arXiv subjects

Andrea J. Goldsmith

Publications and source records attributed to Andrea J. Goldsmith.

70 records · Page 4Linked to original sources

arXiv2012

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

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arXiv2012

Channel Capacity under General Nonuniform Sampling

This paper develops the fundamental capacity limits of a sampled analog channel under a sub-Nyquist sampling rate constraint. In particular, we derive the capacity of sampled analog channels over a general class of time-preserving sampling methods including irregular nonuniform sampling. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest SNR among all spectral sets of support size equal to the sampling rate. The capacity under sub-Nyquist sampling can be attained through filter-bank sampling, or through a single branch of modulation and filtering followed by uniform sampling. The capacity under sub-Nyquist sampling is a monotone function of the sampling rate. These results indicate that the optimal sampling schemes suppress aliasing, and that employing irregular nonuniform sampling does not provide capacity gain over uniform sampling sets with appropriate preprocessing for a large class of channels.

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arXiv2012

Blind Null-space Tracking for MIMO Underlay Cognitive Radio Networks

Blind Null Space Learning (BNSL) has recently been proposed for fast and accurate learning of the null-space associated with the channel matrix between a secondary transmitter and a primary receiver. In this paper we propose a channel tracking enhancement of the algorithm, namely the Blind Null Space Tracking (BNST) algorithm that allows transmission of information to the Secondary Receiver (SR) while simultaneously learning the null-space of the time-varying target channel. Specifically, the enhanced algorithm initially performs a BNSL sweep in order to acquire the null space. Then, it performs modified Jacobi rotations such that the induced interference to the primary receiver is kept lower than a given threshold $P_{Th}$ with probability $p$ while information is transmitted to the SR simultaneously. We present simulation results indicating that the proposed approach has strictly better performance over the BNSL algorithm for channels with independent Rayleigh fading with a small Doppler frequency.

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arXiv2012

Capacity Bounds and Exact Results for the Cognitive Z-interference Channel

We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide an upper bound on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not experience interference is deterministic, our proposed upper bound matches the known lower bound provided by Cao and Chen in 2008. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity under the generalized Gel'fand-Pinsker conditions where a transmitter-receiver pair communicates in the presence of interference noncausally known at the encoder.

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arXiv2011

The Diversity-Multiplexing-Delay Tradeoff in MIMO Multihop Networks with ARQ

We study the tradeoff between reliability, data rate, and delay for half-duplex MIMO multihop networks that utilize the automatic-retransmission-request (ARQ) protocol both in the asymptotic high signal-to-noise ratio (SNR) regime and in the finite SNR regime. We propose novel ARQ protocol designs that optimize these tradeoffs. We first derive the diversity-multiplexing-delay tradeoff (DMDT) in the high SNR regime, where the delay is caused only by retransmissions. This asymptotic DMDT shows that the performance of an N node network is limited by the weakest three-node sub-network, and the performance of a three-node sub-network is determined by its weakest link, and, hence, the optimal ARQ protocol needs to equalize the performance on each link by allocating ARQ window sizes optimally. This equalization is captured through a novel Variable Block-Length (VBL) ARQ protocol that we propose, which achieves the optimal DMDT. We then consider the DMDT in the finite SNR regime, where the delay is caused by both the ARQ retransmissions and queueing. We characterize the finite SNR DMDT of the fixed ARQ protocol, when an end-to-end delay constraint is imposed, by deriving the probability of message error using an approach that couples the information outage analysis with the queueing network analysis. The exponent of the probability of deadline violation demonstrates that the system performance is again limited by the weakest three-node sub-network. The queueing delay changes the consideration for optimal ARQ design: more retransmissions reduce decoding error by lowering the information outage probability, but may also increase message drop rate due to delay deadline violations. Hence, the optimal ARQ should balance link performance while avoiding significant delay.

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arXiv2010

Study of Gaussian Relay Channels with Correlated Noises

In this paper, we consider full-duplex and half-duplex Gaussian relay channels where the noises at the relay and destination are arbitrarily correlated. We first derive the capacity upper bound and the achievable rates with three existing schemes: Decode-and-Forward (DF), Compress-and-Forward (CF), and Amplify-and-Forward (AF). We present two capacity results under specific noise correlation coefficients, one being achieved by DF and the other being achieved by direct link transmission (or a special case of CF). The channel for the former capacity result is equivalent to the traditional Gaussian degraded relay channel and the latter corresponds to the Gaussian reversely-degraded relay channel. For CF and AF schemes, we show that their achievable rates are strictly decreasing functions over the negative correlation coefficient. Through numerical comparisons under different channel settings, we observe that although DF completely disregards the noise correlation while the other two can potentially exploit such extra information, none of the three relay schemes always outperforms the others over different correlation coefficients. Moreover, the exploitation of noise correlation by CF and AF accrues more benefit when the source-relay link is weak. This paper also considers the optimal power allocation problem under the correlated-noise channel setting. With individual power constraints at the relay and the source, it is shown that the relay should use all its available power to maximize the achievable rates under any correlation coefficient. With a total power constraint across the source and the relay, the achievable rates are proved to be concave functions over the power allocation factor for AF and CF under full-duplex mode, where the closed-form power allocation strategy is derived.

