# US 11,909,566 B2 · Method for designing complex-valued channel equalizer > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,909,566 B2 - Document ID: US11909566B2 - Status: Granted - Kind: B2 - Application number: 17/617,294 - Filed: 2021-01-28 - Published: 2023-08-10 - Granted: 2024-02-20 - Earliest claimed: 2020-11-20 - Assignees: Soochow University - Applicants: Soochow University - Inventors: He Huang; Yongliang Zhang; Gangxiang Shen - Web page: https://patentgrep.com/patent/US11909566B2 ## CPC - H04L 25/03165: {using neural networks} - H04L 25/03019: {adaptive, i.e. capable of adjustment during data reception} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) ## Abstract The present invention discloses a method for the design of complex-valued channel equalizer of digital communication systems, including: constructing a channel equalizer by using a complex-valued neural network; collecting the output signal y(n)=[y(n), y(n−1), . . . , y(n−m+1)]T of the nonlinear channel of the underlying digital communication system as the input of complex-valued neural network and s(n−τ) as the desired output, and taking the mean squared error as the loss function for the training of complex-valued neural network, which is optimized by the proposed adaptive complex-valued L-BFGS algorithm, and finally using it to implement the design of channel equalizer for digital communication systems. The present invention proposes the use of a multi-layer feedforward complex-valued neural network to construct complex-valued channel equalizer. A new adaptive complex-valued L-BFGS algorithm is proposed for efficient training of complex-valued neural network, which is eventually applied to facilitate the design of the channel equalizer for digital communication systems. ## Claims ### Claim 1 A method for designing a complex-valued channel equalizer, comprising: constructing a complex-valued channel equalizer by using a complex-valued neural network, wherein the complex-valued channel equalizer is applied to a digital communication system; collecting an output signal y(n)=[y(n), y(n−1), . . . , y(n−m+1)]T of a nonlinear channel of the digital communication system as an input of complex-valued neural network and s(n−τ) as a corresponding desired output, and taking the mean squared error as the loss function J(z,z*); and optimizing the loss function J(z,z*) to obtain an appropriate complex-valued neural network model, and finally using the complex-valued neural network to implement channel equalization, wherein the “optimizing the loss function J(z,z*)” specifically comprises: optimizing the loss function J(z,z*) by an adaptive complex-valued L-BFGS algorithm, in the adaptive complex-valued L-BFGS algorithm, calculating and comparing an approximation degree between the inverse of quasi-Newton matrix and the inverse of Hessian matrix along a particular vector, and selecting a memory size corresponding to the highest degree of approximation as the optimal memory size at the current iteration. ### Claim 2 (depends on 1) The method for designing a complex-valued channel equalizer according to claim 1, wherein in the digital communication system, a complex-valued digital sequence of the nonlinear channel is denoted by s(n), a channel order is h, a channel mapping is f(⋅), a noiseless channel output is ŷ(n), an additive noise is v(n), an actual channel output y(n) is a superposition result of the noiseless channel output and the additive noise and is taken as the input data of the equalizer, an equalizer order is m, and a decision delay of the equalizer is assumed to be τ; a state ns of the channel is a data set generated by a limited character set transmitted through the channel, and a size of the data set is determined by the equalizer order and the channel order; a modulation order of a transmitted signal is M; and thus a transmission function of the channel is described by H ⁡ ( z ) = ∑ i = 0 h a i ⁢ z - i and a quantity of the state ns of the channel is determined by ns Mh m, in this case, an input sequence s(n)=[s(n), . . . , s(n−m 1−h)]T has ns states, after transmission through a noiseless channel, a desired channel output ŷ(n) also has ns states; the equalizer is used to reconstruct a sequence transmitted by a transmit end according to an observed channel output vector y(n)=[y(n), y(n−1), . . . , y(n−m+1)]T with additive noise, herein y(n)=[y(n), y(n−1), . . . , y(n−m+1)]T is a distortion signal with m delays, and m is the equalizer order. ### Claim 3 (depends on 1) The method for designing a complex-valued channel equalizer according to claim 1, wherein a specific implementation process of “in the adaptive complex-valued L-BFGS algorithm, calculating and comparing the approximation degree between the inverse of quasi-Newton matrix and the inverse of Hessian matrix along a particular vector, and selecting a memory size corresponding to the highest degree of approximation as the optimal memory size at the current iteration” is