BER and SER analyses for M-ary modulation schemes under symmetric alpha-stable noise

Symmetric alpha-stable (SαS) distribution has been widely used to model undesirable impulsive noise disturbance in many scenarios. Due to lack of probability density function (pdf) of SαS distribution (except Cauchy and Gaussian cases), the general closed-form expression of the bit error probability or symbol error probability for M-ary modulation schemes has not been derived yet, preventing the derivation of the exact coding gain from being feasible. By employing geometric power involved in zero-order statistics, we create a mapping mechanism which is consistently continuous along the entire range of characteristic values. Then we derive the accurate bit error probability and symbol error probability of M-ary modulation schemes under SαS noise. Our obtained derivations agree well with our simulations, which provide a unified framework for uncoded systems using M-ary modulation under additive white Gaussian noise (AWGN) and additive white symmetric alpha-stable noise (AWSαSN). Also, it enables the design of capacity approaching codes especially for higher-order modulation scenarios.