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.

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关于使用低分辨率量化最小化衰落信道上的符号错误率

我们分析了符号错误概率（SEP） 百万美元 -ary 脉冲幅度调制 ( 百万美元 -PAM) 接收器配备了最佳的低分辨率量化器。我们首先表明最佳检测器可以简化为一个简单的决策规则。使用这种简化，量化的精确 SEP 表达式 百万美元 -PAM 接收器是在 Nakagami- 时获得的 百万美元 考虑衰落信道。导出的表达式能够在最小 SEP 标准下优化量化器和/或星座。我们对等距最优量化的分析 百万美元 -PAM 接收器揭示了错误底限的存在，该错误底限随着量化比特的增加以双指数速率衰减， $b$ . 此外，通过还允许发射机根据衰落信道的统计数据优化星座图，我们证明可以消除错误本底，但衰减指数低于未量化的情况。本文提供了此衰减指数的表征。我们还揭示了 SEP 最佳均匀量化器的中断性能限制。更准确地说，它的衰减指数不会随着 $b$ . 最后，我们证明了量化接收器的衰减指数可以通过接收天线分集技术来补充。