Showing papers by "Mai Vu published in 2007"

MIMO Wireless Linear Precoding

Abstract: This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding A precoded system structure is then described, involving an encoder and a linear precoder Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios

On the capacity of MIMO wireless channels with dynamic CSIT

Abstract: Transmit channel side information (CSIT) can significantly increase MIMO wireless capacity. Due to delay in acquiring this information, however, the time-selective fading wireless channel often induces incomplete, or partial, CSIT. In this paper, we first construct a dynamic CSIT model that takes into account channel temporal variation. It does so by using a potentially outdated channel measurement and the channel statistics, including the mean, covariance, and temporal correlation. The dynamic CSIT model consists of an effective channel mean and an effective channel covariance, derived as a channel estimate and its error covariance. Both parameters are functions of the temporal correlation factor, which indicates the CSIT quality. Depending on this quality, the model covers smoothly from perfect to statistical CSIT. We then summarize and further analyze the capacity gains and the optimal input with dynamic CSIT, asymptotically at low and high SNRs. At low SNRs, dynamic CSIT often multiplicatively increases the capacity for all multi-input systems. The optimal input is typically simple single-mode beamforming. At high SNRs, for systems with equal or fewer transmit than receive antennas, it is well-known that the capacity gain diminishes to zero because of equi-power optimal input. With more transmit than receive antennas, however, the capacity gain is additive. The optimal input then is highly dependent on the CSIT. In contrast to equi-power, it can drop modes for channels with a strong mean or strongly correlated transmit antennas. For such mode-dropping at high SNRs in special cases, simple conditions on the channel K factor or the transmit covariance condition number are subsequently quantified. Next, using a convex optimization program, we study the MIMO capacity with dynamic CSIT non-asymptotically. Particularly, we numerically analyze effects on the capacity of the CSIT quality, the relative number of transmit and receive antennas, and the channel K factor. For example, the capacity gain based on dynamic CSIT is more sensitive to the CSIT quality at higher qualities. The program also helps to evaluate a simple, analytical capacity lower-bound based on the Jensen optimal input. The bound is tight at all SNRs for systems with equal or fewer transmit than receive antennas, and at low SNRs for others.

Scaling Laws of Cognitive Networks

Abstract: Opportunistic secondary spectrum usage has the potential to dramatically increase spectral efficiency and rates of a network of secondary cognitive users. In this work we consider a cognitive network: n pairs of cognitive transmitter and receiver wish to communicate simultaneously in the presence of a single primary transmitter-receiver link. We assume each cognitive transmitter-receiver pair communicates in a realistic single-hop fashion, as cognitive links are likely to be highly localized in space. We first show that under an outage constraint on the primary link's capacity, provided that the density of the cognitive users is constant, the sum-rate of the n cognitive links scales linearly with n as n ? ?. This scaling is in contrast to the sum-rate scaling of ?n seen in multi-hop ad-hoc networks. We then explore the optimal radius of the primary exclusive region: the region in which no secondary cognitive users may transmit, such that the outage constraint on the primary user is satisfied. We obtain bounds that help the design of this primary exclusive region, outside of which cognitive radios may freely transmit.

Scaling Laws of Cognitive Networks

Abstract: We consider a cognitive network consisting of n random pairs of cognitive transmitters and receivers communicating simultaneously in the presence of multiple primary users. Of interest is how the maximum throughput achieved by the cognitive users scales with n. Furthermore, how far these users must be from a primary user to guarantee a given primary outage. Two scenarios are considered for the network scaling law: (i) when each cognitive transmitter uses constant power to communicate with a cognitive receiver at a bounded distance away, and (ii) when each cognitive transmitter scales its power according to the distance to a considered primary user, allowing the cognitive transmitter-receiver distances to grow. Using single-hop transmission, suitable for cognitive devices of opportunistic nature, we show that, in both scenarios, with path loss larger than 2, the cognitive network throughput scales linearly with the number of cognitive users. We then explore the radius of a primary exclusive region void of cognitive transmitters. We obtain bounds on this radius for a given primary outage constraint. These bounds can help in the design of a primary network with exclusive regions, outside of which cognitive users may transmit freely. Our results show that opportunistic secondary spectrum access using single-hop transmission is promising.

Impact of Correlation on Linear Precoding in QSTBC Coded Systems with Linear MSE Detection

Abstract: In this paper, we study a wireless multiple-input multiple-output system in a Rayleigh flat-fading environment with correlation among the transmit antennas. We assume that the receiver has perfect CSI and the transmitter only knows the correlation matrix. The transmitter employs a quasi-orthogonal space-time block code in combination with a linear precoder; the receiver uses a linear MMSE detector. We analyze the optimal transmit precoding strategy that minimizes the average sum MSE at the receiver. We show that, as expected, the optimal precoding directions coincide with the eigenvectors of the transmit correlation matrix. The optimal power allocation, however, only supports at most 2 directions at all SNRs independent of the number of transmit antennas, which correspond to the 2 largest eigenvalues of the transmit correlation matrix. We characterize this optimal power allocation by the necessary and sufficient optimality conditions. At high SNRs, the optimal allocation approaches equal power on the two supported modes. At low SNRs, the weaker mode is dropped and the precoding matrix becomes single-mode beamforming. We provide a closed-form expression characterizing this low-SNR range. Numerical simulations confirm our theoretical analysis.

Adaptive vs. Diversity Transmission for Multiuser MISO Systems with Imperfect CSIT

Abstract: Adaptive transmission techniques including transmit beamforming, preceding, and opportunistic scheduling offer high spectral efficiency when channel state information at the transmitter (CSIT) is accurate, but suffer performance loss when the CSIT quality is poor. Diversity transmission techniques such as space-time coding and frequency interleaving, in contrast, are capable of capturing spatial and spectral diversity without CSIT, hence can provide good performance when CSIT degradation is severe. Between a pair of adaptive and diversity techniques, there exists a switching point in terms of the CSIT-quality; a CSIT- quality higher than this point favors the adaptive technique, but a lower CSIT-quality prefers the diversity one. This paper analyzes several adaptive and diversity schemes for a multiuser multiple-input single-output (MISO) system. Comparative performance in terms of the outage capacity is studied and the CSIT-quality switching points between adaptive and diversity schemes are analyzed. Results are supportive of adaptive transmissions for mobile applications, such as in the downlink of an orthogonal frequency division multiple access (OFDMA) system.