Rohit U. Nabar

Fading relay channels: performance limits and space-time signal design

Cooperative diversity is a transmission technique, where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination, and relay terminals are each equipped with single antenna transceivers. We consider three different time-division multiple-access-based cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplify-and-forward (AF) or decode-and-forward (DF) modes. For each protocol, we study the ergodic and outage capacity behavior (assuming Gaussian code books) under the AF and DF modes of relaying. We analyze the spatial diversity performance of the various protocols and find that full spatial diversity (second-order in this case) is achieved by certain protocols provided that appropriate power control is employed. Our analysis unifies previous results reported in the literature and establishes the superiority (both from a capacity, as well as a diversity point-of-view) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) space-time code design for fading relay channels operating in the AF mode. We show that the corresponding code design criteria consist of the traditional rank and determinant criteria for the case of colocated antennas, as well as appropriate power control rules. Consequently space-time codes designed for the case of colocated multiantenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.

Capacity scaling laws in MIMO relay networks

The use of multiple antennas at both ends of a wireless link, popularly known as multiple-input multiple-output (MIMO) wireless, has been shown to offer significant improvements in spectral efficiency and link reliability through spatial multiplexing and space-time coding, respectively. This paper demonstrates that similar performance gains can be obtained in wireless relay networks employing terminals with MIMO capability. We consider a setup where a designated source terminal communicates with a designated destination terminal, both equipped with M antennas, assisted by K single-antenna or multiple-antenna relay terminals using a half-duplex protocol. Assuming perfect channel state information (CSI) at the destination and the relay terminals and no CSI at the source, we show that the corresponding network capacity scales as C = (M/2) log(K) + O(1) for fixed M, arbitrary (but fixed) number of (transmit and receive) antennas N at each of the relay terminals, and K rarr infin. We propose a protocol that assigns each relay terminal to one of the multiplexed data streams forwarded in a doubly coherent fashion (through matched filtering) to the destination terminal. It is shown that this protocol achieves the cut-set upper bound on network capacity for fixed M and K rarr infin (up to an O(1)-term) by employing independent stream decoding at the destination terminal. Our protocol performs inter-stream interference cancellation in a completely decentralized fashion, thereby orthogonalizing the effective MIMO channel between source and destination terminals. Finally, we discuss the case where the relay terminals do not have CSI and show that simple amplify-and-forward relaying, asymptotically in K, for fixed M and fixed N ges 1, turns the relay network into a point-to-point MIMO link with high-SNR capacity C = (M/2) log(SNR) + O(1), demonstrating that the use of relays as active scatterers can recover spatial multiplexing gain in poor scattering environments

Selecting an optimal set of transmit antennas for a low rank matrix channel

Previous work has shown that the use of multiple antennas in a fading environment results in a linear increase in capacity. This paper examines the capacity of a multiple antenna element array (MEA) in a quasi-static flat fading environment with a rank deficient channel. We assume that the channel is known at the receiver and the existence of a feedback path to the transmitter. For a particular channel realization, we show that the judicious use of fewer transmit antennas when the channel matrix is ill-conditioned can increase system capacity. We develop a criterion for selecting an optimum set of transmit antennas. This selection is optimal in the sense that the capacity of the resulting MEA system is greater than that for any other configuration with the same number of transmit antennas chosen from the original set. The resulting channel is full rank.

Performance of multiantenna signaling techniques in the presence of polarization diversity

Multiple-input multiple-output (MIMO) antenna systems employ spatial multiplexing to increase spectral efficiency or transmit diversity to improve link reliability. The performance of these signaling strategies is highly dependent on MIMO channel characteristics, which, in turn, depend on antenna height and spacing and richness of scattering. In practice, large antenna spacings are often required to achieve significant multiplexing or diversity gain. The use of dual-polarized antennas (polarization diversity) is a promising cost- and space-effective alternative, where two spatially separated uni-polarized antennas are replaced by a single antenna structure employing orthogonal polarizations. This paper investigates the performance of spatial multiplexing and transmit diversity (Alamouti (see IEEE J. Select. Areas Commun., vol.16, p.1451-58, Oct. 1998) scheme) in MIMO wireless systems employing dual-polarized antennas. In particular, we derive estimates for the uncoded average symbol error rate of spatial multiplexing and transmit diversity and identify channel conditions where the use of polarization diversity yields performance improvements. We show that while improvements in terms of symbol error rate of up to an order of magnitude are possible in the case of spatial multiplexing, the presence of polarization diversity generally incurs a performance loss for transmit diversity techniques. Finally, we provide simulation results to demonstrate that our estimates closely match the actual symbol error rates.

