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