Power Allocation Constraint and Error Rate Analysis for Multi-User PD-NOMA System Employing M–Ary PSK

This letter determines the power allocation constraint (PAC) for a
$K$
-user power domain non-orthogonal multiple access (PD-NOMA) system, where each user employs an identical
$M-$
ary phase-shift keying modulation scheme. The angular periphery method is used to derive the PAC that determines the range of the power allocation factor to ensure reliable error performance. Further, analytical expressions for the bit error rate (BER), average BER, and diversity order of
$K-$
user PD-NOMA are derived under Nakagami-
$m$
fading channel with the help of order statistics for a generalized value of
$M$
. Numerical results demonstrate the importance of the proposed PAC and display the appropriate water-falling nature of error rate curves when following the PAC. Moreover, the analysis also gives insight about the optimal value of the power allocation factor to minimize error performance.