can play an important role in hydrology, atmosphere monitoring, fire monitoring and marine buoy and sea sample acquisition systems, and the network has the inherent characteristics of short data length, signal burst and gap because the network particularly pays attention to the problem of energy consumption, so that the large data dependency of the traditional detection method cannot be met. Therefore, a blind processing method capable of reducing data amount dependence and being practically applied is urgently needed, and the blind processing method has to be capable of quickly detecting Quadrature Phase Shift Keying (QPSK) and Quadrature Amplitude Modulation (QAM) signals, reducing data amount dependence, and having the characteristics of simple structure and low software and hardware costs.
Echo State Networks (ESNs)) and corresponding learning algorithms open up a new road ESN for research of recurrent neural networks and follow up on nonlinear dynamics ESN methods, which are of interest because of the advantages of accurate model, strong modeling capability, biological rationality, expansibility, and economy. The method introduces an internal network called a reserve pool, when an external input sequence enters the internal network, a complex and various nonlinear state space is excited in the internal network, and then a simple reading network is used for obtaining network output. Because the calculation amount of training is greatly reduced, the local minimum phenomenon which is difficult to avoid by most of learning algorithms based on gradient descent is avoided, and meanwhile, good modeling precision can be obtained; in the ESN method, by introducing the reserve pool, the weight matrix has sparsity, and only part of output weights need to be updated. As a new feedback neural network paradigm, the dynamic characteristic of the feedback neural network is inherited, and the learning difficulty of the feedback neural network is overcome.
Disclosure of Invention
The invention aims to overcome the serious dependence of the existing signal detection method on the data quantity and does not consider the characteristics of the signal of the modern communication system, such as burstiness and short data frames, and provides a signal rapid detection method based on an echo state network.
The technical scheme of the invention is as follows: a signal fast detection method based on an echo state network is characterized by comprising the following steps:
the first step is as follows: suppose a source signaling sequence snThe system is independently and equally distributed, does not lose generality, does not consider noise influence, does not participate in any training sequence, and a single-input multi-output wireless communication system receiving equation and a signal detection equation can be expressed as follows
XN＝SΓH
Wherein: the superscript H denotes the conjugate transpose, q denotes the oversampling factor/number of receive antennas, and Γ ═ ΓL(Hi) Is (H)iI-0, 1, …, L),is the impulse response, L, of the communication channelhFor channel order, L is equalizer length, (X)N)N×(L+1)q＝[xL(t)，…，xL(t+N-1)]TIs a receiving data array and a transmitting signal array is S (t) ═ sN(t)，sN(t-1)，…，sN(t-M-L)]N×(L+M+1)；
The second step is that: firstly, randomly generating a group of random initial sequences as initial input to enter a reservoir W array, outputting a group of new serial sequences after the action of the reservoir W array, and generating an output signal array s (t-1) after the serial sequences are subjected to serial-parallel conversion; the output signal array and the weight matrix W of the ESN networkoutThe sequence v (t-1) is obtained after multiplication, andextracting the amplitude and phase of the new sequence by computing | and Arg (-) respectively, then performing nonlinear mapping in an amplitude reading function operator f (| ·|) and a phase reading function operator g (-) respectively, recombining the mapped amplitude and phase into a polar coordinate expression form to form a new output sequence s (t), and passing the output sequence through a time delay unit z-1After the action, the new input of the storage pool is fed back to the network, and the network runs repeatedly until the algorithm converges;
the third step: designing a read-out function based on characteristics of a signal to be detected
Noting a single read function as
Where a represents the amplitude of the signal point,representing the phase of the signal point, f (A) representing the amplitude map of the read-out function,representing the phase map of the read-out function, j representing the unit of an imaginary number, exp (-) is an exponential function,
(1) when the original transmitted signal is a PSK signal
