Demodulation Of Faster-Than-Nyquist Signaling Based On Recurrent Neural Network

Traditional communication theory states that when the signal transmission rate exceeds the Nyquist rate,the inter-symbol interference will lead to decreased communication performance,so in reality orthogonal modulation is often preferred.Mazo discovered in 1975 that when the transmitted pulse is an ideal sine pulse,the normalized minimum Euclidean distance of the signal keeps unchanged at a symbol rate of no more than 25%of the Nyquist rate,so similar performance can be obtained at high signal-to-noise ratio region,and called this technology FTN(Faster-Than-Nyquist)Signaling.When using non-sinc pulse modulation,FTN Signaling can provide higher system capacity than Nyquist rate transmission,showing great potential.This paper mainly studies the theory of FTN Signaling,and focuses on the recurrent neural network based FTN demodulation.FTN Signaling introduces inter-symbol interference,so MLSE is required in order to obtain the optimal performance.MLSE requires exact channel information and the complexity is too high which is often unaffordable in reality.The neural network based FTN demodulation can be trained directly according to the training data and the received signal.The traditional demodulation requires matching filtering,whitening,equalization,decision and other steps,and the neural network can be trained end-to-end,which may get better use of real environment,showing great potential.In this paper,the feasibility of recurrent neural network based FTN demodulation is verified by simulation.The performance of neural network under different parameters is simulated.Firstly,the theory of FTN Signaling is analyzed and studied in detail.The concept of FTN Signaling is introduced and its Mazo limit is analyzed.Then we introduce and analyze the concept of constrained channel capacity,establish the discrete model of FTN transmission,analyze the property of observation matrix in discrete model,discuss MLSE detection of FTN transmission together with two simple linear equalization algorithm,and simulate and analyze the performance of these algorithms.Secondly,the neural network model is analyzed and studied.The feedforward neural network and the recurrent neural network are introduced.The matrix form of the back propagation algorithm is deduced.Variants of gradient descent based algorithms are introduced.We train a Softmax regression model to demodulate BPSK singal and compare the result with ideal error performance.Finally,the demodulation of FTN Signaling by using forward neural network and recurrent neural network is studied.The Softmax regression model is compared with linear equalization method,both showing limitation in cancelling the inter-symbol interference introduced by the FTN signaling.The MLP model and the RNN model based demodulation is studied in detail with parameters,it is found that the with enough training data,both model can achieve near-optimal performance,and RNN can achieve near-ideal bit error rate performance with very few parameters,which verifies the feasibility of RNN in demodulation in FTN Signaling.