G. D. Forney

Bio: G. D. Forney is an academic researcher from Mansfield University of Pennsylvania. The author has contributed to research in topics: Mutual information & Additive white Gaussian noise. The author has an hindex of 1, co-authored 1 publications receiving 112 citations.

Generalized Decision-Feedback Equalization for Packet Transmission with ISI and Gaussian Noise

Abstract: A general theory for transmission of finite-length packets over channels with inter-symbol interference and additive Gaussian noise is developed. The theory is based on general principles of maximum-likelihood (ML) and linear minimum-mean-squared error (MMSE) estimation, innovations and modal representations of random vectors via Cholesky factorizations, eigendecompositions, and information theory. Using these principles, equivalent forward and backward channel models with desirable properties are developed. Fundamental relations between these theories are presented; for example, the mutual information I(X; Y) between the input X and output Y, when X is a Gaussian vector, is equal to log Rx′x′/Re′e′, where Rx′x′ and Re′e′ are the effective determinants of the covariance matrices of the effective input and of the input linear MMSE estimation error, respectively. A Generalized Decision Feedback Equalization (GDFE) receiver structure is developed and is shown to be canonical for arbitrary linear Gaussian channels- i.e., a reliably transmitted data rate of I(X; Y) can be approached arbitrarily closely with this receiver structure on any linear Gaussian channel with any input covariance matrix Rxx. For optimal Rxx, the performance of this receiver is in aggregate the same as the well-known vector coding (VC) structure, but in detail the structure is quite different from VC or other previously proposed block DFE receiver structures.

Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization

Abstract: This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multiple-input multiple-output (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schur-convex functions. Once the optimal structure of the transmit-receive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closed-form expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peak-to-average ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel water-filling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.

Nested linear/lattice codes for structured multiterminal binning

Abstract: Network information theory promises high gains over simple point-to-point communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning scheme. Wyner (1974, 1978) and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, previous work proposed the idea of nested codes, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We review these developments and explore their tight relation to concepts such as combined shaping and precoding, coding for memories with defects, and digital watermarking. We also propose a few novel applications adhering to a unified approach.

Exploiting Multi-Antennas for Opportunistic Spectrum Sharing in Cognitive Radio Networks

Abstract: In cognitive radio (CR) networks, there are scenarios where the secondary (lower priority) users intend to communicate with each other by opportunistically utilizing the transmit spectrum originally allocated to the existing primary (higher priority) users. For such a scenario, a secondary user usually has to tradeoff between two conflicting goals at the same time: one is to maximize its own transmit throughput; and the other is to minimize the amount of interference it produces at each primary receiver. In this paper, we study this fundamental tradeoff from an information-theoretic perspective by characterizing the secondary user's channel capacity under both its own transmit-power constraint as well as a set of interference-power constraints each imposed at one of the primary receivers. In particular, this paper exploits multi-antennas at the secondary transmitter to effectively balance between spatial multiplexing for the secondary transmission and interference avoidance at the primary receivers. Convex optimization techniques are used to design algorithms for the optimal secondary transmit spatial spectrum that achieves the capacity of the secondary transmission. Suboptimal solutions for ease of implementation are also presented and their performances are compared with the optimal solution. Furthermore, algorithms developed for the single-channel transmission are also extended to the case of multichannel transmission whereby the secondary user is able to achieve opportunistic spectrum sharing via transmit adaptations not only in space, but in time and frequency domains as well. Simulation results show that even under stringent interference-power constraints, substantial capacity gains are achievable for the secondary transmission by employing multi-antennas at the secondary transmitter. This is true even when the number of primary receivers exceeds that of secondary transmit antennas in a CR network, where an interesting "interference diversity" effect can be exploited.

Sum capacity of Gaussian vector broadcast channels

Abstract: This paper characterizes the sum capacity of a class of potentially nondegraded Gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers. Coordination is allowed among the transmit terminals, but not among the receive terminals. The sum capacity is shown to be a saddle-point of a Gaussian mutual information game, where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information. The sum capacity is achieved using a precoding strategy for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown to correspond to a decision-feedback equalizer that decomposes the broadcast channel into a series of single-user channels with interference pre-subtracted at the transmitter.