Wireless MIMO Switching

In a generic switching problem, a switching pattern consists of a one-to-one mapping from a set of inputs to a set of outputs (i.e., a permutation). We propose and investigate a wireless switching framework in which a multi-antenna relay is responsible for switching traffic among a set of $N$ stations. We refer to such a relay as a MIMO switch. With beamforming and linear detection, the MIMO switch controls which stations are connected to which stations. Each beamforming matrix realizes a permutation pattern among the stations. We refer to the corresponding permutation matrix as a switch matrix. By scheduling a set of different switch matrices, full connectivity among the stations can be established. In this paper, we focus on "fair switching" in which equal amounts of traffic are to be delivered for all $N(N-1)$ ordered pairs of stations. In particular, we investigate how the system throughput can be maximized. In general, for large $N$ the number of possible switch matrices (i.e., permutations) is huge, making the scheduling problem combinatorially challenging. We show that for N=4 and 5, only a subset of $N-1$ switch matrices need to be considered in the scheduling problem to achieve good throughput. We conjecture that this will be the case for large $N$ as well. This conjecture, if valid, implies that for practical purposes, fair-switching scheduling is not an intractable problem.Comment: Submitted to IEEE Transactions on Wireless Communicatio

Joint Phase Tracking and Channel Decoding for OFDM Physical-Layer Network Coding

This paper investigates the problem of joint phase tracking and channel decoding in OFDM based Physical-layer Network Coding (PNC) systems. OFDM signaling can obviate the need for tight time synchronization among multiple simultaneous transmissions in the uplink of PNC systems. However, OFDM PNC systems are susceptible to phase drifts caused by residual carrier frequency offsets (CFOs). In the traditional OFDM system in which a receiver receives from only one transmitter, pilot tones are employed to aid phase tracking. In OFDM PNC systems, multiple transmitters transmit to a receiver, and these pilot tones must be shared among the multiple transmitters. This reduces the number of pilots that can be used by each transmitting node. Phase tracking in OFDM PNC is more challenging as a result. To overcome the degradation due to the reduced number of per-node pilots, this work supplements the pilots with the channel information contained in the data. In particular, we propose to solve the problems of phase tracking and channel decoding jointly. Our solution consists of the use of the expectation-maximization (EM) algorithm for phase tracking and the use of the belief propagation (BP) algorithm for channel decoding. The two problems are solved jointly through iterative processing between the EM and BP algorithms. Simulations and real experiments based on software-defined radio show that the proposed method can improve phase tracking as well as channel decoding performance.Comment: 7 pages, 8 figure

Frequency-Asynchronous Multiuser Joint Channel-Parameter Estimation, CFO Compensation and Channel Decoding

This paper investigates a channel-coded multiuser system operated with orthogonal frequency-division multiplexing (OFDM) and interleaved division multiple-access (IDMA). To realize the potential advantage of OFDM-IDMA, two challenges must be addressed. The first challenge is the estimation of multiple channel parameters. An issue is how to contain the estimation errors of the channel parameters of the multiple users, considering that the overall estimation errors may increase with the number of users because the estimations of their channel parameters are intertwined with each other. The second challenge is that the transmitters of the multiple users may be driven by different RF oscillators. The associated frequency asynchrony may cause multiple CFOs at the receiver. Compared with a single-user receiver where the single CFO can be compensated away, a particular difficulty for a multiuser receiver is that it is not possible to compensate for all the multiple CFOs simultaneously. To tackle the two challenges, we put forth a framework to solve the problems of multiuser channel-parameter estimation, CFO compensation, and channel decoding jointly and iteratively. The framework employs the space alternating generalized expectation-maximization (SAGE) algortihm to decompose the multisuser problem into multiple single-user problems, and the expectation-conditional maximization (ECM) algorithm to tackle each of the single-user subproblems. Iterative executions of SAGE and ECM in the framework allow the two aforementioned challenges to be tackled in an optimal manner. Simulations and real experiments based on software-defined radio indicate that, compared with other approaches, our approach can achieve significant performance gains.Comment: This work is accepted for publication by IEEE TVT at Jan. 201

