Shaped O set QPSK Capacity

In this work we compute the capacities and the pragmatic capacities of militarystandard shaped-o set quadrature phase-shift keying (SOQPSK-MIL) and aeronautical telemetry SOQPSK (SOQPSK-TG). In the pragmatic approach, SOQPSK is treated as a modulation scheme as opposed to an encoder, and no iterations are performed between the SOQPSK demodulator and the outer binary decoder. We also evaluate the capacity of SOQPSK-TG constrained on a reduced complexity detection scheme based on the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM). The spectral efciency of the PAM based SOQPSK-TG (SOQPSK-TG-PAM) is computed and shown to be superior to that of SOQPSK-MIL despite having the same detection complexity. We also show that the natural mapping of SOQPSK between input bits and SOQPSK waveforms maximizes the pragmatic capacity. Any other mapping such as di erential encoding reduces the pragmatic capacity. We then focus on SOQPSK-TG due to its high spectral e ciency and present the performance results of a serially concatenated convolutional code (SCCC) SOQPSK-TG pragmatic scheme (SCCC-SOQPSK-TG), a low-density parity-check code (LDPC) SOQPSK-TG pragmatic scheme (LDPC-SOQPSK-TG), and a serially concatenated coded SOQPSK-TG scheme (SC-SOQPSK-TG). The LDPC scheme performs within 1.05 dB of the SOQPSK-TG capacity curve for various coding rates.