This paper considers the problem of reliable communication over discrete-timechannels whose impulse responses have length $L$ and exactly $S\leq L$ non-zerocoefficients, and whose support and coefficients remain fixed over blocks of$N>L$ channel uses but change independently from block to block. Here, it isassumed that the channel's support and coefficient realizations are bothunknown, although their statistics are known. Assuming Gaussiannon-zero-coefficients and noise, and focusing on the high-SNR regime, it isfirst shown that the ergodic noncoherent channel capacity has pre-log factor$1-\frac{S}{N}$ for any $L$. It is then shown that, to communicate witharbitrarily small error probability at rates in accordance with the capacitypre-log factor, it suffices to use pilot-aided orthogonal frequency-divisionmultiplexing (OFDM) with $S$ pilots per fading block, in conjunction with anappropriate noncoherent decoder. Since the achievability result is proven usinga noncoherent decoder whose complexity grows exponentially in the number offading blocks $K$, a simpler decoder, based on $S+1$ pilots, is also proposed.Its $\epsilon$-achievable rate is shown to have pre-log factor equal to$1-\frac{S+1}{N}$ with the previously considered channel, while its achievablerate is shown to have pre-log factor $1-\frac{S+1}{N}$ when the support of theblock-fading channel remains fixed over time.
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机译：本文考虑了离散时间信道上的可靠通信问题，该离散时间信道的脉冲响应长度为$ L $，正好为$ S \ leq L $非零系数，并且其支持和系数在$ N> L $信道使用的块上保持固定，但逐块独立更改。这里，假设信道的支持和系数实现都是未知的，尽管它们的统计信息是已知的。假设高斯非零系数和噪声，并关注高SNR体制，首先表明遍历非相干信道容量对任何$ L $具有对数对数$ 1- \ frac {S} {N} $。然后表明，要以与容量前对数因子相对应的速率以任意小的错误概率进行通信，就足以使用每个衰落块具有$ S $个导频的导频辅助正交频分多路复用（OFDM），以及适当的速率。非相干解码器。由于使用非相干解码器证明了可实现性结果，该非相干解码器的复杂度在越界块$ K $中呈指数增长，因此还提出了一种基于$ S + 1 $导频的更简单的解码器。具有先前考虑的通道的对数前因子等于$ 1- \ frac {S + 1} {N} $，而其可实现速率显示为具有对数前因子$ 1- \ frac {S + 1} {N} $当衰落信道的支持随着时间的过去保持固定时。
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