The amplitude mapping part of the ESN readout function is first designed:
f(A)＝tanh(A)
where tanh (-) represents a hyperbolic tangent function,
if the modulation is pi/4-quadrature phase shift keying (pi/4-QPSK), M is 4, and θ is the phase angle, the phase mapping of the ESN readout function is:
if the modulation is other types of phase shift keying, the phase mapping of the ESN readout function is:
where a is the attenuation factor, a > 0;
(2) when the original transmission signal is a QAM signal
The 8QAM amplitude function is designed as follows
Wherein a is a number of the attenuation factors,
the phase excitation function of the 8QAM signal is designed as follows
Wherein a is a number of the attenuation factors,
designing and obtaining the amplitude and phase function form of the 16QAM signal by the same method;
the 16QAM amplitude function is of the form
16QAM signal, the phase function is of the form:
whereinWhen the value of i is 1, the value of i,when the value of i is 2, the ratio of i to i is,when the value of i is 3, the value of i,when the value of i is 4, the value of i,
the fourth step: designing weight of ESN network reserve pool and ensuring connection sparsity of ESN network reserve pool
According to the signal model of the first step, firstly constructing a reservoir W array, and receiving a signal matrix XNIs transformed as followsWhere superscript denotes conjugation, the following QR decomposition form exists: <math><mrow>
<msubsup>
<mi>X</mi>
<mi>N</mi>
<mi>T</mi>
</msubsup>
<mo>=</mo>
<mo>[</mo>
<mi>Q</mi>
<mo>,</mo>
<msub>
<mi>Q</mi>
<mi>c</mi>
</msub>
<mo>]</mo>
<mo>·</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>R</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>QR</mi>
</mrow></math> wherein,is an orthogonal matrix, and is characterized by that,and constructing an ESN reservoir W matrix for a non-zero upper triangular matrix: W-QQH，
In order to ensure the sparsity of the reserve pool matrix, the following method is designed:
if it is notThe value of W (a, b) is assigned to 0, otherwise W (a, b) remains unchanged, ρ ∈ [0, 1 ∈]A and b respectively represent the row and column positions of the W matrix elements;
the fifth step: design of update rule of read weight matrix
Construct the following optimization problem
For signal detection problems, a constant modulus criterion is adopted, i.e.Wherein:
R＝E{Re(s)4}/E{Re(s)2}，ui＝[ui，ui-1，…，ui-L+1]Tl-1, L, …, N-1, Re (·) represents the operation of the real part, E (·) is the mathematical expectation operation,
for the insensitive loss function, linear insensitive function is adopted to obtain
Wherein the superscript-1 represents the matrix inversion operation, and then the update rule of the read weight is designed as follows:
where η ∈ (0, 1),for the initial value of the output weight, the center tap is 0.05+ j0.05, and the remaining tap values are 0.
The following is described in further detail with reference to the accompanying drawings:
drawings
FIG. 1 is a schematic diagram of a network suitable for rapidly detecting a signal echo condition according to the present invention;
FIG. 2 is a schematic diagram of signal splitting according to the present invention;
fig. 3 is a graph of read-out functions of the read-out function attenuation factor a of 10, QPSK, 8PSK, 16PSK in the echo state network according to the present invention;
fig. 4 is a graph of an 8QAM phase readout function when the echo state network readout function attenuation factor a is 25 according to the present invention;
FIG. 5 is a schematic diagram of the concave-convex property of the cost function when different norm indexes p are taken;
FIG. 6 is a comparison graph of network signal detection performance in echo state for different signals to be detected according to the present invention;
FIG. 7 is a convergence graph of the echo state network signal detection method according to the present invention for different signals to be detected;
FIG. 8 is a diagram of the trace of the single experiment operation of the ESN algorithm with 1000 data size and 20dB signal-to-noise ratio when the QPSK signal is generated according to the present invention;
FIG. 9 is a diagram of a single experimental operating trace of the ESN algorithm with a data size of 1000, a signal-to-noise ratio of 20dB, and an 8PSK signal according to the present invention;
FIG. 10 is a graph of the single-check running trace of the ESN algorithm with 1000 data size and 20dB signal-to-noise ratio for an 8QAM signal of the present invention;
fig. 11 is a graph of the trace of the single experiment operation of the ESN algorithm with the data size of 1000 and the signal-to-noise ratio of 20dB for the 16QAM signal of the present invention.