Complex Linear Physical-Layer Network Coding

This paper presents the results of a comprehensive investigation of complex linear physical-layer network (PNC) in two-way relay channels (TWRC). A critical question at relay R is as follows: "Given channel gain ratio $\eta = h_A/h_B$, where $h_A$ and $h_B$ are the complex channel gains from nodes A and B to relay R, respectively, what is the optimal coefficients $(\alpha,\beta)$ that minimizes the symbol error rate (SER) of $w_N=\alpha w_A+\beta w_B$ when we attempt to detect $w_N$ in the presence of noise?" Our contributions with respect to this question are as follows: (1) We put forth a general Gaussian-integer formulation for complex linear PNC in which $\alpha,\beta,w_A, w_B$, and $w_N$ are elements of a finite field of Gaussian integers, that is, the field of $\mathbb{Z}[i]/q$ where $q$ is a Gaussian prime. Previous vector formulation, in which $w_A$, $w_B$, and $w_N$ were represented by $2$-dimensional vectors and $\alpha$ and $\beta$ were represented by $2\times 2$ matrices, corresponds to a subcase of our Gaussian-integer formulation where $q$ is real prime only. Extension to Gaussian prime $q$, where $q$ can be complex, gives us a larger set of signal constellations to achieve different rates at different SNR. (2) We show how to divide the complex plane of $\eta$ into different Voronoi regions such that the $\eta$ within each Voronoi region share the same optimal PNC mapping $(\alpha_{opt},\beta_{opt})$. We uncover the structure of the Voronoi regions that allows us to compute a minimum-distance metric that characterizes the SER of $w_N$ under optimal PNC mapping $(\alpha_{opt},\beta_{opt})$. Overall, the contributions in (1) and (2) yield a toolset for a comprehensive understanding of complex linear PNC in $\mathbb{Z}[i]/q$. We believe investigation of linear PNC beyond $\mathbb{Z}[i]/q$ can follow the same approach.Comment: submitted to IEEE Transactions on Information Theor

Building Blocks of Physical-layer Network Coding

This paper investigates the fundamental building blocks of physical-layer network coding (PNC). Most prior work on PNC focused on its application in a simple two-way-relay channel (TWRC) consisting of three nodes only. Studies of the application of PNC in general networks are relatively few. This paper is an attempt to fill this gap. We put forth two ideas: 1) A general network can be decomposed into small building blocks of PNC, referred to as the PNC atoms, for scheduling of PNC transmissions. 2) We identify nine PNC atoms, with TWRC being one of them. Three major results are as follows. First, using the decomposition framework, the throughput performance of PNC is shown to be significantly better than those of the traditional multi-hop scheme and the conventional network coding scheme. For example, under heavy traffic volume, PNC can achieve 100% throughput gain relative to the traditional multi-hop scheme. Second, PNC decomposition based on a variety of different PNC atoms can yield much better performance than PNC decomposition based on the TWRC atom alone. Third, three out of the nine atoms are most important to good performance. Specifically, the decomposition based on these three atoms is good enough most of the time, and it is not necessary to use the other six atoms.Comment: 38 pages, 7 figures, 10 tables, accepted by IEEE SECON 201

Wireless MIMO Switching with Network Coding

In a generic switching problem, a switching pattern consists of a one-to-one mapping from a set of inputs to a set of outputs (i.e., a permutation). We propose and investigate a wireless switching framework in which a multi-antenna relay is responsible for switching traffic among a set of $N$ stations. We refer to such a relay as a MIMO switch. With beamforming and linear detection, the MIMO switch controls which stations are connected to which other stations. Each beamforming matrix realizes a permutation pattern among the stations. We refer to the corresponding permutation matrix as a switch matrix. By scheduling a set of different switch matrices, full connectivity among the stations can be established. In this paper, we focus on "fair switching" in which equal amounts of traffic are to be delivered for all $N(N-1)$ ordered pairs of stations. In particular, we investigate how the system throughput can be maximized. In general, for large $N$ the number of possible switch matrices (i.e., permutations) is huge, making the scheduling problem combinatorially challenging. We show that for the cases of N=4 and 5, only a subset of $N-1$ switch matrices need to be considered in the scheduling problem to achieve good throughput. We conjecture that this will be the case for large $N$ as well. This conjecture, if valid, implies that for practical purposes, fair-switching scheduling is not an intractable problem. We also investigate MIMO switching with physical-layer network coding in this paper. We find that it can improve throughput appreciably.Comment: This manuscript is an extention work of our previous paper "Wireless MIMO Switching" and also with some results of a talk given in CUHK. The major extention is that physical-layer network coding is used and significantly improves the throughput performanc

