High-order circular QAM constellation with high LDPC coding rate for phase noise channels

This paper proposes a design for a high-order circular quadrature amplitude modulation (QAM) constellation using partial low-density parity-check (LDPC) coding associated with parallel double Gray mapping aiming at the application to a microwave radio backhaul to deal with time-varying phase noise channels. In the proposed circular QAM constellation design, we first design the best constellation in which the same number of signal points is mapped to all concentric rings. Then, we decrease the number of signal points in the inner rings and remap the signal points to the newly added rings outside the original rings while maintaining high affinity to the double Gray mapping feature. Computer simulation results show that partial LDPC coding with double Gray mapping decreases the required received signal-to-noise power ratio (SNR) at the bit error rate (BER) of 10−6 by approximately 0.2 dB compared to full LDPC coding for a high LDPC coding rate such as 0.9. We also show that the proposed circular 1024QAM decreases the required received SNR at the average BER of 10−6 by approximately 0.5 dB compared to that for rectangular 1024QAM.