Delay Performance of Wireless Communications With Imperfect CSI and Finite-Length Coding

Abstract

With the rise of critical machine-to-machine applications, next generation wireless communication systems must be designed with strict constraints on the latency and reliability. A key question in this context relates to channel state estimation, which allows the transmitter to adapt the code rate to the channel. In this work, we characterize the trade-off between the estimation sequence length and data codeword length: shorter channel estimation leaves more time for the actual payload transmission but reduces the estimation accuracy and causes more decoding errors. Using lower coding rates can mitigate this effect, but may result in a higher backlog of data at the transmitter. We analyze this trade-off using queueing analysis on top of accurate models of the physical layer, which also account for the finite blocklength of the channel code. Based on a novel closed-form approximation for the error probability given the rate, we show that finding the optimal rate adaptation strategy becomes a convex problem.The optimal rate adaptation strategy and the optimal training sequence length, which both depend on the latency and reliability constraints of the application, can improve the delay performance by an order of magnitude, compared to suboptimal strategies that do not consider those constraints. Index TermsFinite blocklength regime, imperfect CSI, rate adaptation, quasi-static fading, queueing analysisThe authors are with the

NOMA in the Uplink: Delay Analysis With Imperfect CSI and Finite-Length Coding

“…The actual channel coefficients H k are unknown, i.e., random. Given the MMSE estimatesĥ k , the actual channel coefficients are given as [21], [28]…”

“…andγ t,k denoting the SNR during the training phase of user k. The actual SNR Γ k =γ k |H k | 2 of signal k is then given as [21]:…”

“…With sufficient training, the estimation error is relatively small, i.e., |H k | |ĥ k |, and the last term becomes negligible. The term {e −j∠(ĥ k )H k } is Gaussian distributed with variance σ 2 Z,k /2, so we can approximate the distribution of the SNR Γ k of signal k as [21]…”

“…With respect to the delay performance, the effects of finite blocklength coding were studied in [19], [20]. In [21], we have studied the joint impact of imperfect CSI and finite blocklength effects on the delay performance of wireless systems, assuming a single-user single-antenna scenario.…”

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