On Minimizing Symbol Error Rate Over Fading Channels With Low-Resolution Quantization

We analyze the symbol error probability (SEP) of $M$-ary pulse amplitude modulation ($M$-PAM) receivers equipped with optimal low-resolution quantizers. first show that optimum detector can be reduced to a simple decision rule. Using this simplification, an exact SEP expression for quantized $M$-PAM is obtained when Nakagami-$m$ fading channel considered. The derived enables optimization quantizer and/or constellation under minimum criterion. Our analysis quantization equidistant receiver reveals existence floor which decays at double exponential rate increasing bits, $b$. Moreover, by also allowing transmitter optimize based on statistics channel, we prove eliminated but lower decay exponent than unquantized case. Characterization provided in paper. expose outage performance limitations SEP-optimal uniform To more precise, its does not improve Lastly, demonstrate complemented receive antenna diversity techniques.