Zouheir Rezki

Ergodic Capacity of Cognitive Radio Under Imperfect Channel-State Information

A spectrum-sharing communication system where the secondary user is aware of the instantaneous channel-state information (CSI) of the secondary link but knows only the statistics and an estimated version of the secondary transmitter-primary receiver link is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels [with a continuous probability density function (pdf)] under the average and peak transmit power constraints and with respect to the following two different interference constraints: 1) an interference outage constraint and 2) a signal-to-interference outage constraint. When applied to Rayleigh fading channels, our results show, for example, that the interference constraint is harmful at the high-power regime, because the capacity does not increase with the power, whereas at the low-power regime, it has a marginal impact and no-interference performance, which corresponds to the ergodic capacity under average or peak transmit power constraint in the absence of the primary user, may be achieved.

A Unified Framework for the Ergodic Capacity of Spectrum Sharing Cognitive Radio Systems

We consider a spectrum sharing communication scenario in which a primary and a secondary users are communicating, simultaneously, with their respective destinations using the same frequency carrier. Both optimal power profile and ergodic capacity are derived for fading channels, under an average transmit power and an instantaneous interference outage constraints. Unlike previous studies, we assume that the secondary user has a noisy version of the cross link and the secondary link Channel State Information (CSI). After deriving the capacity in this case, we provide an ergodic capacity generalization, through a unified expression, that encompasses several previously studied spectrum sharing settings. In addition, we provide an asymptotic capacity analysis at high and low signal-to-noise ratio (SNR). Numerical results, applied for independent Rayleigh fading channels, show that at low SNR regime, only the secondary channel estimation matters with no effect of the cross link on the capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI. Furthermore, a practical on-off power allocation scheme is proposed and is shown, through numerical results, to achieve the full capacity at high and low SNR regimes and suboptimal rates in the medium SNR regime.

On the Capacity of Nakagami-m Fading Channels with Full Channel State Information at Low SNR

The capacity of flat Rayleigh fading channels with full channel state information (CSI) at the transmitter and at the receiver at asymptotically low SNR has been recently shown to scale essentially as SNR log(1/SNR). In this paper, we investigate the Nakagami-m fading channel capacity with full CSI, and show that the capacity of this channel scales essentially as Ω/m SNR log (1/SNR), where m is the Nakagami-m fading parameter and where Ω is the channel mean-square. We also show that one-bit CSI at the transmitter is enough to achieve this asymptotic capacity using an On-Off power control scheme. Our framework may be seen as a generalization of previous works as it captures the Rayleigh fading channel as a special case by taking m = 1.

Energy Efficient Resource Allocation for Cognitive Radios: A Generalized Sensing Analysis

In this paper, two resource allocation schemes for energy efficient cognitive radio systems are proposed. Our design considers resource allocation approaches that adopt spectrum sharing combined with soft-sensing information, adaptive sensing thresholds, and adaptive power to achieve an energy efficient system. An energy per good-bit metric is considered as an energy efficient objective function. A multi-carrier system, such as, orthogonal frequency division multiplexing, is considered in the framework. The proposed resource allocation schemes, using different approaches, are designated as sub-optimal and optimal. The sub-optimal approach is attained by optimizing over a channel inversion power policy. The optimal approach utilizes the calculus of variation theory to optimize a problem of instantaneous objective function subject to average and instantaneous constraints with respect to functional optimization variables. In addition to the analytical results, selected numerical results are provided to quantify the impact of soft-sensing information and the optimal adaptive sensing threshold on the system performance.

On the Secrecy Capacity of the Wiretap Channel With Imperfect Main Channel Estimation

We study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and eavesdropper channels and is the best known upper bound so far. The upper and lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) is also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for i.i.d. Rayleigh fading channels.

Ergodic Secret Message Capacity of the Wiretap Channel with Finite-Rate Feedback

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.

On the ergodic secrecy capacity of the wiretap channel under imperfect main channel estimation

The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.

Fundamental Limits of Parallel Optical Wireless Channels: Capacity Results and Outage Formulation

Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user time-division multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multi-output OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/post-coding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, this paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the Karush–Kuhn–Tucker conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints.

Low SNR Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels

In this paper, we study the ergodic capacity of free space optical communication systems over Gamma-Gamma atmospheric turbulence fading channels with perfect channel state information at both the transmitter and the receiver. In our framework, we mainly focus on the low signal-to-noise ratio range and show that the ergodic capacity scales proportionally to SNR log4(1/SNR). We show also that one-bit CSI feedback at the transmitter is enough to achieve this capacity using an on-off power control scheme.

Achievable rate of cognitive radio spectrum sharing MIMO channel with space alignment and interference temperature precoding

In this paper, we investigate the spectral efficiency gain of an uplink Cognitive Radio (CR) Multi-Input Multi-Output (MIMO) system in which the Secondary/unlicensed User (SU) is allowed to share the spectrum with the Primary/licensed User (PU) using a specific precoding scheme to communicate with a common receiver. The proposed scheme exploits at the same time the free eigenmodes of the primary channel after a space alignment procedure and the interference threshold tolerated by the PU. In our work, we study the maximum achievable rate of the CR node after deriving an optimal power allocation with respect to an outage interference and an average power constraints. We, then, study a protection protocol that considers a fixed interference threshold. Applied to Rayleigh fading channels, we show, through numerical results, that our proposed scheme enhances considerably the cognitive achievable rate. For instance, in case of a perfect detection of the PU signal, after applying Successive Interference Cancellation (SIC), the CR rate remains non-zero for high Signal to Noise Ratio (SNR) which is usually impossible when we only use space alignment technique. In addition, we show that the rate gain is proportional to the allowed interference threshold by providing a fixed rate even in the high SNR range.