Detailed Description
The burst short frame signal fast detecting method based on echo state network includes the following steps:
the first step assumes a source signaling sequence snAre independently and identically distributed; without loss of generality, without considering noise influence and without any training sequence participation, a Single Input Multiple Output (SIMO) wireless communication system receiving equation and a rapid detection equation can be expressed as follows
XN＝SΓH
Wherein: the superscript H denotes the conjugate transpose, q denotes the oversampling factor/number of receive antennas, and Γ ═ ΓL(Hi) Is (H)iI-0, 1, …, L),is the impulse response, L, of the communication channelhFor channel order, L is equalizer length, (X)N)N×(L+1)q＝[xL(t)，…，xL(t+N-1)]TIs a receiving data array and a transmitting signal array is S (t) ═ sN(t)，sN(t-1)，…，sN(t-M-L)]N(L+M+1)；
The second step is that: (as shown in fig. 1), constructing an echo state network suitable for signal fast detection, wherein | · | is a signal point amplitude (modulus) operation, and f (| · |) represents an amplitude read-out function operator; arg (-) is signal point phase operation, g (-) represents a phase read function operator, and represents the obtained phase, s (t-1), s (t) respectively represent echo state network input and output signal output, z (-) is-1Representing delay, S/P representing serial/parallel conversion of signal frame, S (t-1) representing matrix obtained by serial-parallel conversion of output signal sequence of weight matrix of reserve pool, V (t-1) representing output sequence obtained by multiplying S (t-1) by ESN read weight, e representing natural number, j representing imaginary number unit, freadout(. cndot.) represents the readout function, and the arrow direction represents the signal flow direction.
The workflow of the network is given below in conjunction with fig. 1: firstly, randomly generating a group of random initial sequences as initial input to enter a reservoir W array, outputting a group of new serial sequences after the action of the reservoir W array, and generating an output signal array s (t-1) after the serial sequences are subjected to serial-parallel conversion; the output signal array and the weight matrix W of the ESN networkoutObtaining a sequence v (t-1) after the multiplication, further extracting the amplitude and the phase of a new sequence through | and Arg (-) operation respectively, then entering an amplitude reading function operator f (| and |) and a phase reading function operator g (-) respectively for nonlinear mapping, and then recombining the mapped amplitude and phase into a polar coordinate expression form to form a new output sequence s (t), wherein the output sequence passes through a time delay unit z-1After the action, the new input is fed back to the network as a reserve pool. The network runs repeatedly until the algorithm converges;
the third step: designing a read-out function based on characteristics of a signal to be detected
The invention is suitable for the common PSK and QAM digital modulation modes in the modern wireless communication system; then, the reading function f is carried out according to the signal characteristics of the two types of modulation modesreadoutThe characteristics of the two types of signals are shown in figure 2. Noting a single read function as
Where a represents the amplitude of the signal point,representing the phase of the signal point, f (A) representing the amplitude map of the read-out function,representing the phase map of the read-out function, j representing the imaginary unit, exp (·) being an exponential function.
