Differential detection of quadrature frequency/phase modulated signals

This paper proposes a pilot-symbol-assisted (PSA) signaling format that enables the differential detection of the differentially phase-encoded quadrature frequency/phase modulated (NDQFPM) signal using N orthogonal frequencies. The PSA-NDQFPM signal is transmitted on a frame-by-frame structure. The channel considered is an additive white Gaussian noise channel where the channel phase varies so slowly that it is assumed constant over one frame duration. Each frame consists of J NQFPM pilot symbols and I data blocks, each containing L NDQFPM symbols, with the first symbol differentially phase encoded with respect to pilot symbols. Based on the maximum-likelihood sequence estimation principle, the maximum-likelihood differential-detection (ML-DD) algorithm is developed to detect the PSA-NDQFPM signal on a block-by-block basis. Tight upper and asymptotic bounds are derived and verified by simulation to evaluate the bit error performance of the ML-DD algorithm. Both bandwidth and power efficiencies of PSA-NDQFPM with ML-DD are compared to NQFPM with coherent detection, constant-envelope NQFPM with coherent detection, constant-envelope NDQFPM (also known as NFSK/4DPSK) with ML-DD, and conventional 2DQFPM (also known as DQ²PSK) with ML-DD. It is analytically shown that PSA-NDQFPM with ML-DD has lower power efficiency than NQFPM with coherent detection and NFSK/4DPSK with ML-DD, but still can provide noticeably higher power efficiency than DQ ²PSK with ML-DD when a medium frame length is used. Due to the use of pilot symbols, PSA-NDQFPM with a medium frame length has marginally lower bandwidth efficiency than its coherent counterpart NQFPM, but still yields significantly higher bandwidth efficiency than constant-envelope NQFPM and NFSK/4DPSK