The capacity of SOQPSK-TG

In this paper we compute the capacity and the pragmatic capacity of aeronautical telemetry shaped-offset quadrature phase-shift keying (SOQPSK-TG). In the pragmatic approach, SOQPSK-TG is treated as a modulation scheme as opposed to an encoder, and no iterations are performed between the SOQPSK-TG 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 efficiency of the PAM based SOQPSK-TG (SOQPSK-TG-PAM) is computed and shown to be superior to that of military-standard SOQPSK (SOQPSK-MIL) despite having the same detection complexity. We also show that the natural mapping of SOQPSK-TG between input bits and SOQPSK-TG waveforms maximizes the pragmatic capacity. Any other mapping such as differential encoding, reduces the pragmatic capacity. Finally, we present the performance results of a SCCC SOQPSK-TG pragmatic scheme, a LDPC SOQPSK-TG pragmatic scheme, and a SCCC scheme with SOQPSK-TG as the inner code. The LDPC scheme performs within 1.05 dB of the capacity curve for various coding rates.