(1) When the original transmitted signal is a PSK signal
The amplitude mapping part of the ESN readout function is first designed:
f(A)＝tanh(A)
where tanh (-) represents a hyperbolic tangent function,
then, the PSK phase constraint is
s∈T＝{exp(j2π(m-1)/M)，m＝1，2，…，M}
Here, exp (·) is an exponential function, j is an imaginary unit, M represents the number of constellation points of PSK, and pi is a circumferential ratio,
if the modulation is pi/4-quadrature phase shift keying (pi/4-QPSK), M is 4, and θ is the phase angle, the phase mapping of the ESN readout function is:
if the modulation is other types of phase shift keying, the phase mapping of the ESN readout function is:
where a is attenuation factor, a is greater than 0, and its value not only controls the steepness of the function but also affects the number of inflection points of the function; it is worth noting that the pi/4-QPSK and 8PSK signal phase functions are formed by compounding and splicing single-section S-shaped functions, are similar in form and all present a multi-step curve phenomenon. The difference is that for pi/4-QPSK signals, except the difference of the number and the position of steps, the phase function has a platform at the position of +/-pi/4 and +/-3 pi/4, and does not have a platform at the position of an origin; for 8PSK signals, the location of the platform (see FIG. 3) must have a platform in addition to appearing at { + - π/4, + - π/2, + -3 π/4, 0, π } locations; this is closely related to the constellation itself (see fig. 2);
(2) when the original transmission signal is a QAM signal
Unlike the case of MPSK signals, QAM signals have multiple amplitudes and phases simultaneously. Expressing QAM signal as polar coordinate form, thenWherein a represents the signal point mode value,representing the phase of the signal point correspondences, exp (-) is an exponential function, j is an imaginary unit,
for square 16QAM, for example, the modulus in polar coordinate form isPhase isWhere arctan (·) is an arctangent function, pi is the circumferential ratio,
the 8QAM amplitude function is designed as follows
Wherein a is an attenuation factor which controls the steepness of the function graph, the effect of multiple thresholds cannot be achieved if the value of the attenuation factor a is too small, and when the value of a tends to infinity, a step similar to the special step of the step function appears, which indicates that the discrete vibration is dispersedThe amplitude function is included in the functional form, just a special case of it. The amplitude threshold occurs atAndat corresponding positions of (a) and (b) are respectively the two threshold differencesAnd
designing an 8QAM signal and a phase function; since the 8QAM constellation points themselves have a symmetric nature with respect to the coordinate axes, then all the second are made、The phase of the constellation point for the third and fourth quadrants can be simply calculated from the phase of the first quadrant. But the design of the 8QAM phase function becomes slightly more complicated due to the non-uniform variation of the phase distribution.
The phase excitation function of the 8QAM signal is designed as follows
Fig. 4 shows a 8QAM phase readout function pattern when the echo state network readout function attenuation factor a is 25.
The same method can be designed to obtain the amplitude and phase function form of the 16QAM signal.
The 16QAM amplitude function is of the form
16QAM signal, the phase function is of the form:
whereinWhen the value of i is 1, the value of i,when the value of i is 2, the ratio of i to i is,when the value of i is 3, the value of i,when the value of i is 4, the value of i,
of course, the same method can also obtain the amplitude and phase function expression forms of the 32QAM and 64QAM signal read-out functions, which are not listed;
the fourth step: designing weight of ESN network reserve pool and ensuring connection sparsity of ESN network reserve pool
According to the signal model of the first step, firstly constructing a reservoir W array, and receiving a signal matrix XNIs transformed as follows <math><mrow>
<msubsup>
<mi>X</mi>
<mi>N</mi>
<mi>T</mi>
</msubsup>
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</mrow></math> Wherein the superscript denotes conjugation. Then the following QR decomposition form exists: <math><mrow>
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<mi>X</mi>
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<mo>=</mo>
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</mrow></math> wherein,is an orthogonal matrix, and is characterized by that,is a non-zero upper triangular matrix. And further constructing an ESN reserve pool W matrix: W-QQH。
From knowledge of the condition numbers, the condition numbers in fact represent the sensitivity of the matrix computation to errors. For the linear system of equations Bx ═ B, if the condition number of B is large, a small change in B can cause a large change in solution x, and the numerical stability is poor. On the contrary, if the condition number of B is small, B has a slight change, x has a slight change, and the numerical stability is good. It can also represent the variation of x with B unchanged and with a slight variation of B. When the weight matrix of the ESN reserve pool is constructed by the QR decomposition unitary matrix method of the received signal matrix, the matrix W is possibly ill-conditioned, and the ill-conditioned weight matrix can possibly cause the performance of the algorithm to be damaged or even fail; the invention introduces a method for cutting off undersize singular values to reduce the condition number of the weight matrix.