Characterizing the statistical properties of mutual information in MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver. Taking into account spatial fading correlation both at the transmitter and the receiver, a tight closed-form lower-bounds is provided for ergodic capacity and an accurate closed-form approximations of the variance of mutual information are derived over such channels. Based on these results, we investigate the impact of the number of antennas and transmit and receive correlation on ergodic capacity and on the variance of mutual information and draw insights into the tradeoff between diversity gain and spatial multiplexing gain.

Near-optimal selection of transmit antennas for a MIMO channel based on Shannon capacity

Current wireless MIMO (multiple transmit and receive antenna) systems are designed with the assumption that the fading channel is estimated perfectly at the receiver while the transmitter has no channel knowledge. If even a small amount of information is fed back to the transmitter, the capacity of the resulting channel increases appreciably. We consider a low-scattering, quasistatic environment where the matrix channel is rank deficient. Previous results (Gore et al. 2000, and Nabar et al. 2000) for such a channel indicate that channel capacity can be increased by a judicious choice of fewer transmit antennas. The optimal subset of transmit antennas is computed by the receiver as the subset that induces the highest Shannon capacity of all subsets of the same cardinality. Here we describe a computationally efficient, near-optimal search technique for the optimal subset based on classical waterpouring. We also provide enhanced search techniques based on partial waterpouring and uniform pourer allocation over the strongest channel modes that outperform waterpouring at high signal to noise ratios.

Measurement and characterization of broadband MIMO fixed wireless channels at 2.5 GHz

We study the channel typical for cellular broadband fixed wireless applications. A measurement system for a two-element-transmit by two-element-receive antenna configuration was built, Measurements were conducted in a suburban environment with dual antenna polarization and transmit separation. We present results on K-factor, cross-polarization discrimination (XPD) and Doppler spectrum. Our results address the influence of distance and antenna height for K-factor and XPD. We also comment on the properties of a fixed wireless channel and describe its Doppler spectrum.

Transmit optimization for spatial multiplexing in the presence of spatial fading correlation

Multiple-input multiple-output (MIMO) wireless systems employ spatial multiplexing to increase data rate. The performance of spatial multiplexing is highly dependent on channel statistics which in turn depend on antenna spacing and richness of scattering. It has been shown Bolcskei and Paulraj, (see Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, Oct./Nov. 2000) that the presence of transmit correlation can have a detrimental effect on the performance of multi-antenna signaling techniques. We present a novel scheme to (partly) mitigate the performance loss of spatial multiplexing in the presence of highly correlated fading at the transmitter. The adaption to be performed at the transmitter is a form of power allocation and/or relative phase adjustment between the different symbol streams to be multiplexed. We consider the cases of dual-polarized as well as uni-polarized antennas and derive estimates of the uncoded average symbol error rate as a function of channel statistics, power allocation and phase adjustment. We then optimize power allocation and phase adjustment and demonstrate that this form of preprocessing can yield SNR gains of up to 4 dB over the case where no precoding is employed.

Space-time signal design for fading relay channels

Cooperative diversity is a transmission technique where multiple users pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. We examine space-time signal design for a simple amplify-and-forward relay channel. We show that the code design criteria for the relay case consist of the traditional rank and determinant criteria as well as appropriate power control rules. While proper signal design and power control can indeed achieve full spatial diversity gain, the potential benefit of relay-assisted communication over direct communication depends strongly on the channel conditions. In particular, we present a switching criterion based on which the source terminal may opt to forego relay-assisted communication and communicate with the destination terminal directly. The criterion is based on the cut-off rate of the effective channel - the physical channel in conjunction with finite constellation and maximum-likelihood (ML) decoding.

Performance limits of amplify-and-forward based fading relay channels

In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination and relay terminals are each equipped with single antenna transceivers. We consider three different TDMA-based cooperative protocols that vary the degree of broadcasting and receive collision. For each protocol, the relay terminal simply amplifies-and-forwards the signal received from the source terminal to the destination. We study the ergodic and outage capacity behavior of each of the protocols assuming Gaussian codebooks and show that full spatial diversity (second-order in this case) is achieved by certain protocols provided that appropriate power control is employed. Finally, we establish the superiority (both from a capacity as well as a diversity point-of-view) of a new protocol proposed in this paper.