In medium-size Massive MIMO systems, the minimum mean square error parallel interference cancellation (MMSE-PIC) based Soft-Input Soft-Output (SISO) detector is often used due to its relatively low complexity and good bit error rate (BER) performance. The computational complexity of MMSE-PIC for detecting a block of data is dominated by the computation of a Gram matrix and a matrix inversion. They have computational complexity of O(K 2 M) and O(K 3), respectively, where K is the number of uplink users with one transmit antenna each and M is the number of receive antennas at the base station. In this letter, by using an L (typically L ≤ 3) terms of Neumann series expansion to approximate the matrix inversion, we reduce the total computational complexity to O(LKM). Compared with alternative algorithms which focus on reducing the complexity of the matrix inversion only, the proposed method can also avoid calculating the Gram matrix explicitly and thus significantly reducing the total complexity.
This paper presents a theoretical boundedness and convergence analysis of online gradient method for the training of two-layer feedforward neural networks. The well-known linear difference equation is extended to apply to the general case of linear or nonlinear activation functions. Based on this extended difference equation, we investigate the boundedness and convergence of the parameter sequence of concern, which is trained by finite training samples with a constant learning rate. We show that the uniform upper bound of the parameter sequence, which is very important in the training procedure, is the solution of an inequality regarding the bound. It is further verified that, for the case of linear activation function, a solution always exists and, moreover, the parameter sequence can be uniformly upper bounded, while for the case of nonlinear activation function, some simple adjustment methods on the training set or the activation function can be derived to improve the boundedness property. Then, for the convergence analysis, it is shown that the parameter sequence can converge into a zone around an optimal solution at which the error function attains its global minimum, where the size of the zone is associated with the learning rate. Particularly, for the case of perfect modeling, a strong global convergence result, where the parameter sequence can always converge to an optimal solution, is proved.
In an orthogonal frequency division multiplexing (OFDM) system, the linear-minimum-mean-square-error (LMMSE) based channel estimator often requires a matrix inversion with cubic complexity. In this letter, by employing a K terms Neumann series expansion to approximate the matrix inversion, the computational complexity is reduced to O(N log L) per channel realization where N is the number of subcarriers and L is the number of non-zero time domain channel taps. Extensive simulation results show that even with small K (K ≤ 2), the performance loss caused by the proposed approximation is marginal.
To achieve time synchronization in underwater networks, a linear regression is often applied over a set of sendingreceiving timestamps, assuming the participating timestamps are consistent. In this paper, we show that collisions, which are not uncommon during signal exchange in underwater environment, would lead to inconsistent timestamps. These inconsistent timestamps are outliers. However, existing synchronization approaches ignore the presence of outliers. To obtain a reliable synchronization, we propose a robust algorithm that identifies and eliminates the outliers by employing Cook's distance before applying linear regression. We justify the proposed algorithm in a mobile underwater environment through extensive simulations.
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