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arXiv2009

Multiple Multicasts with the Help of a Relay

The problem of simultaneous multicasting of multiple messages with the help of a relay terminal is considered. In particular, a model is studied in which a relay station simultaneously assists two transmitters in multicasting their independent messages to two receivers. The relay may also have an independent message of its own to multicast. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a "cognitive" relay is characterized, including the cases of partial and rate-limited cognition. Then, achievable rate regions for the cMACr model are presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case, called the cMACr without cross-reception, in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. The capacity region is characterized for a binary modulo additive cMACr without cross-reception, showing the optimality of binary linear block codes, thus highlighting the benefits of physical layer network coding and structured codes. Results are extended to the Gaussian channel model as well, providing achievable rate regions for DF and CF, as well as for a structured code design based on lattice codes. It is shown that the performance with lattice codes approaches the upper bound for increasing power, surpassing the rates achieved by the considered random coding-based techniques.

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arXiv2008

The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.

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arXiv2008

Interference Channels with Correlated Receiver Side Information

The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel code separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel code separation is again shown to be optimal. As a special case, for a class of Z-interference channels, when the side information of the receiver facing interference is a deterministic function of the interfering source, necessary and sufficient conditions for reliable transmission are provided in the form of single letter expressions. As a byproduct of these joint source-channel coding results, the capacity region of a class of Z-channels with degraded message sets is also provided.

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arXiv2008

Lossy Source Transmission over the Relay Channel

Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels. Then the Gaussian relay channel where the source and the side information are jointly Gaussian is analyzed. For this Gaussian model, several new source-channel cooperation schemes are introduced and analyzed in terms of the squared-error distortion at the destination. A comparison of the proposed upper bounds with the cut-set lower bound is given, and it is seen that joint source-channel cooperation improves the reconstruction quality significantly. Moreover, the performance of the joint code is close to the lower bound on distortion for a wide range of source and channel parameters.

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arXiv2008

Joint source and channel coding for MIMO systems: Is it better to be robust or quick?

We develop a framework to optimize the tradeoff between diversity, multiplexing, and delay in MIMO systems to minimize end-to-end distortion. We first focus on the diversity-multiplexing tradeoff in MIMO systems, and develop analytical results to minimize distortion of a vector quantizer concatenated with a space-time MIMO channel code. In the high SNR regime we obtain a closed-form expression for the end-to-end distortion as a function of the optimal point on the diversity-multiplexing tradeoff curve. For large but finite SNR we find this optimal point via convex optimization. We then consider MIMO systems using ARQ retransmission to provide additional diversity at the expense of delay. For sources without a delay constraint, distortion is minimized by maximizing the ARQ window size. This results in an ARQ-enhanced multiplexing-diversity tradeoff region, with distortion minimized over this region in the same manner as without ARQ. Under a source delay constraint the problem formulation changes to account for delay distortion associated with random message arrival and random ARQ completion times. We use a dynamic programming formulation to capture the channel diversity-multiplexing tradeoff at finite SNR as well as the random arrival and retransmission dynamics; we solve for the optimal multiplexing-diversity-delay tradeoff to minimize end-to-end distortion associated with the source encoder, channel, and ARQ retransmissions. Our results show that a delay-sensitive system should adapt its operating point on the diversity-multiplexing-delay tradeoff region to the system dynamics. We provide numerical results that demonstrate significant performance gains of this adaptive policy over a static allocation of diversity/multiplexing in the channel code and a static ARQ window size.

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arXiv2007

A Game-Theoretic Approach to Energy-Efficient Modulation in CDMA Networks with Delay QoS Constraints

A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user's delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.

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arXiv2007

A Game-Theoretic Approach to Energy-Efficient Modulation in CDMA Networks with Delay Constraints

A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user's delay constraint. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. The effect of trellis-coded modulation on energy efficiency is also discussed.

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arXiv2007

Capacity Gain from Two-Transmitter and Two-Receiver Cooperation

Capacity improvement from transmitter and receiver cooperation is investigated in a two-transmitter, two-receiver network with phase fading and full channel state information available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal transmitter cooperation channel, then encoding jointly with dirty paper coding. The receivers cooperate by using Wyner-Ziv compress-and-forward over an analogous orthogonal receiver cooperation channel. To account for the cost of cooperation, the allocation of network power and bandwidth among the data and cooperation channels is studied. It is shown that transmitter cooperation outperforms receiver cooperation and improves capacity over non-cooperative transmission under most operating conditions when the cooperation channel is strong. However, a weak cooperation channel limits the transmitter cooperation rate; in this case receiver cooperation is more advantageous. Transmitter-and-receiver cooperation offers sizable additional capacity gain over transmitter-only cooperation at low SNR, whereas at high SNR transmitter cooperation alone captures most of the cooperative capacity improvement.

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arXiv2007

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.

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arXiv2005

Capacity Gain from Transmitter and Receiver Cooperation

Capacity gain from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. When all nodes have equal average transmit power along with full channel state information (CSI), it is proved that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the nodes but only receiver phase CSI is available. In addition, when the nodes have equal average power with receiver phase CSI only, cooperation is shown to offer no capacity improvement over a non-cooperative scheme with the same average network power. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Moreover, it is shown that full CSI is essential in transmitter cooperation, while optimal power allocation is essential in receiver cooperation.

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