Asynchronous Convolutional-Coded Physical-Layer Network Coding

This paper investigates the decoding process of asynchronous convolutional-coded physical-layer network coding (PNC) systems. Specifically, we put forth a layered decoding framework for convolutional-coded PNC consisting of three layers: symbol realignment layer, codeword realignment layer, and joint channel-decoding network coding (Jt-CNC) decoding layer. Our framework can deal with phase asynchrony and symbol arrival-time asynchrony between the signals simultaneously transmitted by multiple sources. A salient feature of this framework is that it can handle both fractional and integral symbol offsets; previously proposed PNC decoding algorithms (e.g., XOR-CD and reduced-state Viterbi algorithms) can only deal with fractional symbol offset. Moreover, the Jt-CNC algorithm, based on belief propagation (BP), is BER-optimal for synchronous PNC and near optimal for asynchronous PNC. Extending beyond convolutional codes, we further generalize the Jt-CNC decoding algorithm for all cyclic codes. Our simulation shows that Jt-CNC outperforms the previously proposed XOR-CD algorithm and reduced-state Viterbi algorithm by 2dB for synchronous PNC. For phase-asynchronous PNC, Jt-CNC is 4dB better than the other two algorithms. Importantly, for real wireless environment testing, we have also implemented our decoding algorithm in a PNC system built on the USRP software radio platform. Our experiment shows that the proposed Jt-CNC decoder works well in practice.Comment: 28 pages, journal versio

Proportional Fairness in Multi-channel Multi-rate Wireless Networks-Part I: The Case of Deterministic Channels

This is Part I of a two-part paper series that studies the use of the proportional fairness (PF) utility function as the basis for capacity allocation and scheduling in multi-channel multi-rate wireless networks. The contributions of Part I are threefold. (i) First, we lay down the theoretical foundation for PF. Specifically, we present the fundamental properties and physical/economic interpretation of PF. We show by general mathematical arguments that PF leads to equal airtime allocation to users for the single-channel case; and equal equivalent airtime allocation to users for the multi-channel case, where the equivalent airtime enjoyed by a user is a weighted sum of the airtimes enjoyed by the user on all channels, with the weight of a channel being the price or value of that channel. We also establish the Pareto efficiency of PF solutions. (ii) Second, we derive characteristics of PF solutions that are useful for the construction of PF-optimization algorithms. We present several PF-optimization algorithms, including a fast algorithm that is amenable to parallel implementation. (iii) Third, we study the use of PF utility for capacity allocation in large-scale WiFi networks consisting of many adjacent wireless LANs. We find that the PF solution simultaneously achieves higher system throughput, better fairness, and lower outage probability with respect to the default solution given by today's 802.11 commercial products. Part II of this paper series extends our investigation to the time-varying-channel case in which the data rates enjoyed by users over the channels vary dynamically over tim

An Optimal Decoding Strategy for Physical-layer Network Coding over Multipath Fading Channels

We present an optimal decoder for physical-layer network coding (PNC) in a multipath fading channels. Previous studies on PNC have largely focused on the single path case. For PNC, multipath not only introduces inter-symbol interference (ISI), but also cross-symbol interference (Cross-SI) between signals simultaneously transmitted by multiple users. In this paper, we assume the transmitters do not have channel state information (CSI). The relay in the PNC system, however, has CSI. The relay makes use of a belief propagation (BP) algorithm to decode the multipath-distorted signals received from multiple users into a network-coded packet. We refer to our multipath decoding algorithm as MP-PNC. Our simulation results show that, benchmarked against synchronous PNC over a one-path channel, the bit error rate (BER) performance penalty of MP-PNC under a two-tap ITU channel model can be kept within 0.5dB. Moreover, it outperforms a MUD-XOR algorithm by 3dB -- MUD-XOR decodes the individual information from both users explicitly before performing the XOR network-coding mapping. Although the framework of fading-channel PNC presented in this paper is demonstrated based on two-path and three-path channel models, our algorithm can be easily extended to cases with more than three paths.Comment: Submitted to IEEE Transactions on Vehicular Technolog

AlphaSeq: Sequence Discovery with Deep Reinforcement Learning

Sequences play an important role in many applications and systems. Discovering sequences with desired properties has long been an interesting intellectual pursuit. This paper puts forth a new paradigm, AlphaSeq, to discover desired sequences algorithmically using deep reinforcement learning (DRL) techniques. AlphaSeq treats the sequence discovery problem as an episodic symbol-filling game, in which a player fills symbols in the vacant positions of a sequence set sequentially during an episode of the game. Each episode ends with a completely-filled sequence set, upon which a reward is given based on the desirability of the sequence set. AlphaSeq models the game as a Markov Decision Process (MDP), and adapts the DRL framework of AlphaGo to solve the MDP. Sequences discovered improve progressively as AlphaSeq, starting as a novice, learns to become an expert game player through many episodes of game playing. Compared with traditional sequence construction by mathematical tools, AlphaSeq is particularly suitable for problems with complex objectives intractable to mathematical analysis. We demonstrate the searching capabilities of AlphaSeq in two applications: 1) AlphaSeq successfully rediscovers a set of ideal complementary codes that can zero-force all potential interferences in multi-carrier CDMA systems. 2) AlphaSeq discovers new sequences that triple the signal-to-interference ratio -- benchmarked against the well-known Legendre sequence -- of a mismatched filter estimator in pulse compression radar systems.Comment: 48 pages, 13 figure