Analytical Models for the Computation of Error Probability of Multi-Level Phase Shift Keying Modulation Scheme

Abstract

In this paper, analytical models for the computation of error probability (BER) of the Multi-level Phase Shift Keying (MPSK) modulation scheme is presented. Analytical models for computing MPSK bit error probability based on Q function, error function (erf) and complementary error function (erfc) are presented. Also, an analytical model for computing the symbol error rate for MPSK is presented. Furthermore, a generalized analytical expression for BER as a function of modulation order (M) and energy per bit to noise power density ratio (Eb/No) is presented. The BER was computed for various values of M (2 ≤ M ≤ 256) and Eb/No (0 dB ≤ Eb/No ≤ 14 Db). The results showed that at Eb/No =12 dB, a BER of 9.006E-09 is realized for M =2 and M =4 whereas BER of 1.056E-01 is realized for M = 256. Also, for the same M = 2 , the value of BER decreased from 1.2501E-02 at Eb/No = 4 dB to 9.0060E-09at Eb/No =12 dB. Generally, the results showed that for the MPSK modulation scheme, for a given value of Eb/No, the lower modulation order (M) has a lower BER and for a given modulation order, (M) the BER decreases as Eb/No increases.