Ravi Narasimhan

On the distribution of SINR for the MMSE MIMO receiver and performance analysis

This correspondence studies the statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for the minimum mean-square error (MMSE) receiver in multiple-input multiple-output (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flat-fading with unequal powers. The SINR can be decomposed into two independent random variables: SINR=SINR/sup ZF/+T, where SINR/sup ZF/ corresponds to the SINR for a zero-forcing (ZF) receiver and has an exact Gamma distribution. This correspondence focuses on characterizing the statistical properties of T using the results from random matrix theory. First three asymptotic moments of T are derived for uncorrelated channels and channels with equicorrelations. For general correlated channels, some limiting upper bounds for the first three moments are also provided. For uncorrelated channels and correlated channels satisfying certain conditions, it is proved that T converges to a Normal random variable. A Gamma distribution and a generalized Gamma distribution are proposed as approximations to the finite sample distribution of T. Simulations suggest that these approximate distributions can be used to estimate accurately the probability of errors even for very small dimensions (e.g., two transmit antennas).

Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments

Individual Outage Rate Regions for Fading Multiple Access Channels

In this paper, outage regions are computed for the quasi-static fading multiple access channel (MAC) with constraints on the individual user outage probabilities and no channel state information at the transmitters (CSIT). An outage rate region is defined as the set of rate vectors for which the user outage probability constraints are satisfied simultaneously. Outage probability is typically defined in terms of a common outage event, defined as the event that a target user rate vector lies outside the achievable region of the MAC, conditioned on the fading state. In contrast, rate regions without CSIT are computed in this paper based on individual outage events and individual probability constraints that are satisfied simultaneously. An individual outage event for a given user occurs if the users message is not correctly decoded, irrespective of the decoding success of the messages for other users. Individual outage rate regions are useful for the MAC with heterogeneous user channels and quality-of-service (QoS) requirements. Explicit outage rate regions and total throughputs are computed for the two-user fading MAC. It is shown that rate regions and throughputs are significantly larger using individual outage probabilities than using the common outage probability.

Queue proportional scheduling via geometric programming in fading broadcast channels

For fading broadcast channels (BC), a throughput optimal scheduling policy called queue proportional scheduling (QPS) is presented via geometric programming (GP). QPS finds a data rate vector such that the expected rate vector over all fading states is proportional to the current queue state vector and is on the boundary of the ergodic capacity region of a fading BC. Utilizing the degradedness of BC for each fading state, QPS is formulated as a geometric program that can be solved with efficient algorithms. The GP formulation of QPS is also extended to orthogonal frequency-division multiplexing (OFDM) systems in a fading BC. The throughput optimality of QPS is proved, and it is shown that QPS can arbitrarily scale the ratio of each users average queueing delay. Throughput, delay, and fairness properties of QPS are numerically evaluated in a fading BC and compared with other scheduling policies such as the well-known maximum weight matching scheduling (MWMS). Simulation results for Poisson packet arrivals and exponentially distributed packet lengths demonstrate that compared with MWMS, QPS provides a significant decrease in average queueing delay and has more desirable fairness properties

Throughput-Delay Performance of Half-Duplex Hybrid-ARQ Relay Channels

The throughput-delay performance of a half-duplex relay channel with hybrid-automatic retransmission request (HARQ) is analyzed in this paper. The protocol uses a form of incremental redundancy HARQ transmission with assistance from the relay via space-time coding if the relay decodes the message before the destination. The packet delay constraint is represented by L, the maximum number of HARQ rounds. An outage is declared if the packet is unsuccessful after L HARQ rounds. A delay-limited throughput is defined in this paper to explicitly account for finite delay constraints and associated non-zero packet outage probabilities. For small outage probabilities, this delay-limited throughput is greater than the conventional long-term average throughput. An exact expression is obtained for the outage probability to compare the throughput-delay performance of this half-duplex relay protocol with direct transmission. The delay-limited throughput of the relay channel is significantly larger than that of direct transmission for a wide range of signal-to-noise ratios (SNRs), target outage probabilities, delay constraints and relay positions.

Error propagation analysis of V-BLAST with channel-estimation errors

In this letter, expressions are given for the symbol-error rate (SER) of the Vertical Bell Laboratories Layered Space-Time (V-BLAST) system, taking into account error propagation due to channel-estimation errors. In addition to error propagation, suboptimal substream ordering due to imperfect channel estimates is accounted for. First, the conditional SER is determined using the distribution of the signal-to-interference-plus-noise ratio of each substream, conditioned on the channel estimate. Then, the average SER as a function of the channel estimation error-to-signal ratio (ESR) is upper bounded by averaging over the distribution of the channel estimates. The upper bound on the SER is tighter than previous bounds in the literature. Comparisons with exact simulations demonstrate the accuracy of the SER expressions for a large range of ESRs.

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.

Finite-SNR diversity performance of rate-adaptive MIMO systems

The diversity performance of a multiple-input multiple-output (MIMO) wireless system is analyzed at finite signal-to-noise ratios (SNRs) when the data rate increases with SNR. The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. A lower bound on the outage probability of the MIMO system is used to characterize the diversity performance. It is seen that the achievable diversity gains at finite SNRs are significantly lower than asymptotic values given in the literature. This diversity characterization is useful in determining suitable rate adaptation strategies at realistic SNRs.

Finite-SNR diversity-multiplexing tradeoff of space-time codes

A novel framework is presented to characterize the tradeoff between diversity and multiplexing of space-time codes at finite signal-to-noise ratios (SNR). The diversity gain of a space-time code is defined by the slope at a particular SNR of the outage probability versus SNR curve for a multiplexing gain defined by the ratio of the system spectral efficiency to the capacity of an additive white Gaussian noise (AWGN) channel. The finite-SNR diversity-multiplexing tradeoff is evaluated for orthogonal space-time block codes and spatial multiplexing with horizontal encoding. The tradeoff curves provide a characterization of achievable diversity and multiplexing gains for a given space-time code at SNR encountered in practice. It is seen that the achievable diversity gains at finite SNR are significantly lower than the asymptotic values given in the literature.

Estimation of mobile speed and average received power in wireless systems using best basis methods

A new method is presented for estimating the mobile speed and the average received power in general wireless environments. The locally stationary received signal is expanded into a local exponential basis using best basis methods. An estimate of the time-varying Doppler spectrum is obtained together with an estimate of the maximum Doppler frequency, which is proportional to the mobile speed. The average received power is then estimated by integrating the time-varying spectrum. Simulations demonstrate good tracking of variable mobile speed and average received power for a wide range of angular distributions of incident power. The speed and power estimates are also used to detect the corner effect in urban cellular systems to improve the handoff performance and reduce the call dropping rate.