Incompatibility of Trellis-Based NonCoherent SOQPSK Demodulators for Use in FEC Applications

Abstract

Abstract : This paper examines the compatibility/incompatibility of trellis-based noncoherent shaped offset quadrature phase shift keying (SOQPSK) demodulators for use in forward error correction (FEC) applications. The noncoherent demodulators are of the type given in [1, 2]. These demodulators do not explicitly estimate and track the phase offset in the received signal, as is done by a coherent demodulator. Instead, they have implicit phase estimators associated with each state (survivor) in the trellis. We show, however, that these implicit phase estimators still lock onto the carrier phase, in a manner similar to that of a coherent demodulator. Furthermore, because of the extremely low signal-to-noise ratio (SNR) in FEC applications, the phase lock sometimes slips by 180 degrees, which causes the demodulator output symbols to be inverted. We show that this is a relatively minor problem for a serially concatenated convolutional code (SCCC), mainly because the SCCC system uses differential encoding and this encoding is immune to 180 degree phase shifts. On the other hand, a low density parity check (LDPC) coded system does not use differential encoding. Thus, in LDPC systems the 180 degree phase shift proves to be quite catastrophic. The solution to this problem is to adjust the forgetting factor parameter of the noncoherent detector to a value that yields a tighter phase lock. However, this diminishes the noncoherent nature of the demodulator. Therefore, another way of stating our conclusion is that coherent demodulators should be used in FEC applications, especially those using LDPC codes. In the end, while disappointing, this conclusion does not come as a major surprise, because one would not expect noncoherent demodulation to be applicable when differential encoding is not used.