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.

In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) increases as e increases. Particularly, n increased from 2 at e = 0.01 to n = 8 at e =1. The implication is that it takes more iterations to arrive at the value of E with the desired accuracy or error performance (which in this case is set to 10^(-12)). Another implication is that a good choice of the initial value of E is essential especially as the value of e increases. As such, effort should be made to develop a means of estimating the initial value of E which will reduce the convergence cycle for higher values of e.