Reverse compute and forward: A low-complexity architecture for downlink distributed antenna systems

Abstract

We consider a distributed antenna system where L antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity R0, and serve K user terminals (UTs). This system model has been widely investigated both for the uplink and the downlink, which are instances of the general multiple-access relay and broadcast relay networks. In this work we focus on the downlink, and propose a novel downlink precoding scheme nicknamed "Reverse Quantized Compute and Forward"(RQCoF). For this scheme we obtain achievable rates and compare with the state-of-the-art available in the literature. We also provide simulation results for a realistic network with fading with K > L UTs, and show that channel-based user selection produces large benefits and essentially removes the problem of rank deficiency in the system matrix. 1 I. SYSTEM AND PROBLEM DEFINITIONWe consider a distributed antenna system (DAS) with K user terminals (UTs) and L "antenna terminals" (ATs). All UTs and ATs have a single antenna each. The ATs are connected with a central processor (CP) via wired links of fixed rate R 0 . We study the downlink scenario, where the CP wishes to deliver independent messages to the UTs. This is a simple instance of a broadcast relay network, where the ATs operate as relays. In this work we focus on the sum-rate and assume that the CP and all UTs have perfect channel state information (more general results are provided in [1]). If R 0 → ∞, the problem reduces to the well-known vector Gaussian broadcast channel, the capacity region of which is achieved by Dirty Paper Coding (DPC). However, for fixed finite R 0 , DPC and other widely considered linear precoding schemes cannot be applied in a straightforward manner. A simple DAS system, the so-called Soft-Handoff model, was investigated in [2], by introducing a "compressed" version of DPC (CDPC), where the CP performs joint DPC under per-antenna power constraint and then sends the compressed (or quantized) codewords to the corresponding ATs via the wired links. While this scheme is expected to be near-optimal for very large R 0 , it is generally suboptimal at finite (possibly small) R 0 . Also, DPC 1 This research was supported by the KCC (Korea Communications Commission), Korea, under the R&D program supervised by the KCA (Korea Communications Agency) (KCA-2012-11-921-04-001 performed by ETRI). is notoriously difficult to be implemented in practice, due to the nested lattice coding construction and lattice quantization steps involved (See for example [3], [4]).Motivated by Compute-and-Forward (CoF) [5] (or quantized compute-and-forward (QCoF) [6]), we propose a novel coding strategy named Reverse QCoF (RQCoF) for the DAS downlink with finite backhaul link capacity R 0 . In QCoF and RQCoF the coding block length n can be arbitrarily large but the shaping block length is restricted to 1 (scalar quantization [6]). However, we would like to point out that the same approach can be straightforwardly applied to CoF based schemes, where also the shaping...

Integer-Forcing Linear Receivers

“…It is well-suited to scenarios where a single receiver, equipped with multiple antennas, must recover multiple data streams (i.e., an uplink channel). Recent work has shown that the principles underlying integer-forcing can be applied in a broader context including downlink channels [50], [77] and interference channels [78]. In another line of work, integer-forcing was applied to the intersymbol interference channel by adding the requirement that the codebook is cyclic [51].…”

Uplink-Downlink Duality for Integer-Forcing

“…We employ a nested lattice codebook to ensure that the codebook is closed under integer-linear combinations so that the users can decode linear combinations of the transmitted codewords. Additionally, as first proposed by Hong and Caire [17], [18], we apply a precoding step over the finite field in order to "pre-invert" the linear combinations before mapping the messages to codewords. This step guarantees that the integerlinear combinations recovered by the users correspond to their desired messages.…”

“…This technique, which was first proposed by Hong and Caire [17], [18], allows each receiver to decode any integer-linear combination of the codewords in order to reduce the effective noise but still recover its desired message. These papers focused on the important special case where all users employ the same fine and coarse lattices, and thus have equal powers and must tolerate the worst effective noise across receivers.…”

“…In the MIMO MAC, these integer-linear combinations are solved for the original codewords [16]. In the MIMO BC, the transmitter applies the inverse linear transform to its messages prior to encoding, so that each integer-linear combination corresponds to the desired message of that user [17], [18]. Here, we demonstrate that integerforcing transceivers satisfy uplink-downlink duality for the sum rate in the sense of [10].…”

Physical Layer Network Coding Based on Integer Forcing Precoded Compute and Forward

“…The selection of integer coefficients of linear combination at the relay has been studied in [7], where the authors provide a scheme to choose sub-optimal integer coefficients without using CSI at the relay. Further, in [8,9], precoding-postcoding techniques have been studied in order to minimize the effects of the non-integer channel penalty in some scenarios, particularly, using the spatial orientation of signals.…”