ITC/USA 2006 Conference Proceedings / The Forty-Second Annual International Telemetering Conference and Technical Exhibition / October 23-26, 2006 / Town and Country Resort & Convention Center, San Diego, California / The optimum detector for shaped offset QPSK (SOQPSK) is a trellis detector which has high complexity (as measured by the number of detection filters and trellis states) due to the memory inherent in this modulation. In this paper we exploit the cross-correlated, trellis-coded, quadrature modulation (XTCQM) representation of SOQPSK-TG to formulate a reduced complexity detector. We show that a factor of 128 reduction in the number of trellis states of the detector can be achieved with a loss of only 0.2 dB in bit error rate performance as compared to optimum at P(b) = 10^(-5).