Abstract-In this paper, we provide a complete study on the training based channel estimation issues for relay networks that employ the amplify-and-forward (AF) transmission scheme. We first point out that separately estimating the channel from source to relay and relay to destination suffers from many drawbacks. Then we provide a new estimation scheme that directly estimates the overall channels from the source to the destination. The proposed channel estimation well serves the AF based space time coding (STC) that was recently developed. There exists many differences between the proposed channel estimation and that in the traditional single input single out (SISO) and multiple input single output (MISO) systems. For example, a relay must linearly precode its received training sequence by a sophisticatedly designed matrix in order to minimize the channel estimation error. Besides, each relay node is individually constrained by a different power requirement because of the non-cooperation among all relay nodes. We study both the linear least-square (LS) estimator and the minimum mean-square-error (MMSE) estimator. The corresponding optimal training sequences, as well as the optimal precoding matrices are derived from an efficient convex optimization process.Index Terms-Channel estimation, amplify and forward relay networks, cooperative communications, optimal training, optimal precoding.

Abstract-In this paper, we consider distributed space-time coding for two-way wireless relay networks, where communication between two terminals is assisted by relay nodes. Relaying protocols using two, three, and four time slots are proposed. The protocols using four time slots are the traditional amplify-and-forward (AF) and decode-and-forward (DF) protocols, which do not consider the property of the two-way traffic. A new class of relaying protocols, termed as partial decode-and-forward (PDF), is developed for the two time slots transmission, where each relay first removes part of the noise before sending the signal to the two terminals. Protocols using three time slots are proposed to compensate the fact that the two time slots protocols cannot make use of direct transmission between the two terminals. For all protocols, after processing their received signals, the relays encode the resulting signals using a distributed linear dispersion (LD) code. The proposed AF protocols are shown to achieve the diversity order of min (1 (log log log )), where is the number of relays, is the total power of the network, and is the number of symbols transmitted during each time slot. When random unitary matrix is used for LD code, the proposed PDF protocols resemble random linear network coding, where the former operates on the unitary group and the latter works on the finite field. Moreover, PDF achieves the diversity order of min but the conventional DF can only achieve the diversity order of 1. Finally, we find that two time slots protocols also have advantages over four-time-slot protocols in media access control (MAC) layer.

Abstract-This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper advocates a much more refined, information-theoretic criterion, namely the mutual information (MI) between PMU measurements and power system states. The proposed MI criterion not only includes observability as a special case, but also rigorously models the uncertainty reduction on power system states from PMU measurements. Thus, it can generate highly informative PMU configurations. The MI criterion can also facilitate robust PMU placement by explicitly modeling probabilistic PMU outages. We propose a greedy PMU placement algorithm, and show that it achieves an approximation ratio of for any PMU placement budget. We further show that the performance is the best that one can achieve, in the sense that it is NP-hard to achieve any approximation ratio beyond . Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate near-optimal performance of the proposed PMU placement algorithm.Index Terms-Electric power systems, greedy algorithm, mutual information, phasor measurement unit, submodular functions.

We propose relaying strategies for uncoded two-way relay channels, where two terminals transmit simultaneously to each other with the help of a relay. In particular, we consider a memoryless system, where the signal transmitted by the relay is obtained by applying an instantaneous relay function to the previously received signal. For binary antipodal signaling, a class of so called absolute (abs)-based schemes is proposed in which the processing at the relay is solely based on the absolute value of the received signal. We analyze and optimize the symbol-error performance of existing and new abs-based and non-abs-based strategies under an average power constraint, including abs-based and non-abs-based versions of amplify and forward (AF), detect and forward (DF), and estimate and forward (EF). Additionally, we optimize the relay function via functional analysis such that the average probability of error is minimized at the high signal-to-noise ratio (SNR) regime. The optimized relay function is shown to be a Lambert W function parameterized on the noise power and the transmission energy. The optimized function behaves like abs-AF at low SNR and like abs-DF at high SNR, respectively; EF behaves similarly to the optimized function over the whole SNR range. We find the conditions under which each class of strategies is preferred. Finally, we show that all these results can also be generalized to higher order constellations. Index Terms-Two-way channel, wireless relay networks, functional analysis. I. INTRODUCTION T WO-WAY communication is a common scenario where two parties simultaneously transmit information to each other. The two-way channel was first considered by Shannon [3], who derived inner and outer bounds on the capacity region. Recently, the two-way relay channel (TWRC) has drawn renewed interest from both academic and industrial communities [4]-[10] due to its potential application to cellular networks and peer-to-peer networks. AF and DF protocols for one-way relay channels are extended to the half-duplex Gaussian TWRC in [6] and the general full-duplex discrete TWRC in [5]. In [7], network coding is used to increase the sum-rate of two users. With network coding, each node in a

