Physical Layer Cooperation:Theory and Practice

Information theory has long pointed to the promise of physical layer cooperation in boosting the spectral efficiency of wireless networks. Yet, the optimum relaying strategy to achieve the network capacity has till date remained elusive. Recently however, a relaying strategy termed Quantize-Map-and-Forward (QMF) was proved to achieve the capacity of arbitrary wireless networks within a bounded additive gap. This thesis contributes to the design, analysis and implementation of QMF relaying by optimizing its performance for small relay networks, proposing low-complexity iteratively decodable codes, and carrying out over-the-air experiments using software-radio testbeds to assess real-world potential and competitiveness. The original QMF scheme has each relay performing the same operation, agnostic to the network topology and the channel state information (CSI); this facilitates the analysis for arbitrary networks, yet comes at a performance penalty for small networks and medium SNR regimes. In this thesis, we demonstrate the benefits one can gain for QMF if we optimize its performance by leveraging topological and channel state information. We show that for the N-relay diamond network, by taking into account topological information, we can exponentially reduce the QMF additive approximation gap from $\Theta(N)$ bits/s/Hz to $\Theta(\log N)$ bits/s/Hz, while for the one-relay and two-relay networks, use of topological information and CSI can help to gain as much as $6$ dB. Moreover, we explore what benefits we can realize if we jointly optimize QMF and half-duplex scheduling, as well as if we employ hybrid schemes that combine QMF and Decode-and-Forward (DF) relay operations. To take QMF from being a purely information-theoretic idea to an implementable strategy, we derive a structure employing Low-Density-Parity-Check (LDPC) ensembles for the relay node operations and message-passing algorithms for decoding. We demonstrate through extensive simulation results over the full-duplex diamond network, that our designs offer a robust performance over fading channels and achieves the full diversity order of our network at moderate SNRs. Next, we explore the potential real-world impact of QMF and present the design and experimental evaluation of a wireless system that exploits relaying in the context of WiFi. We deploy three main competing strategies that have been proposed for relaying, Amplify-and-Forward (AF), DF and QMF, on the WarpLab software radio platform. We present experimental results--to the best of our knowledge, the first ones--that compare QMF, AF and DF in a realistic indoor setting. We find that QMF is a competitive scheme to the other two, offering in some cases up to 12% throughput benefits and up to 60% improvement in frame error-rates over the next best scheme. We then present a more advanced architecture for physical layer cooperation (termed QUILT), that seamlessly adapts to the underlying network configuration to achieve competitive or better performance than the best current approaches. It combines on-demand, opportunistic use of DF or QMF followed by interleaving at the relay, with hybrid decoding at the destination that extracts information from even potentially undecodable received frames. We theoretically quantify how our design choices affect the system performance. We also deploy QUILT on WarpLab and show through over-the-air experiments up to $5$ times FER improvement over the next best cooperative protocol

Towards integrating Quantize-Map-Forward relaying into LTE

We present a method to integrate the Quantize-Map-Forward (QMF) relaying scheme [1] into the standard LTE operation, for a two-relay diamond network configuration. Our approach implements QMF using mainly existing LTE modules and functionalities, and results in minimal changes in the standard link-layer LTE operation. In particular, the destination operation is only affected in that we adapt the log-likelihood ratio (LLR) calculations at the decoder input to take into account the existence of relays; thus, the decoding complexity and operations (apart the LLR calculations) are not modified. We report extensive performance evaluations of our scheme using the OpenAirInterface (OAI) link-level simulation tools.(1

Low Complexity Scheduling and Coding for Wireless Networks

The advent of wireless communication technologies has created a paradigm shift in the accessibility of communication. With it has come an increased demand for throughput, a trend that is likely to increase further in the future. A key aspect of these challenges is to develop low complexity algorithms and architectures that can take advantage of the nature of the wireless medium like broadcasting and physical layer cooperation. In this thesis, we consider several problems in the domain of low complexity coding, relaying and scheduling for wireless networks. We formulate the Pliable Index Coding problem that models a server trying to send one or more new messages over a noiseless broadcast channel to a set of clients that already have a subset of messages as side information. We show through theoretical bounds and algorithms, that it is possible to design short length codes, poly-logarithmic in the number of clients, to solve this problem. The length of the codes are exponentially better than those possible in a traditional index coding setup. Next, we consider several aspects of low complexity relaying in half-duplex diamond networks. In such networks, the source transmits information to the destination through $n$ half-duplex intermediate relays arranged in a single layer. The half-duplex nature of the relays implies that they can either be in a listening or transmitting state at any point of time. To achieve high rates, there is an additional complexity of optimizing the schedule (i.e. the relative time fractions) of the relaying states, which can be $2^n$ in number. Using approximate capacity expressions derived from the quantize-map-forward scheme for physical layer cooperation, we show that for networks with $n\leq 6$ relays, the optimal schedule has atmost $n+1$ active states. This is an exponential improvement over the possible $2^n$ active states in a schedule. We also show that it is possible to achieve at least half the capacity of such networks (approximately) by employing simple routing strategies that use only two relays and two scheduling states. These results imply that the complexity of relaying in half-duplex diamond networks can be significantly reduced by using fewer scheduling states or fewer relays without adversely affecting throughput. Both these results assume centralized processing of the channel state information of all the relays. We take the first steps in analyzing the performance of relaying schemes where each relay switches between listening and transmitting states randomly and optimizes their relative fractions using only local channel state information. We show that even with such simple scheduling, we can achieve a significant fraction of the capacity of the network. Next, we look at the dual problem of selecting the subset of relays of a given size that has the highest capacity for a general layered full-duplex relay network. We formulate this as an optimization problem and derive efficient approximation algorithms to solve them. We end the thesis with the design and implementation of a practical relaying scheme called QUILT. In it the relay opportunistically decodes or quantizes its received signal and transmits the resulting sequence in cooperation with the source. To keep the complexity of the system low, we use LDPC codes at the source, interleaving at the relays and belief propagation decoding at the destination. We evaluate our system through testbed experiments over WiFi

