Adaptive nonlinear least bit error-rate detection for symmetrical RBF beamforming

Adaptive Fuzzy Neural Filtering for Decision Feedback Equalization and Multi-Antenna Systems

“…Moreover, BER performance of MMSE and MBER beamformers in the rank-deficient system will be very poor. Due to the nonlinear classification ability as mentioned in Section 1.1, the BBF realized by a RBF detector has shown a significant improvement over the MMSE and MBER ones, especially in the rank-deficient multi-antenna system [19], [47], [48]. Recently, a symmetric property of BBF [8] is exploited to design a novel symmetric RBF (SRBF) BF [47]- [48].…”

“…This SRBF BF can obtain better BER performance and simpler training procedure than the classical RBF one. Differing from the clustering method, the MBER method [47] based on a stochastic approximation of Parzen window density estimation also can be used to train the parameters of RBF as demonstrated in [47]. Unfortunately, RBF BF trained by an enhanced k-means clustering [48] or the MBER algorithm still needs large amounts of hidden nodes and training data to achieve satisfactory BER performance.…”

“…Note that the multi-antenna array model is completely the same as that in [6], [19], [46], [47], [57]. It is assumed that the system supports M users, and each user transmits a modulated signal on the same carrier frequency of ω = 2πf.…”

“…Traditionally, MMSE-based gradient descent methods are used for optimizing the parameters of a nonlinear detection [35], [38], [43], [44]. However, minimizing the MSE does not necessarily produce a low BER [5]- [9], [47] and hence an adaptive MBER-based gradient descent method recently has been proposed for a nonlinear structure [47]. In this chapter, we slightly modify the adaptive MBER method for the proposed SCFNN-related beamformers, which is summarized as follows.…”

“…In this chapter, we slightly modify the adaptive MBER method for the proposed SCFNN-related beamformers, which is summarized as follows. First, the decision variable = • is defined [47] and the probability density function of can be adaptively estimated by [47] …”