Compute-and-Forward Strategies for Cooperative Distributed Antenna Systems

We study a distributed antenna system where $L$ antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity $R_0$, and serve $K$ user terminals (UTs). We contribute to the subject in the following ways: 1) for the uplink, we apply the "Compute and Forward" (CoF) approach and examine the corresponding system optimization at finite SNR; 2) For the downlink, we propose a novel precoding scheme nicknamed "Reverse Compute and Forward" (RCoF); 3) In both cases, we present low-complexity versions of CoF and RCoF based on standard scalar quantization at the receivers, that lead to discrete-input discrete-output symmetric memoryless channel models for which near-optimal performance can be achieved by standard single-user linear coding; 4) For the case of large $R_0$, we propose a novel "Integer Forcing Beamforming" (IFB) scheme that generalizes the popular zero-forcing beamforming and achieves sum rate performance close to the optimal Gaussian Dirty-Paper Coding. The proposed uplink and downlink system optimization focuses specifically on the ATs and UTs selection problem. We present low-complexity ATs and UTs selection schemes and demonstrate, through Monte Carlo simulation in a realistic environment with fading and shadowing, that the proposed schemes essentially eliminate the problem of rank deficiency of the system matrix and greatly mitigate the non-integer penalty affecting CoF/RCoF at high SNR. Comparison with other state-of-the art information theoretic schemes, such as "Quantize reMap and Forward" for the uplink and "Compressed Dirty Paper Coding" for the downlink, show competitive performance of the proposed approaches with significantly lower complexity.Comment: Submitted to IEEE Transactions on Information Theor

Structured Lattice Codes for 2 \times 2 \times 2 MIMO Interference Channel

We consider the 2\times 2\times 2 multiple-input multipleoutput interference channel where two source-destination pairs wish to communicate with the aid of two intermediate relays. In this paper, we propose a novel lattice strategy called Aligned Precoded Compute-and-Forward (PCoF). This scheme consists of two phases: 1) Using the CoF framework based on signal alignment we transform the Gaussian network into a deterministic finite field network. 2) Using linear precoding (over finite field) we eliminate the end-to-end interference in the finite field domain. Further, we exploit the algebraic structure of lattices to enhance the performance at finite SNR, such that beyond a degree of freedom result (also achievable by other means). We can also show that Aligned PCoF outperforms time sharing in a range of reasonably moderate SNR, with increasing gain as SNR increases.Comment: submitted to ISIT 201

On Interference Networks over Finite Fields

We present a framework to study linear deterministic interference networks over finite fields. Unlike the popular linear deterministic models introduced to study Gaussian networks, we consider networks where the channel coefficients are general scalars over some extension field \FF_{p^m} (scalar $m$-th extension-field models), $m \times m$ diagonal matrices over \FF_p ($m$-symbol extension ground-field models), and $m \times m$ general non-singular matrices (MIMO ground field models). We use the companion matrix representation of the extension field to convert $m$-th extension scalar models into MIMO ground-field models where the channel matrices have special algebraic structure. For such models, we consider the $2 \times 2 \times 2$ topology (two-hops two-flow) and the 3-user interference network topology. We derive achievability results and feasibility conditions for certain schemes based on the Precoding-Based Network Alignment (PBNA) approach, where intermediate nodes use random linear network coding (i.e., propagate random linear combinations of their incoming messages) and non-trivial precoding/decoding is performed only at the network edges, at the sources and destinations. Furthermore, we apply this approach to the scalar $2\times 2\times 2$ complex Gaussian IC with fixed channel coefficients, and show two competitive schemes outperforming other known approaches at any SNR, where we combine finite-field linear precoding/decoding with lattice coding and the Compute and Forward approach at the signal level. As a side result, we also show significant advantages of vector linear network coding both in terms of feasibility probability (with random coding coefficients) and in terms of coding latency, with respect to standard scalar linear network coding, in PBNA schemes.Comment: submitted to IEEE Transactions on Information Theor

