Fast RLS algorithms in Combined Adaptive Array and Fractionally-Spaced Feed-Forward/Feed-Backward Equalizer

This paper considers the usage of the fast Recursive Least Squares (RLS) adaptive filtering algorithms for the weights calculation in the combined adaptive unit, which consists of an antenna array and a channel equalizer. The weights of the fractionally-spaced Feed-Forward (FF) filter of the equalizer are split and used simultaneously as the antenna array weights. The array output signal is combined with that of the Feed-Backward (FB) filter of the equalizer. Because the FF filter operates at the up-sampled rate and the FB filter of the equalizer operates at the symbol rate, the multichannel fast RLS algorithms cannot be used in the considered adaptive unit directly. It is proposed to use a polyphase representation of the FF filter to solve this problem. In this case, the architecture of the adaptive unit is presented as a multichannel adaptive filter with unequal number of weights in channels. The paper considers the architecture of the adaptive unit and the details of its FF part. The mathematical details of the multichannel fast RLS algorithm (Fast Kalman, FK), used for the adaptive unit weights calculation, are presented. The simulation of the array/equalizer demonstrates the ability of the proposed unit to steer the main lobe of the antenna array radiation pattern towards the desired signal source without a priory search of the source angular location and, at the same time, to remove the signals of the external interferences and the intersymbol interference in the array output signal. The simulation has been carried out, using a linear array with 16 omnidirectional antennas. It operates in the condition of -30 dB Signal-to-Interference Ratio and 10...30 dB Signal-to-Noise Ratio. The array receives the Phase Shift Keying (8-PSK) desired signal, passed through a two-rays communication channel with about -65 dB gaps in the channel amplitude-frequency response.