A new connectivity metric is proposed for cognitive radio networks. The analysis is developed based on a generalized model for cognitive radio networks where multiple primary users with independent activity factors are considered. The adjacent matrix elements, representing the weights associated to the network graph edges, are set proportional to the activity factors of primary users. It is shown that the proposed connectivity metric is a monotonically decreasing measure with the primary users activity factors. Furthermore, the metric efficiently determines the network connectivity under different primary users activities. The proposed connectivity metric is compared to the probability of finding a route metric which is commonly used as a measure for network connectivity. It is shown that the proposed metric captures the behavior of the probability of finding a route method with significant complexity reduction. Compared to the algebraic connectivity metric, the proposed metric is more robust in the presence of isolated nodes. Finally, the proposed metric can be utilized to analytically study and design cognitive radio networks.

A novel statistical channel model for multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems impaired by atmospheric and misalignment fading is developed. A slow-fading channel model is considered and the outage probability is derived as a performance measure. The diversity gain defined as the signal-to-noise ratio (SNR) exponent at high SNR is analyzed. Interestingly in the presence of misalignment fading the diversity gain depends only on the misalignment variance and is independent of the number of transmitters M and receivers N. Increasing the number of transmitters and receivers only results in a lower probability of outage for a given SNR, however, the rate of change is unaffected. Contrary to this case, the diversity gain of MIMO FSO systems in the presence of atmospheric fading and no misalignment is shown to be proportional to the number of transmitters and receivers, in particular the product MN.

Lower and upper bounds on the capacity of wireless optical intensity pulse amplitude modulation channels under nonnegativity and average optical power constraints are derived. A lower bound is derived based on source entropy maximization over a family of discrete nonuniform distributions with equally spaced mass points. A closed form for the maxentropic discrete input distribution is provided. Compared to previously reported bounds, the derived lower bound is tight at both low and high signal-to-noise ratios (SNRs). In addition, a closed-form upper bound is derived based on signal space geometry via a sphere packing argument. The proposed bound is tight at low SNRs and incurs a small gap to the channel capacity at high SNRs. The derived bounds asymptotically describe the optical intensity channel capacity at low SNRs, where a majority of such links operate.

The design and analysis of capacity-approaching input signalling for optical intensity channels are presented. Both peak and average optical power constraints are considered in the analysis. The capacity-achieving distribution for this channel is discrete with a finite number of mass points. In practice, finding this distribution requires solving a complex non-linear optimization at every SNR. In this work, we present a closed form discrete capacity-approaching distribution derived via source entropy maximization. The computation of this distribution is substantially less complex than previous optimization approaches and can be easily computed for different SNRs. The information rates using the derived maxentropic distribution are shown to be negligibly far away from the channel capacity found by non-linear optimization in the SNR range -6 to 6 dB.

This work considers the design of capacity-approaching, non-uniform optical intensity signalling in the presence of average and peak amplitude constraints. Although it is known that the capacity-achieving input distribution is discrete with a finite number of mass points, finding it requires complex non-linear optimization at every SNR. In this work, a simple expression for a capacity-approaching distribution is derived via source entropy maximization. The resulting mutual information using the derived discrete non-uniform input distribution is negligibly far away from the channel capacity. The computation of this distribution is substantially less complex than previous optimization approaches and can be easily computed at different SNRs. A practical algorithm for non-uniform optical intensity signalling is presented using multi-level coding followed by a mapper and multi-stage decoding at the receiver. The proposed signalling is simulated on free-space optical channels and outage capacity is analyzed. A significant gain in both rate and probability of outage is achieved compared to uniform signalling, especially in the case of channels corrupted by fog.

Wireless mesh networks (WMN) must often be upgraded as usage demands evolve. This is usually done by adding gateways which serve to increase the backhaul capacity of the network. In this paper we study the problem of this type of capacity augmentation using free-space optical (FSO) backhaul links. A joint clustering and gateway placement problem is formulated which includes the strong rate-distance dependence of practical FSO links. The formulation incorporates the positions of existing wireline gateways and minimizes the number of additional hybrid-FSO/RF gateways which are needed to satisfy the new target capacity requirements. A genetic algorithm solution is proposed, and the performance of our algorithm is compared to an optimal solution generated using an integer linear programming (ILP) formulation. Various scenarios are considered which demonstrate the value of using FSO backhaul links to obtain post-deployment capacity upgrades in response to evolving user traffic.

Analysis and design of near capacity approaching non-uniform signaling for optical intensity pulse amplitude modulation (PAM) channels is presented. A discrete nonuniform source distribution with quantized-level probabilities is presented. The proposed source distribution approaches the channel capacity while remaining practical for implementation. A significant gap in the mutual information between the non-uniform quantized-level distributions and uniform M-ary PAM is obtained. For example, at low SNR, non-uniform binary signalling has over four times the rate of uniform constellations. Multilevel coding and multistage decoding are proposed to approach the rate gains due to non-uniform signaling.

Improved upper and lower bounds on the capacity of wireless optical intensity channels under non-negativity and average optical power constraints are derived. We consider intensity modulated/direct detection (IM/DD) channels with pulse amplitude modulation (PAM). Utilizing the signal space geometry and a sphere packing argument, an upper bound is derived. Compared to previous work, the derived upper bound is tighter at low signal-to-noise ratios. In addition, a lower bound is derived based on source entropy maximization over discrete distributions. The proposed distribution provides a tighter lower bound compared to previous continuous distributions. The derived bounds asymptotically describe the capacity of PAM optical intensity channels at both low and high SNR.

In this paper, we present new approaches to blind channel estimation and equalization based on second order statistics (SOS). We first consider the case of minimum phase channels where the equalizer is designed based on the criterion of autocorrelation matching. We cast the problem as a convex optimization program that can be efficiently solved using interior point methods. Then we consider the equalization of single-input multiple-output (SIMO) channels. Due to oversampling, the equivalent channel matrix possesses a particular structure which enables us to estimate the channel based only on the information contained in the covariance matrix at zero delay. Simulation examples are provided to demonstrate the performance advantage of the proposed algorithms compared to existing techniques.