15.2 Threshold Detection Performance of GMSK Signal with BT=0.5

This paper considers the detection performance of a serial thresholding receiver for preceded bina~ GMSK signal with BT=O. 5. The conditional symbol (biij error probability of the GMSK signal with carrier phase and timing errors is derived and compared to that of unfiltered BPSK. It is shown that the GMSK signal has practically the same performance as the ideal BPSK signal in the absence of sync errors and that the GMSK signal is more sensitive to carrier phase error but much more robust to symbol timing error than is the BPSK signal. INTRODUCTION Gaussian filtered minimum shift keying is a member of the class of continuous phase modulation signal with a constant signal envelope and a spectrum that can be made compact with the appropriate choice of the signal BT product. The constant envelope GMSK signals can be amplified by saturated amplifiers without the concomitant spectral regrowth of filtered PSK signals. These properties make GMSK an attractive signal to use in frequency division multiple access communication systems where the transmitters are operated at maximum power output efficiency. This paper assesses the detection performance of a GMSK signal with BT=0.5 for a serial receiver operating with or without symbol timing or carrier phase errors. The performance analysis is based on a Pulse Amplitude Modulation (PAM) representation of the complex envelope of the GMSK signal attributed to Laurent [1], as well as a simple preceding algorithm for absolute phase encoding described in the next section. The paper is organized into five sections. After describing the GMSK communication system and its components in the next section, we derive in the third section the symbol error probability performance of the receiver. The fourth section presents numerical performance results of the receiver and compares these performance to those of unfiltered BPSK. The fifth section concludes the paper. SYSTEM DESCRIPTION Figure 1 shows a diagram of the GMSK communication system. The system consists of a data source, a data precoder, a GMSK modulator, a communication channel, a receiver, and a data sink. Descriptions of the GMSK modulator, data precoder, and receiver follow. d!i ‘ {*’} ak =(–l)kd d k k-1