In order to ensure the sparsity of the reserve pool matrix, the following method is designed:
if it is notThe value of W (a, b) is assigned to 0, otherwise W (a, b) remains unchanged. Rho is equal to [0, 1 ]]For example, ρ is 0.5, and a and b respectively denote the row and column positions of the W matrix elements. Note cond (-) is a matrix condition number operation, and we observe the change of W condition number (see table 1), and we can find that the W condition number is greatly reduced by this method from table 1.
TABLE 18 PSK, data Length 500, SIMO with a factor q of 4, 30dB condition number vs. p (condition number before un-sparse W: 1.1411 × 1020)
| ρ | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
| cond(W) | 1.4785×106 | 4.0351×105 | 2.4782×105 | 5.6897×104 | 5.5779×104 |
The fifth step: design of update rule of read weight matrix
The geometric meaning of the vector norm (as shown in FIG. 5) can be known
When p is more than 1, the p norm is a convex function, p is less than or equal to 1, and the p norm is not a convex function. The convexity of the two-norm is crucial to solving the optimization problem. The present invention then uses the norm for the case where p is 2 to construct the following optimization problem
For signal detection problems, a constant modulus criterion is adopted, i.e.Wherein:
R＝E{Re(s)4}/E{Re(s)2}，ui＝[ui，ui-1，…，ui-L+1]Tl-1, L, …, N-1, Re (·) represents the operation of the real part, and E (·) is the mathematical expectation operation.
For the insensitive loss function, the invention adopts a linear insensitive function, and
whereinAnd I is a unit array.
Thereby obtaining
Where the superscript-1 represents the matrix inversion operation. Then, designing a read weight updating rule as follows:
where η ∈ (0, 1),for the initial value of the output weight, the center tap is 0.05+ j0.05, and the remaining tap values are 0.
Simulation example
The following simulation results, which are not specifically described, all adopt a roll-off raised cosine function p (T) with a roll-off factor of 0.1, and a 2-path multipath channel c (T) ═ δ (T) -0.7 δ (T-T/3), where T is a sampling period; thereby obtaining an oversampled channel impulse response <math><mrow>
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</mrow></math> Is the convolution operator; the oversampling factor q is set to 3. The SNR is 20dB, the Monte Carlo experiment number is 200, and a linear loss function is used, with ∈ 1. N is 1000, and the read weight number L is 9. Fig. 6 is a comparison graph of network signal detection performance in echo state for different signals to be detected according to the present invention.
Fig. 7 is a convergence graph of the echo state network signal detection method according to the present invention for different signals to be detected. Fig. 8 is a graph of the single experiment operation trace of the ESN algorithm with 1000 data size and 20dB signal-to-noise ratio for QPSK signal of the present invention. Fig. 9 is a diagram of a single experimental run of the ESN algorithm with a data size of 1000 and a signal-to-noise ratio of 20dB for an 8PSK signal according to the present invention.
Fig. 10 is a graph of the single experiment operation trace of the ESN algorithm with 1000 data size and 20dB signal-to-noise ratio for the 8QAM signal of the present invention. Fig. 11 is a graph of the trace of the single experiment operation of the ESN algorithm with the data size of 1000 and the signal-to-noise ratio of 20dB for the 16QAM signal of the present invention.