Abstract-In this letter, we present cyclic-prefix (CP) based noise-variance and power-delay-profile estimators for Orthogonal Frequency Division Multiplexing (OFDM) systems. Signal correlation due to the use of the CP is exploited without requiring additional pilot symbols. A heuristic estimator and a class of approximate maximum likelihood (ML) estimators are proposed. The proposed algorithms can be applied to both unitary and non-unitary constellations. These algorithms can be readily used for applications such as minimum mean-square error (MMSE) channel estimation.

Abstract-This work considers two-way relay channels (TWRC), where two terminals transmit simultaneously to each other with the help of a relay node. For single antenna systems, we propose several new transmission schemes for both amplify-and-forward (AF) protocol and decode-and-forward (DF) protocol where the channel state information is not required. These new schemes are the counterpart of the traditional noncoherent detection or differential detection in point-to-point communications. Differential modulation design for TWRC is challenging because the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF protocols, where the latter can be considered as performing differential network coding at the physical layer. As the exact ML detector is prohibitively complex, we propose several suboptimal alternatives including decision feedback detectors and prediction-based detectors. All these strategies work well as evidenced by the simulation results. The proposed protocols are especially useful when the required average data rate is high. In addition, we extend the protocols to the multiple-antenna case and provide the design criterion of the differential unitary space time modulation (DUSTM) for TWRC.Index Terms-Differential modulation, physical layer network coding, two-way relay networks.

Abstract-We consider energy efficient network coding design in wireless networks with multiple unicast sessions. Our approach decomposes multiple unicast sessions into a superposition of multicast and unicast sessions, with coding occurring only within each session. We give an optimization approach that is more general than the existing poison-remedy optimization formulation. For the case of wireless, we consider XOR coding and give an achievable rate region for a primary interference model. To simplify network operation, we give an oblivious backpressure algorithm which does not optimize overhearing of transmissions, and a practical protocol called COPR based on the oblivious backpressure algorithm. Simulation experiments show that COPR largely reduces network power consumption over existing algorithms. I. INTRODUCTIONIn this paper, we consider energy efficient cross-layer optimization for wireless networks by exploiting network coding and multiple-reception gain. We focus on network coding across multiple unicast sessions, or intersession network coding. Optimal intersession network coding design is an open problem; various suboptimal algorithms have been proposed, e.g.Our approach decomposes multiple unicast sessions into a superposition of multicast and unicast sessions, with coding occurring only within each session. For the case of wireless networks, we consider simple one-hop XOR coding as in COPE [1], where each node uses knowledge of what its neighbors have overheard to perform opportunistic network coding such that each encoded packet can be decoded immediately at the next hop. Reference [1] demonstrated substantial throughput gains for network coding that grow with the level of congestion. In this paper we consider the benefit of network coding for energy saving in power-constrained settings with less congestion. In doing so we develop general techniques that apply also to the case of throughput optimization and congestion control in wireless networks.To exploit multiple-reception gain, we model the network as a directed hypergraph. The achievable rate region of one-hop XOR coding is determined under a primary interference model. It is difficult and complicated to design dynamic scheduling and coding algorithms to achieve the entire rate region as it typically requires optimization over overheard flows. To simplify network operation, an oblivious backpressure algorithm is proposed which does not optimize overheard flows. The link scheduling problem is found to be a maximum weighted hypergraph matching problem, which can be solved distributedly by

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