as follows: separately calculating g t c = [ 2 ⁢ ∇ z * J ⁡ ( z , z * ) T , 2 ⁢ ∇ z J ⁡ ( z , z * ) T ] T , s t c = z t c - z t - 1 , and ⁢ ⁢ y t c = g t c - g c t - 1 according to the loss function J(z,z*), wherein z c t = ( z t , z t * ) T ; respectively calculating γ c t = s c t - 1 3 ⁢ s c t - 1 and ω c t = y c t - 1 3 ⁢ y c t - 1 in a multi-step quasi-Newton formula by using s c y ⁢ and ⁢ y c t ; according to the formula: H ^ t m = ( V t - 2 H ⁢ … ⁢ V t - m H ) ⁢ H ^ t m ⁢ 0 ( V t - m ⁢ … ⁢ V t - 2 ) + ρ c t - m ( V t - 2 H ⁢ … ⁢ V t - m + 1 H ) ⁢ γ c t - m ⁢ γ c t - m H ( V t - m + 1 ⁢ … ⁢ V t - 2 ) + ρ c t - m + 1 ( V t - 2 H ⁢ … ⁢ V t - m + 2 H ) ⁢ γ c t - m + 1 ⁢ γ c t ⁢ m + 1 H ( V t - m + 2 ⁢ … ⁢ V t - 2 ) calculating a matrix Ĥtm, which is the quasi-Newton matrix and is used to depict the approximation degree between the inverse of the quasi-Newton matrix and the inverse of Hessian matrix; herein, the superscript H denotes conjugate transpose, ρ c t = 1 / ( ω c t H ⁢ γ c t ) V t = I - ρ c t ⁢ ω c t ⁢ γ c t , H ^ t m ⁢ 0 = ω c t - 1 H ⁢ γ c t - 1 ω c t - 1 ⁢ ω c t - 1 ; given an upper bound M of memory size, calculating the approximation degree between Ĥtm and the inverse of Hessian matrix for m=1, 2, . . . , M according to a formula e m = ( H ^ t m ⁢ ω c t - γ c t ) H ⁢ ( H ^ t m ⁢ ω c t - γ c t ) ; based on the foregoing calculated em, selecting a corresponding value of m achieving the minimum of em as the optimal memory size m* of the complex-valued L-BFGS algorithm; when the optimal memory size is determined, calculating a search direction at the current iteration with the help of H ^ t = ( V t - 1 H ⁢ ⋯ ⁢ V t - m H ) ⁢ H ^ t 0 ( V t - m ⁢ ⋯ ⁢ V t - 1 ) + ρ c t - m ( V t - 1 H ⁢ ⋯ ⁢ V t - m + 1 H ) ⁢ s c t - m ⁢ s c t - m H ( V t - m + 1 ⁢ ⋯ ⁢ V t - 1 ) + ρ c t - m + 1 ( V t - 1 H ⁢ ⋯ ⁢ V t - m + 2 H ) ⁢ s c t - m + 1 ⁢ s c t - m + 1 H ( V t - m + 2 ⁢ ⋯ ⁢ V t - 1 ) + ⋯ + ρ c t - 1 ⁢ s c t - 1 ⁢ s c t - 1 H calculating a search direction by p c t T = - H ^ t ⁢ g c t ; and then, using a line search condition: J ⁡ ( z c t + α t ⁢ p c t ) ≤ J ⁡ ( z c t ) + k 1 ⁢ α t ⁢ p c t ⁢ ∂ J ⁡ ( z c t ) ∂ z c t p c t T ⁢ ∂ J ⁡ ( z c t + α t ⁢ p c t ) ∂ z c t ≥ k 2 ⁢ p c t T ⁢ ∂ J ⁡ ( z c t ) ∂ z c t calculating a step size, wherein k1 takes value from the interval (0,0.5), and k2 takes value from the interval (k1, 1), to obtain a parameter update formula as z c t = z c t - 1 + α t ⁢ p c t T . ### Claim 4 (depends on 3) The method for designing a complex-valued channel equalizer according to claim 3, wherein a specific process of “appropriately adjusting the value of M according to a change trend of the optimal memory size selected in several previous iterations” comprises: given a window size W, calculating a predicted value mf,t* of the memory size at the current iteration according to a formula m f , t * = m t - W * + m t - W + 1 * + ⋯ + m t - 1 * W , wherein mt* denotes the optimal memory size at iteration t; and given constants c1 and c2, if mf,t*(1−c2)M, M=M+1; or otherwise, M is kept unchanged. ### Claim 5 (depends on 3) The method for designing a complex-valued channel equalizer according to claim 3, wherein a new search direction is designed by superimposing a plurality of directions, at the tth iteration, multiple memory sizes can be selected, so that a plurality of directions are calculated, and then these directions are superimposed to obtain the search direction at the current iteration. ### Claim 6 (depends on 5) The method for designing a complex-valued channel equalizer according to claim 5, wherein a specific process “a new search direction is designed by superimposing a plurality of directions, at the tth iteration, multiple memory sizes can be selected, so that a plurality of directions are calculated, and then these directions are superimposed to obtain the search direction at the current iteration” is: given a positive integer K, calculating an average memory size according to K memory sizes mw1*, mw2*, . . . , mwK* selected at the wth iteration, m _ w = m w ⁢ 1 * + m w ⁢ 2 * + ⋯ + m wK * K , calculating the predicted value m f , t * = m _ t - W + m _ t - W + 1 + ⋯ + m _ t - 1 W of the memory size at the current iteration by using an average value mW (w=t−W, t−W+1, . . . , t−1) of memory sizes in the previous W iterations; adjusting M according to the predicted value by using the foregoing adaptive adjustment method; and calculating K memory sizes at the tth iteration according to the modified M, to obtain K directions, and then superimposing these directions to obtain the search direction at the current iteration. ### Claim 7 (depends on 1) A computer device, comprising: a memory, a processor, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor is configured to execute the program to implement the steps in the method according to claim 1. ### Claim 8 (depends on 1) A processor, configured to execute a program, wherein the program is executed to implement the method according to claim 1.