A Sphere Decoder with Approximate QR Decomposition for Frequency-Selective Channels

This paper presents a method to significantly reduce the preprocessing complexity of the sphere decoder (SD) in frequency-selective channels. The method consists of calculating an approximate QR decomposition (AQRD) of the channel matrix, making use of its special Toeptliz and block-Topelitz structure in single and multiple-antenna frequency-selective channels, respectively. The AQRD obtains the QR decomposition of a small submatrix of the channel matrix and extends that result to the rest of the matrix, resulting in a considerable complexity reduction compared to the original full QR decomposition (FQRD). Simulation results show that, despite the lower complexity of the AQRD, it causes only a small bit error rate (BER) performance degradation in the SD.