Mai Vu

Cognitive radio networks

In recent years, the development of intelligent, adaptive wireless devices called cognitive radios, together with the introduction of secondary spectrum licensing, has led to a new paradigm in communications: cognitive networks. Cognitive networks are wireless networks that consist of several types of users: often a primary user (the primary license-holder of a spectrum band) and secondary users (cognitive radios). These cognitive users employ their cognitive abilities to communicate without harming the primary users. The study of cognitive networks is relatively new and many questions are yet to be answered. In this article we highlight some of the recent information theoretic limits, models, and design of these promising networks.

MIMO Wireless Linear Precoding

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.

Optimal linear precoders for MIMO wireless correlated channels with nonzero mean in space-time coded systems

This paper proposes linear precoder designs exploiting statistical channel knowledge at the transmitter in a multiple-input multiple-output (MIMO) wireless system. The paper focuses on channel statistics, since obtaining real-time channel state information at the transmitter can be difficult due to channel dynamics. The considered channel statistics consist of the channel mean and transmit antenna correlation. The receiver is assumed to know the instantaneous channel precisely. The precoder operates along with a space-time block code (STBC) and aims to minimize the Chernoff bound on the pairwise error probability (PEP) between a pair of block codewords, averaged over channel fading statistics. Two PEP design criteria are studied-minimum distance and average distance. The optimal precoder with an orthogonal STBC is established, using a convex optimization framework. Different relaxations then extend the solution to systems with nonorthogonal STBCs. In both cases, the precoder is a function of both the channel mean and the transmit correlation. A linear precoder acts as a combination of a multimode beamformer and an input shaping matrix, matching each side to the channel and to the input signal structure, respectively. Both the optimal beam direction and the power of each mode, obtained via a dynamic water-filling process, depend on the signal-to-noise ratio (SNR). Asymptotic analyses of the results reveal that, for all STBCs, the precoder approaches a single-mode beamformer on the dominant right singular vector of the channel mean as the channel K factor increases. On the other hand, as the SNR increases, it approaches an equipower multiple-mode beamformer, matched to the eigenvectors of the transmit correlation. Design examples and numerical simulation results for both orthogonal and nonorthogonal STBC precoding solutions are provided, illustrating the precoding array gain.

On the primary exclusive region of cognitive networks

In this paper, we consider a cognitive network in which a single primary transmitter communicates with primary receivers within an area of radius RO, called the primary exclusive region (PER). Inside this region, no cognitive users may transmit. Outside the PER, provided that the cognitive transmitters are at a minimal distance isinp from a primary receiver, they may transmit concurrently with the primary user. We determine bounds on the primary exclusive radius RO and the guard band isinp to guarantee an outage performance for the primary user. Specifically, for a desired rate CO and an outage probability beta, the probability that the primary users rate falls below CO is less than beta. This performance guarantee holds even with an arbitrarily large number of cognitive users uniformly distributed with constant density outside the primary exclusive region.

Cognitive Networks Achieve Throughput Scaling of a Homogeneous Network

Two distinct, but overlapping, networks that operate at the same time, space, and frequency is considered. The first network consists of n randomly distributed primary users, which form an ad hoc network. The second network again consists of m randomly distributed ad hoc secondary users or cognitive users. The primary users have priority access to the spectrum and do not need to change their communication protocol in the presence of the secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users to bring little loss to the primary networks throughput. By introducing preservation regions around primary receivers, a modified multihop routing protocol is proposed for the cognitive users. Assuming m=nβ with β >; 1, it is shown that the secondary network achieves almost the same throughput scaling law as a stand-alone network while the primary network throughput is subject to only a vanishingly small fractional loss. Specifically, the primary network achieves the sum throughput of order n1/2 and, for any δ >; 0, the secondary network achieves the sum throughput of order m1/2-δ with an arbitrarily small fraction of outage. Thus, almost all secondary source-destination pairs can communicate at a rate of order m-1/2-δ.

Scaling Laws of Cognitive Networks

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 links 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.

MISO Capacity with Per-Antenna Power Constraint

We establish in closed-form the capacity and the optimal signaling scheme for a MISO channel with per-antenna power constraint. Two cases of channel state information are considered: constant channel known at both the transmitter and receiver, and Rayleigh fading channel known only at the receiver. For the first case, the optimal signaling scheme is beamforming with the phases of the beam weights matched to the phases of the channel coefficients, but the amplitudes independent of the channel coefficients and dependent only on the constrained powers. For the second case, the optimal scheme is to send independent signals from the antennas with the constrained powers. In both cases, the capacity with per-antenna power constraint is usually less than that with sum power constraint.

Matched filtering with rate back-off for low complexity communications in very large delay spread channels

We study the possibility to transmit data over channels with large delay spreads under the constraint of a very simple receiver which has only one tap. Such a scheme is of interest when a cost-efficient way to transmit potentially high data rates are sought after. We investigate the performance of the optimal prefilter for this scheme and compare it to a simplified, so-called time-reversal (TR) prefilter which has very low complexity. At low SNRs, the TR prefilter and the optimal prefilter are equivalent. At high SNRs, the TR prefilter achieves a performance that is independent from the delay spread of the channel and hence its performance is the same for any bandwidth. In applications where bandwidth is abundant, such as ultra-wide band (UWB) communications, any required performance can be obtained by TR prefilters with a rate back-off transmission (i.e. transmission rate lower than the allowable bandwidth). Similar performance can also be obtained with full-rate transmission using several transmit antennas. This performance is guaranteed, since the high diversity of the large delay spread channel effectively eliminates any fading.

On the capacity of MIMO wireless channels with dynamic CSIT

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.

Improved Capacity Scaling in Wireless Networks With Infrastructure

This paper analyzes the impact and benefits of infrastructure support in improving the throughput scaling in networks of n randomly located wireless nodes. The infrastructure uses multiantenna base stations (BSs), in which the number of BSs and the number of antennas at each BS can scale at arbitrary rates relative to n. Under the model, capacity scaling laws are analyzed for both dense and extended networks. Two BS-based routing schemes are first introduced in this study: an infrastructure-supported single-hop (ISH) routing protocol with multiple-access uplink and broadcast downlink and an infrastructure-supported multihop (IMH) routing protocol. Then, their achievable throughput scalings are analyzed. These schemes are compared against two conventional schemes without BSs: the multihop (MH) transmission and hierarchical cooperation (HC) schemes. It is shown that a linear throughput scaling is achieved in dense networks, as in the case without help of BSs. In contrast, the proposed BS-based routing schemes can, under realistic network conditions, improve the throughput scaling significantly in extended networks. The gain comes from the following advantages of these BS-based protocols. First, more nodes can transmit simultaneously in the proposed scheme than in the MH scheme if the number of BSs and the number of antennas are large enough. Second, by improving the long-distance signal-to-noise ratio (SNR), the received signal power can be larger than that of the HC, enabling a better throughput scaling under extended networks. Furthermore, by deriving the corresponding information-theoretic cut-set upper bounds, it is shown under extended networks that a combination of four schemes IMH, ISH, MH, and HC is order-optimal in all operating regimes.