On the Performance of Optimized Dense Device-to-Device Wireless Networks

We consider a D2D wireless network where $n$ users are densely deployed in a squared planar region and communicate with each other without the help of a wired infrastructure. For this network, we examine the 3-phase hierarchical cooperation (HC) scheme and the 2-phase improved HC scheme based on the concept of {\em network multiple access}. Exploiting recent results on the optimality of treating interference as noise in Gaussian interference channels, we optimize the achievable average per-link rate and not just its scaling law. In addition, we provide further improvements on both the previously proposed hierarchical cooperation schemes by a more efficient use of TDMA and spatial reuse. Thanks to our explicit achievable rate expressions, we can compare HC scheme with multihop routing (MR), where the latter can be regarded as the current practice of D2D wireless networks. Our results show that the improved and optimized HC schemes yield very significant rate gains over MR in realistic conditions of channel propagation exponents, signal to noise ratio, and number of users. This sheds light on the long-standing question about the real advantage of HC scheme over MR beyond the well-known scaling laws analysis. In contrast, we also show that our rate optimization is non-trivial, since when HC is applied with off-the-shelf choice of the system parameters, no significant rate gain with respect to MR is achieved. We also show that for large pathloss exponent the sum rate is a nearly linear function of the number of users $n$ in the range of networks of practical size. This also sheds light on a long-standing dispute on the effective achievability of linear sum rate scaling with HC. Finally, we notice that the achievable sum rate for large $\alpha$ is much larger than for small $\alpha$. This suggests that HC scheme may be a very effective approach for networks operating at mm-waves.Comment: Revised and resubmitted to IEEE Transactions on Information Theor

Two-Unicast Two-Hop Interference Network: Finite-Field Model

In this paper we present a novel framework to convert the $K$-user multiple access channel (MAC) over \FF_{p^m} into the $K$-user MAC over ground field \FF_{p} with $m$ multiple inputs/outputs (MIMO). This framework makes it possible to develop coding schemes for MIMO channel as done in symbol extension for time-varying channel. Using aligned network diagonalization based on this framework, we show that the sum-rate of $(2m-1)\log{p}$ is achievable for a $2\times 2\times 2$ interference channel over \FF_{p^m}. We also provide some relation between field extension and symbol extension.Comment: Submitted to ITW 201

A Supervised-Learning Detector for Multihop Distributed Reception Systems

We consider a multihop distributed uplink reception system in which $K$ users transmit independent messages to one data center of $N_{\rm r} \geq K$ receive antennas, with the aid of multihop intermediate relays. In particular, each antenna of the data center is equipped with one-bit analog-to-digital converts (ADCs) for the sake of power-efficiency. In this system, it is extremely challenging to develop a low-complexity detector due to the non-linearity of an end-to-end channel transfer function (created by relays' operations and one-bit ADCs). Furthermore, there is no efficient way to estimate such complex function with a limited number of training data. Motivated by this, we propose a supervised-learning (SL) detector by introducing a novel Bernoulli-like model in which training data is directly used to design a detector rather than estimating a channel transfer function. It is shown that the proposed SL detector outperforms the existing SL detectors based on Gaussian model for one-bit quantized (binary observation) systems. Furthermore, we significantly reduce the complexity of the proposed SL detector using the fast kNN algorithm. Simulation results demonstrate that the proposed SL detector can yield an attractive performance with a significantly lower complexity.Comment: Accepted to IEEE Transactions on Vehicular Technolog

A pairwise maximum entropy model describes energy landscape for spiral wave dynamics of cardiac fibrillation

Heart is an electrically-connected network. Spiral wave dynamics of cardiac fibrillation shows chaotic and disintegrated patterns while sinus rhythm shows synchronized excitation patterns. To determine functional interactions between cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the sequential electrical activity maps acquired from the 2D computational simulation of human atrial fibrillation. Then, we constructed energy landscape and estimated hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. Four types of the wave dynamics were considered: sinus rhythm; single stable rotor; single rotor with wavebreak; and multiple wavelet. The MEM could describe all types of wave dynamics (both accuracy and reliability>0.9) except the multiple random wavelet. Both of the sinus rhythm and the single stable rotor showed relatively high pairwise interaction coefficients among the cardiomyocytes. Also, the local energy minima had relatively large basins and high energy barrier, showing stable attractor properties. However, in the single rotor with wavebreak, there were relatively low pairwise interaction coefficients and a similar number of the local minima separated by a relatively low energy barrier compared with the single stable rotor case. The energy landscape of the multiple wavelet consisted of a large number of the local minima separated by a relatively low energy barrier, showing unstable dynamics. These results indicate that the MEM provides information about local and global coherence among the cardiomyocytes beyond the simple structural connectivity. Energy landscape analysis can explain stability and transitional properties of complex dynamics of cardiac fibrillation, which might be determined by the presence of 'driver' such as sinus node or rotor.Comment: Presented at the 62nd Biophysical Society Annual Meeting, San Francisco, California, 201