Information Theoretic Limits of MIMO Interference and Relay Networks

In this thesis, the information theoretic performance limits of two important building blocks of the general multi-user wireless network, namely, the interference channel and the relay channel, are characterized. We consider both time-invariant and time-varying or fading channel. In the first part, we focus on the 2-user interference channel with time-invariant channel coefficients. First, we characterize the capacity region of a class of MIMO IC called strong in partial order ICs. It turns out that for this class of channels decoding both the messages at both the receivers is optimal, i.e., the capacity region is identical to that of the compound multiple access channel (MAC). The defining constraints on the channel coefficients for the class of strong in partial order ICs enable us to derive a novel tight upper bound to the sum rate of the channel --- a problem that is very difficult for general channel coefficients. To avoid this difficulty for the general IC, we next derive upper and lower bounds which are not identical but are within a constant number of bits to each other which characterizes the capacity region of the 2-user multi-input multi-output (MIMO) Gaussian interference channel (IC) with an arbitrary number of antennas at each node to within a constant gap that is independent of the signal-to-noise ratio (SNR) and all channel parameters. In contrast to an earlier result in [Telatar and Tse, ISIT, 2007], where both the achievable rate region and upper bounds to the capacity region of a general class of interference channels was specified as the union over all possible input distributions here we provide, a simple and an explicit achievable coding scheme for the achievable region and an explicit outer bound. We also illustrate an interesting connection of the simple achievable coding scheme to MMSE estimators at the receivers. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC. We also analyze the channel\u27s performance in the high SNR regime, which is obtained from the explicit expressions of the approximate capacity region and the resulting asymptotic rate region is known as the generalized degrees of freedom (GDoF) region. A close examination of the super position coding scheme which is both GDoF and approximate capacity optimal reveals that joint signal-space and signal-level interference alignment is necessary to achieve the GDoF region of the channel. The admissible DoF-splits between the private and common messages of the HK scheme are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques (at high SNR) on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time-sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime - where single-user DoF performance can be achieved simultaneously for both users- depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the SISO case. For asymmetric numbers of antennas at the four nodes the shape of the symmetric GDoF curve can be a \u22distorted W\u22 curve to the extent that for certain MIMO ICs it is a \u22V\u22 curve. In the second part of the thesis, we concentrate on time varying fading channels. We first characterize the fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading MIMO Z interference channel (ZIC) with channel state information at the transmitters (CSIT) and arbitrary number of antennas at each node. A short-term average power constraint is assumed. It is shown that a variant of the superposition coding scheme described above, where the 2nd transmitter\u27s signal depends on the channel matrix to the first receiver and the 1st user\u27s transmit signal is independent of CSIT, can achieve the full CSIT DMT of the ZIC. We also characterize the achievable DMT of a transmission scheme, which does not utilize any CSIT and show that for some range of multiplexing gains, the full CSIT DMT of the ZIC can be achieved by it. The size of this range of multiplexing gains depends on the system parameters such as the number of antennas at the four nodes (referred to hereafter as “antenna configuration”), signal-to-noise ratios (SNR) and interference-to-noise ratio (INR) of the direct links and cross link, respectively. Interestingly, for certain special cases such as when the interfered receiver has a relatively larger number of antennas than that at the other nodes or when the INR is stronger than the SNRs, the No-CSIT scheme can achieve the F-CSIT DMT for all multiplexing gains. Thus, under these circumstances, the optimal DMT of the MIMO ZIC with F-CSIT is same as the DMT of the corresponding ZIC with No-CSIT. For other channel configurations, the DMT achievable by the No-CSIT scheme serves as a lower bound to the fundamental No-CSIT DMT of the MIMO ZIC. We also characterize the fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward (DCF) protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information (CSI) at the relay. In this work, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this work enables the in-depth comparisons herein of full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes