Performance of polar codes with MIMO-OFDM under frequency selective fading channel

This paper presents the BER performance analysis of polar codes with MIMO-OFDM under frequency selective channel, which has not been disclosed so far. Multiple-input multiple-output (MIMO) has been widely implemented or standardized to improve the throughput performance of wireless communications. Forward error correction (FEC) codes are also key techniques for stably improving bit error rate (BER) and have been studied as well as a demodulation scheme. FEC is required to be composed of simple encoder and decoder while achieving good BER performance as much as possible. Polar codes emerged as a promising FEC scheme. This code has a simple recursive encoder structure by using a phenomenon called "channel polarization". In addition, it has been reported that polar codes provably achieve the theoretical limit for communication systems with a successive cancellation decoder based on likelihood ratio. An calculation complexity of polar codes is less than that of low density parity check (LDPC) codes. Therefore, polar codes are an effective technique in realizing low electric power consumption to meet one of the demand conditions of 5G. Based on legacy detection schemes as zero forcing (ZF) and maximum likelihood detection (MLD), computer simulation results reveal the fundamental BER performance with controlling coding rate. Moreover, there is a problem that the log likelihood ratio (LLR) of MLD detection for soft-decision decoding can not be obtained. Therefore, in this paper, we investigate the likelihood function of MLD detection in the proposed system.