Claims (1)
1. A signal rapid detection method based on an echo state network is characterized by comprising the following steps:
the first step is as follows: suppose a source signaling sequence snThe receiving equation and the rapid detection equation of the single-input multi-output wireless communication system can be expressed as follows without loss of generality, noise influence and participation of any training sequence
XN＝SΓH
Wherein: the superscript H denotes the conjugate transpose, q is the oversampling factorNumber of sub/receiving antennas, gamma beingL(Hi) Is (H)iI-0, 1, …, L),is the impulse response, L, of the communication channelhIs the channel order, L is the equalizer length,is a receiving data array and a transmitting signal array is S (t) ═ sN(t)，sN(t-1)，…，sN(t-M-L)]N×(L+M+1)；
The second step is that: firstly, randomly generating a group of random initial sequences as initial input to enter a reservoir W array, outputting a group of new serial sequences after the action of the reservoir W array, and generating an output signal array s (t-1) after the serial sequences are subjected to serial-parallel conversion; the output signal array and the weight matrix W of the ESN networkoutMultiplying to obtain a sequence v (t-1), extracting the amplitude and phase of a new sequence through | and Arg (-) operation, entering an amplitude read function operator f (| and |) and a phase read function operator g (-) to perform nonlinear mapping, recombining the mapped amplitude and phase into a polar coordinate expression form to form a new output sequence s (t), and passing the output sequence through a time delay unit z-1After the action, the new input is fed back to the network as a reserve pool, and the network runs repeatedly until the algorithm converges;
the third step: designing a read-out function based on characteristics of a signal to be detected
Noting a single read function as
Where a represents the amplitude of the signal point,representing the phase of a signal pointF (A) represents an amplitude map of the read-out function,representing the phase map of the read-out function, j representing the unit of an imaginary number, exp (-) is an exponential function,
(1) when the original transmitted signal is a PSK signal
The amplitude mapping part of the ESN readout function is first designed:
f(A)＝tanh(A)
where tanh (-) represents a hyperbolic tangent function,
if the modulation is pi/4-quadrature phase shift keying (pi/4-QPSK), M is 4, and θ is the phase angle, the phase mapping of the ESN readout function is:
if the modulation is other types of phase shift keying, the phase mapping of the ESN readout function is:
where a is the attenuation factor, a > 0;
(2) when the original transmission signal is a QAM signal
The 8QAM amplitude function is designed as follows
Wherein a is a number of the attenuation factors,
the phase excitation function of the 8QAM signal is designed as follows
Wherein a is a number of the attenuation factors,
the same design obtains the amplitude and phase function form of the 16QAM signal,
the 16QAM amplitude function is of the form
16QAM signal, the phase function is of the form:
whereinWhen the value of i is 1, the value of i,when the value of i is 2, the ratio of i to i is,when the value of i is 3, the value of i,when the value of i is 4, the value of i,
the fourth step: designing weight of ESN network reserve pool and ensuring connection sparsity of ESN network reserve pool
According to the signal model of the first step, firstly constructing a reservoir W array, and receiving a signal matrix XNIs transformed as followsWhere superscript denotes conjugation, the following QR decomposition form exists: <math>
<mrow>
<msubsup>
<mi>X</mi>
<mi>N</mi>
<mi>T</mi>
</msubsup>
<mo>=</mo>
<mo>[</mo>
<mi>Q</mi>
<mo>,</mo>
<msub>
<mi>Q</mi>
<mi>c</mi>
</msub>
<mo>]</mo>
<mo>·</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>R</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>QR</mi>
</mrow>
</math> wherein,is an orthogonal matrix, and is characterized by that,and constructing an ESN reservoir W matrix for a non-zero upper triangular matrix: W-QQH，
In order to ensure the sparsity of the reserve pool matrix, the following method is designed:
if it is notThe value of W (a, b) is assigned to 0, otherwise W (a, b) remains unchanged, ρ ∈ [0, 1 ∈]A and b respectively represent the row and column positions of the W matrix elements;
the fifth step: design of update rule of read weight matrix
Construct the following optimization problem
For signal detection problems, a constant modulus criterion is adopted, i.e.Wherein:
R＝E{Re(s)4}/E{Re(s)2}，ui＝[ui，ui-1，…，ui-L+1]Tl-1, L, …, N-1, Re (·) represents the operation of the real part, E (·) is the mathematical expectation operation,
for the insensitive loss function, linear insensitive function is adopted to obtain
Wherein the superscript-1 represents the matrix inversion operation, and then the update rule of the read weight is designed as follows:
where η ∈ (0, 1),for the initial value of the output weight, the center tap is 0.05+ j0.05, and the remaining tap values are 0.
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