Supervised-Learning for Multi-Hop MU-MIMO Communications with One-Bit Transceivers

This paper considers a nonlinear multi-hop multi-user multiple-input multiple-output (MU-MIMO) relay channel, in which multiple users send information symbols to a multi-antenna base station (BS) with one-bit analog-to-digital converters via intermediate relays, each with one-bit transceiver. To understand the fundamental limit of the detection performance, the optimal maximum-likelihood (ML) detector is proposed with the assumption of perfect and global channel state information (CSI) at the BS. This multi-user detector, however, is not practical due to the unrealistic CSI assumption and the overwhelming detection complexity. These limitations are addressed by presenting a novel detection framework inspired by supervised-learning. The key idea is to model the complicated multihop MU-MIMO channel as a simplified channel with much fewer and learnable parameters. One major finding is that, even using the simplified channel model, a near ML detection performance is achievable with a reasonable amount of pilot overheads in a certain condition. In addition, an online supervised-learning detector is proposed, which adaptively tracks channel variations. The idea is to update the model parameters with a reliably detected data symbol by treating it as a new training (labelled) data. Lastly, a multi-user detector using a deep neural network is proposed. Unlike the model-based approaches, this model-free approach enables to remove the errors in the simplified channel model, while increasing the computational complexity for parameter learning. Via simulations, the detection performances of classical, model-based, and model-free detectors are thoroughly compared to demonstrate the effectiveness of the supervised-learning approaches in this channel.Comment: 32 pages, 6 figure

Uplink Multiuser Massive MIMO Systems with Low-Resolution ADCs: A Coding-Theoretic Approach

This paper considers an uplink multiuser massive multiple-input-multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs), in which K users with a single-antenna communicate with one base station (BS) with Nr antennas. In this system, we present a novel multiuser MIMO detection framework that is inspired by coding theory. The key idea of the proposed framework is to create a code C of length 2Nr over a spatial domain. This code is constructed by a so-called auto-encoding function that is not designable but is completely described by a channel transformation followed by a quantization function of the ADCs. From this point of view, we convert a multiuser MIMO detection problem into an equivalent channel coding problem, in which a codeword of C corresponding to users' messages is sent over 2Nr parallel channels, each with different channel reliability. To the resulting problem, we propose a novel weighted minimum distance decoding (wMDD) that appropriately exploits the unequal channel reliabilities. It is shown that the proposed wMDD yields a non-trivial gain over the conventional minimum distance decoding (MDD). From coding-theoretic viewpoint, we identify that bit-error-rate (BER) exponentially decreases with the minimum distance of the code C, which plays a similar role with a condition number in conventional MIMO systems. Furthermore, we develop the communication method that uses the wMDD for practical scenarios where the BS has no knowledge of channel state information. Finally, numerical results are provided to verify the superiority of the proposed method.Comment: Submitted to IEEE TW

A Novel Cooperative Strategy for Wireless Multihop Backhaul Networks

The 5G wireless network architecture will bring dense deployments of base stations called {\em small cells} for both outdoors and indoors traffic. The feasibility of their dense deployments depends on the existence of a high data-rate transport network that can provide high-data backhaul from an aggregation node where data traffic originates and terminates, to every such small cell. Due to the limited range of radio signals in the high frequency bands, multihop wireless connection may need to be established between each access node and an aggregation node. In this paper, we present a novel transmission scheme for wireless multihop backhaul for 5G networks. The scheme consists of 1) {\em group successive relaying} that established a relay schedule to efficiently exploit half-duplex relays and 2) an optimized quantize-map-and-forward (QMF) coding scheme that improves the performance of QMF and reduces the decoding complexity and the delay. We derive an achievable rate region of the proposed scheme and attain a closed-form expression in the asymptotic case for several network models of interests. It is shown that the proposed scheme provides a significant gain over multihop routing (based on decode-and-forward), which is a solution currently proposed for wireless multihop backhaul network. Furthermore, the performance gap increases as a network becomes denser. For the proposed scheme, we then develop energy-efficient routing that determines {\em groups} of participating relays for every hop. To reflect the metric used in the routing algorithm, we refer to it as {\em interference-harnessing} routing. By turning interference into a useful signal, each relay requires a lower transmission power to achieve a desired performance compared to other routing schemes. Finally, we present a low-complexity successive decoder, which makes it feasible to use the proposed scheme in practice.Comment: Parts of this paper will be presented at GLOBECOM 2015. arXiv admin note: text overlap with arXiv:1003.5966 by other author