Fading Channels: Capacity and Channel Coding Rate in the Finite-Blocklength Regime
Fading Channels: Capacity and Channel Coding Rate in the Finite-Blocklength Regime
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衰落信道：有限块长度机制中的容量和信道编码率
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发表时间：
2015
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通讯作者：
Wei Yang
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文献类型：
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作者：
Wei Yang
无线衰落信道通信基本极限的信息论研究通常依赖于简化的假设，如完美的信道状态信息（CSI），无限的块长度，和错误的消失概率。虽然这些假设对于大多数当前无线通信系统是合理的，但是对于下一代无线系统它们可能是不准确的。事实上，下一代无线系统将需要支持更广泛的功能，例如超高数据速率、极低延迟和低能耗，对于这些功能，上面列出的假设可能无效。这篇论文在一组与未来无线系统更相关的假设下，研究衰落信道的基本限制。
首先，我们描述了瑞利块衰落多输入多输出（MIMO）信道的容量没有先验CSI在发送器和接收器在高信噪比制度。我们表明，酉空时调制，这是容量实现的MIMO系统具有少量的天线，是不是容量实现时，天线的总数超过衰落信道的相干时间，这种情况是相关的大型MIMO系统。我们还提供了输入分布，实现大MIMO衰落信道的容量。
其次，我们研究了MIMO准静态衰落信道上给定块长度和错误概率的最大可达速率，受到对发送码字的不同功率约束：短期（即，每码字）功率约束和长期（即，所有码字的平均值）功率约束。对于短期功率约束的信道，我们证明了中断容量-尽管是一个渐近量-是一个尖锐的代理有限块长度的基本限制慢衰落信道。具体而言，信道色散-一个数量，衡量退避容量在有限块长度制度-被证明是零，无论是否衰落实现可用在发射机和/或接收机。当存在长期功率约束时，情况完全不同。在这种情况下，如果发射机具有完美CSI，则中断容量高于短期功率约束情况。然而，接近中断容量，需要更长的块长度的代码。在这两种情况下，我们开发了易于评估的近似的最大可实现的速率，并证明其准确性相比，nonasymptomatic可扩展性和匡威界。
最后，我们调查的最小能量需要发送$k$信息比特在MIMO瑞利块衰落信道，在接收机有和没有CSI的给定的可靠性。众所周知，当k趋于无穷大时，每比特的最小能量与噪声电平之间的比率收敛到k-1.59 dB，而不管CSI在接收机处是否可用。我们表明，缺乏CSI在接收器导致收敛速度减慢到$-1.59$ dB作为$k 与完美接收机CSI的情况相比，具体地，在无CSI的情况下，到$-1.59$ dB的差距与$（（log k）/k）^{1/3}$成比例，而当在接收器处有完美CSI可用时，该间隙与$1/sqrt{k}$成比例。
Information-theoretic studies on the fundamental limits of communication over wireless fading channels typically rely on simplifying assumptions, such as perfect channel state information (CSI), infinite blocklength, and vanishing probability of error. Although these assumptions are reasonable for most of the current wireless communication systems, they may be inaccurate for next-generation wireless systems. Indeed, next-generation wireless systems will need to support a much wider range of features, such as ultra-high data rate, extremely low latency, and low energy consumption, for which the assumptions listed above may not be valid. This thesis investigates the fundamental limits of fading channels under a set of assumptions that are more relevant for future wireless systems.
First, we characterize the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels with no a priori CSI at the transmitter and the receiver in the high signal-to-noise ratio regime. We show that unitary space time modulation, which is capacity-achieving for MIMO systems with a small number of antennas, is not capacity-achieving when the total number of antennas exceeds the coherence time of the fading channel, a situation that is relevant for large-MIMO systems. We also provide the input distribution that achieves the capacity of large-MIMO fading channels.
Second, we study the maximal achievable rate for a given blocklength and error probability over MIMO quasi-static fading channels, subject to different power constraints on the transmitted codewords: the short-term (i.e., per-codeword) power constraint and the long-term (i.e., average-over-all-codeword) power constraint. For channels subject to a short-term power constraint, we prove that outage capacity---despite being an asymptotic quantity---is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion---a quantity that measures the backoff from capacity in the finite-blocklength regime---is shown to be zero regardless of whether the fading realizations are available at the transmitter and/or the receiver. The situation is drastically different when a long-term power constraint is present. In this case, if the transmitter has perfect CSI, then the outage capacity is higher than in the short-term power constraint case. Approaching the outage capacity, however, requires codes with much longer blocklengths. In both cases, we develop easy-to-evaluate approximations for the maximal achievable rate and demonstrate their accuracy by comparison to nonasymptotic achievability and converse bounds.
Finally, we investigate the minimum energy required to transmit $k$ information bits with a given reliability over a MIMO Rayleigh block-fading channel, with and without CSI at the receiver. It is well known that the ratio between the minimum energy per bit and the noise level converges to $-1.59$ dB as $k$ goes to infinity, regardless of whether CSI is available at the receiver or not. We show that lack of CSI at the receiver causes a slowdown in the speed of convergence to $-1.59$ dB as $k oinfty$ compared to the case of perfect receiver CSI. Specifically, in the no-CSI case, the gap to $-1.59$ dB is proportional to $((log k) /k)^{1/3}$, whereas when perfect CSI is available at the receiver, this gap is proportional to $1/sqrt{k}$.