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Gallager Bounds for Noncoherent Decoders in Fading Channels

机译：衰落信道中非相​​干解码器的Gallager界

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摘要

Recently, Gallager''s bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound.
机译：最近，已使用Gallager的边界技术来推导衰落信道中编码系统的严格性能边界。迄今为止，该领域中的大多数工作都涉及相干解码。本文研究了衰落信道中非相​​干系统的Gallager界。与相干解码不同，以衰落系数为条件的非相干解码器/检测器的准确错误概率不允许采用封闭形式的表达式。本文采用Chernoff技术克服了这一困难。尽管Chernoff技术在一定程度上削弱了边界，但它可以推导非相干衰落信道的平均极限（LBA）边界和Gallager边界为封闭形式。数值算例表明，所提出的边界是收敛的，并且比常规的联合边界更紧密。

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