Research On Optimal Signal Design Strategy In Multi-User System Based On Widely Linear Model

The improper Gaussian signaling(IGS)has attracted increasing research interest due to its contribution to the performance improvement of the communication system recently.Different from the conventional proper Gaussian signaling(PGS),the IGS introduces the pseudo-covariance,which brings about additional degree of freedom.It is obvious that traditional signal processing methods are based on the properness of the transmit signal,which is unable to fully exploit improperness(in other words,the correlation characters of pseudo-random signal)of complex-valued signal.On the contrary,the optimum methods based on particular criterions are developed for these problems by applying the widely linear model to fully exploit the real and imaginary parts of complex-valued signal.Thus,we also propose widely linear(WL)precoding,which efficiently maps proper informationbearing signals to improper transmitted signals for any given pair of transmit covariance and pseudo-covariance matrices,to maximize the capacity of multi-user communication systems.Z-Interference Channel(Z-IC)and X-Interference Channel(X-IC)are two common interference channels,this thesis conducts numerous research on the optimal signals design strategy to enlarge the capacity of multi-user communication systems in various interference conditions.The main work and contributions are summarized as follows:Considering the improvement of the capacity in the Z-IC,a thoroughly optimal signal design strategy is proposed to achieve the Pareto boundary(boundary of the achievable rate region)with IGS,which is under the assumption that the interference was treated as Gaussian noise.Specifically,we show that the Pareto boundary has two different schemes determined by the two paths characterizing the improperly transmitted signals.Moreover,several concise closed-form expressions for calculating each user's optimal transmitted power,covariance,and pseudo-covariance of improperly transmitted signals are deduced in each scheme.The effectiveness of the proposed optimal signal design strategy is supported by simulation experiments,which also clearly show the superiority of IGS.This thesis also provides a simple way to achieve the required rate region by the proposed optimal signal design strategy.With which,we also go deeper into acquiring a closed-form solution for quickly finding the optimal circularity coefficient that maximizes the sum rate.Finally,we provide an intensive discussion of the structure of the Pareto boundary,which is characterized by the degree of impropriety measured by the covariance and the pseudo-covariance of transmit signals.Considering the condition of applying the improper IGS in X-IC,this paper investigates the achievable rate region of the channels.Different from conventional PGS,whose achievable rate depends on the input signals' covariances only,the capacity of channels with IGS is a function with the signals' covariances and pseudo-covariances,which can be concluded from Shannon's theorem.Thus,the additional degree of freedom provided by pseudo-covariance,which is conventionally set to be zero with PGS,is available to improve the achievable rate.By treating the interference as Gaussian noise,we analyze the mathematical expression of capacity.Particularly,for the case of two-user simple input,simple output(SISO)-IC,we propose two thoroughly optimal signaling schemes in terms of covariances and pseudo-covariances to achieve the Pareto boundary in situations of employing PGS and employing IGS,respectively.Numerical simulation results show that the proposed signaling strategies can achieve higher achievable rate.Furthermore,a closed-form expression is derived for the optimal signaling parameters,hence,the proposed scheme takes less computational complexity.Finally,we give an in-depth discussion about the structure of the Pareto boundary,which is characterized by the degree of impropriety measured by the covariance and the pseudo-covariance of signals transmitted by two users.