Erik Stauffer

Finite-SNR diversity-multiplexing tradeoffs in fading relay channels

We analyze the diversity-multiplexing tradeoff in a fading relay channel at finite signal-to-noise ratios (SNRs). In this framework, the rate adaptation policy is such that the target system data rate is a multiple of the capacity of an additive white Gaussian noise (AWGN) channel. The proportionality constant determines how aggressively the system scales the data rate and can be interpreted as a finite-SNR multiplexing gain. The diversity gain is given by the negative slope of the outage probability with respect to the SNR. Finite-SNR diversity performance is estimated using a constrained max-flow min-cut upper bound on the relay channel capacity. Moreover, the finite-SNR diversity-multiplexing tradeoff is characterized for three practical decode and forward half-duplex cooperative protocols with different amounts of broadcasting and simultaneous reception. For each configuration, system performance is computed as a function of SNR under a system-wide power constraint on the source and relay transmissions. Our analysis yields the following findings; (i) improved multiplexing performance can be achieved at any SNR by allowing the source to transmit constantly, (ii) both broadcasting and simultaneous reception are desirable in half-duplex relay cooperation for superior diversity-multiplexing performance, and (iii) the diversity-multiplexing tradeoff at finite-SNR is impacted by the power partitioning between the source and the relay terminals. Finally, we verify our analytical results by numerical simulations.

Optimal Peak-to-Average Power Ratio Reduction in MIMO-OFDM Systems

Recent work has used convex optimization to minimize the peak-to-average power ratio (PAR) of OFDM signals subject to a constraint on the constellation error vector magnitude (EVM). This paper extends the PAR optimization technique to multiple-input multiple-output (MIMO) OFDM systems with channel precoding. In MIMO systems with a large OFDM symbol size, it is infeasible to solve the optimization problem by direct methods such as Cholesky factorization. Instead, we propose an iterative conjugate-gradient (CG) method to find an approximate solution with far lower memory and latency requirements. Simulation results are presented for a MIMO-OFDM system with 4 antennas and 1024 carriers. The PAR can be reduced from 11.5 dB to 4.3 dB for QPSK with -20 dB EVM, and from 11.5 dB to 5.5 dB for 16-QAM with -30 dB EVM. The tradeoff between PAR reduction and computational complexity is also examined to determine the number of CG iterations needed to reach within 1 dB of the globally optimal solution.

Computing the Optimal Amount of Constellation Distortion in OFDM Systems

The primary disadvantage of orthogonal frequency-division multiplexing (OFDM) is the high time-domain peak-to-average power ratio (PAR) that severely limits the transmitter power efficiency. The PAR can be globally minimized by distorting the OFDM constellation subject to a constraint on the error vector magnitude (EVM). In this paper, we demonstrate that an optimal amount of EVM exists for minimizing the transmitter power consumption while maintaining a constant bit error rate (BER) at the receiver. Alternatively, the EVM value may be chosen to maximize the channel capacity while maintaining a constant power consumption at the transmitter. Both EVM levels are only a function of the required signal-to-noise ratio at the OFDM receiver.

Minimizing outage probability for arbitrary channel distributions

MIMO wireless systems have been a focus of research for several years, mainly because of the promise of increased channel capacity, extended range, and increased reliability. An aspect of this ongoing research has been concerned with transmit precoding given partial information of the channel. This work focuses on designing a transmit covariance to minimize the probability of outage for a given target data rate over a fading MIMO channel whose distribution is known to the transmitter. This problem is addressed by formulating a convex problem via a heuristic relaxation. Structure of the problem is utilized to simplify the numerical implementation. Finally, the performance of this technique relative to other simpler techniques is considered, therefore showing the utility of this computational technique in evaluating other heuristics.

Code Rate-Diversity-Multiplexing Tradeoff

Multiple antenna systems can be used to increase system reliability or to increase system capacity. Initially, space-time codes were designed to achieve one of these two types of gain. Recently, though, a tradeoff between these two system resources has been characterized by the diversity-multiplexing tradeoff. Achieving this optimal performance frontier requires proper coding. For diversity optimality, the signal transmitted from each antenna must redundantly describe the message bits. This redundancy has been quantified by the rate of a space-time code, which relates space-time codebook size to constituent single-input-single-output (SISO) constellation size. Achievable diversity has also been shown to decrease with increasing rates, which establishes the diversity-rate tradeoff. In this work, we consider a generalized notion of the rate of the space-time code, which we refer to as the code rate Rc, and the associated diversity-code rate tradeoff. We then generalize the diversity-multiplexing and diversity-code rate tradeoffs and find that a new diversity-multiplexing tradeoff exists as a function of the code rate.

Partially Cooperative MIMO Channels with Scaled Identity Transmit Covariance

Recently, there has been a great deal of interest on the performance of MIMO wireless systems as the MIMO fading channel offers an increase in capacity and reliability over that of a SISO channel. When channel state information is not known at the transmitter, the level of performance obtained depends on the degree of cooperation between the transmit antennas. With no cooperation between the antennas, horizontally coded spatial multiplexing is diversity suboptimal since each message bit is encoded and transmitted by only one antenna. An optimal scheme, on the other hand, codes message bits across all transmit antennas. This work generalizes and quantifies the level of cooperation between transmit antennas with the cooperation parameter R c and then finds upper and lower bounds for the achievable data rates for such a system using a scaled identity transmit covariance matrix. These bounds are found to be tight for certain values of Rc and the data rate Rt. Finally, these bounds are useful in computing the outage probability and diversity order of partially cooperative MIMO systems when channel state information is not known at the transmitter

On Precoding for High Spatial Rate Space-Time Codes

MIMO wireless systems have been studied over the past few years due to the promise of increased capacity and reliability. Additional performance gains are possible when channel state information is available at the transmitter (CSI-T). In this work, we consider the case of partial CSI-T (channel transmit covariance) and revisit precoder design for high rate space-time codes which do not have a unique minimum error matrix. Using a set of minimum error matrices combined with traditional MIMO precoder design results in improved performance over that of previous design techniques based a single minimum error matrix.

On Duobinary Turbo Codes for Block Fading Channels

Diversity coding for fading channels has been an area of active research for many years. In particular, performance hounds and code construction for several families of codes have been studied for block fading channels. In this work, we consider duobinary turbo codes for block fading channels. A simple decodability condition guaranteeing full diversity based on decodable subsets is introduced. The performance of systematic duobinary turbo codes is analyzed with regard to the channel interleaver and confirmed with simulations. An interesting relationship between the frame size and distance spectrum of these tailbiting codes is revealed