In this paper, new sum-of-sinusoids statistical simulation models are proposed for Rayleigh fading channels. These new models employ random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and cross correlations of the quadrature components, and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly, even if the number of sinusoids is as small as a single-digit integer. Moreover, the probability density functions of the envelope and phase, the level crossing rate, the average fade duration, and the autocorrelation of the squared fading envelope which contains fourth-order statistics of the new simulators, asymptotically approach the correct ones as the number of sinusoids approaches infinity, while good convergence is achieved even when the number of sinusoids is as small as eight. The new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels, multiple-input multiple-output channels, and diversity combining scenarios. Statistical properties of one of the new simulators are evaluated by numerical results, finding good agreements.

An improved sum-of-sinusoids simulation model is proposed for Rayleigh fading channels. The new model employs random initial phase, and conditional random Doppler frequency for all individual sinusoids. The second-order statistics of the new simulator match the desired ones exactly even if the number of sinusoids is a single-digit integer. Other key statistics of the new simulator approach the desired ones of Clarke's (1968) reference model as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Moreover, the new simulator can be directly used to generate multiple uncorrelated fading waveforms; it is also pointed out that a class of 16 different simulators, which have identical statistical properties, can be developed for Rayleigh fading channels.

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to the L ₁-norm optimization criterion while using multiple projections. The features of the APA and the L ₁-norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.

We study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex-valued vector channels. This mutual information is a nonlinear and non-concave function of the precoder parameters, posing a major obstacle to precoder design optimization. Our work presents three main contributions: First, we prove that the mutual information is a concave function of a matrix which itself is a quadratic function of the precoder matrix. Second, we propose a parameterized iterative algorithm for finding optimal linear precoders to achieve the global maximum of the mutual information. The proposed iterative algorithm is numerically robust, computationally efficient, and globally convergent. Third, we demonstrate that maximizing the mutual information between a discrete constellation input and the corresponding output of a vector channel not only provides the highest practically achievable rate but also serves as an excellent criterion for minimizing the coded bit error rate. Our numerical examples show that the proposed algorithm achieves mutual information very close to the channel capacity for channel coding rate under 0.75, and also exhibits a large gain over existing linear precoding and/or power allocation algorithms. Moreover, our examples show that certain existing methods are susceptible to being trapped at locally optimal precoders.

The statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency

Reservoir computing (RC) is a class of neuromorphic computing approaches that deals particularly well with time-series prediction tasks. It significantly reduces the training complexity of recurrent neural networks and is also suitable for hardware implementation whereby device physics are utilized in performing data processing. In this paper, the RC concept is applied to detecting a transmitted symbol in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Due to wireless propagation, the transmitted signal may undergo severe distortion before reaching the receiver. The nonlinear distortion introduced by the power amplifier at the transmitter may further complicate this process. Therefore, an efficient symbol detection strategy becomes critical. The conventional approach for symbol detection at the receiver requires accurate channel estimation of the underlying MIMO-OFDM system. However, in this paper, we introduce a novel symbol detection scheme where the estimation of the MIMO-OFDM channel becomes unnecessary. The introduced scheme utilizes an echo state network (ESN), which is a special class of RC. The ESN acts as a black box for system modeling purposes and can predict nonlinear dynamic systems in an efficient way. Simulation results for the uncoded bit error rate of nonlinear MIMO-OFDM systems show that the introduced scheme outperforms conventional symbol detection methods.