Optimal Throughput-Diversity-Delay Tradeoff in MIMO ARQ Block-Fading Channels

Abstract

In this paper, we consider an automatic-repeat-request (ARQ) retransmission protocol signaling over a block-fading multiple-input, multiple-output (MIMO) channel. Unlike previous work, we allow for multiple fading blocks within each transmission (ARQ round), and we constrain the transmitter to fixed rate codes constructed over complex signal constellations. In particular, we examine the general case of average input-power-constrained constellations as well as the practically important case of finite discrete constellations. This scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing techniques over a MIMO ARQ channel. Two cases of fading dynamics are considered, namely short-term static fading where channel fading gains change randomly for each ARQ round, and long-term static fading where channel fading gains remain constant over all ARQ rounds pertaining to a given message. As our main result, we prove that for the block-fading MIMO ARQ channel with discrete input signal constellation satisfying a short-term power constraint, the optimal signal-to-noise ratio (SNR) exponent is given by a modified Singleton bound, relating all the system parameters. To demonstrate the practical significance of the theoretical analysis, we present numerical results showing that practical Singleton-bound-achieving maximum distance separable codes achieve the optimal SNR exponent.A. Chuang is with the School

MIMO ARQ With Multibit Feedback: Outage Analysis

“…The outage performance of systems with K = 2, 3, 8, 16 is illustrated in Figure 5. We observe that the outage diversity achieved by constant transmit power and by power adaptation for K = 2 is 3 and 4 as given in (20) and (19), respectively. For K ≥ 3, the outage diversity is 5 as predicted from (16).…”

“…We numerically compare the optimal rate-diversity-delay over a block-fading channel with BL fading blocks [20]. From Theorem 1, the…”

“…This tradeoff has only been studied for INR-ARQ systems with one-bit ACK/NACK feedback in [19][20][21]. In particular, reference [19] characterizes the rate-diversity-delay tradeoff of Gaussian input MIMO INR-ARQ systems with both constant and adaptive transmit power.…”

“…In particular, reference [19] characterizes the rate-diversity-delay tradeoff of Gaussian input MIMO INR-ARQ systems with both constant and adaptive transmit power. Reference [20] studies the tradeoff for MIMO INR-ARQ systems with rotated discrete input constellation, which increases the system diversity at the cost of increasing signal constellation size and hence the decoding complexity. Inspired by [20], the results of [21] show that power adaptation offers significant gains in outage probability of INR-ARQ transmission.…”

“…Reference [20] studies the tradeoff for MIMO INR-ARQ systems with rotated discrete input constellation, which increases the system diversity at the cost of increasing signal constellation size and hence the decoding complexity. Inspired by [20], the results of [21] show that power adaptation offers significant gains in outage probability of INR-ARQ transmission. In this paper, we extend the results of [21] to INR-ARQ systems with multi-bit feedback [22].…”