Ahmed A. Farid

Outage Capacity Optimization for Free-Space Optical Links With Pointing Errors

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10-5. Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.

Diversity Gain and Outage Probability for MIMO Free-Space Optical Links with Misalignment

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.

Capacity Bounds for Wireless Optical Intensity Channels With Gaussian Noise

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.

Channel capacity and non-uniform signalling for free-space optical intensity channels

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.

Free-Space Optical Gateway Placement in Hybrid Wireless Mesh Networks

The capacity of wireless mesh networks (WMN) must usually be upgraded as usage demands evolve over time. This is normally done by adding gateways which serve to increase the backhaul capacity of the network. In this paper we consider adding capacity in this manner using free-space optical (FSO) backhaul links. To accomplish this, we formulate a joint clustering and gateway placement problem 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 target capacity requirements. After showing the complexity of the problem, a solution that is motivated by genetic algorithms is proposed. The performance of our algorithm is then compared to an optimal solution generated via an integer linear program (ILP) for small WMNs. The proposed algorithm is then modified to allow for balancing the traffic load that is carried by each gateway in the WMN. Many scenarios are considered which demonstrate the value of using FSO backhaul links to obtain post-deployment capacity upgrades in response to changes in user traffic.

Upper and Lower Bounds on the Capacity of Wireless Optical Intensity Channels

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.

Outage Capacity for MISO Intensity-Modulated Free-Space Optical Links With Misalignment

The outage capacity of slow-fading free-space optical channels is analyzed for a multiple-input/single-output configuration in the presence of atmospheric and misalignment fading. A spatial repetition code is considered at the transmitter and a closed-form expression for the outage capacity is developed. In addition, a simple asymptotic closed-form expression is derived at high signal-to-noise ratio. Two methods are considered for system design using the derived outage capacity results with different beam configurations. The outage capacity is optimized over a predetermined set using numerical techniques. Using the asymptotic form of the outage capacity, however, a closed form for the optimum beamwidth is derived. A comparison of simulation results in both cases gives very similar performance indicating the effectiveness of the asymptotic form to provide a near-optimum expression for the beamwidth.

Diversity gains for MIMO wireless optical intensity channels with atmospheric fading and misalignment

A general channel model for multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems impaired by atmospheric and misalignment fading is developed. The outage probability as a performance measure is derived and the diversity gain is analyzed. It is shown that the diversity gain is independent of the number of transmitters and receivers and only determined based on the misalignment parameters.

Capacity of Optical Intensity Channels with Peak and Average Power Constraints

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.

Spectrally factorized optical OFDM

A novel bandwidth efficient method to implement orthogonal frequency division multiplexing (OFDM) on intensity modulated direct detection (IM/DD) channels is presented and termed spectrally factorized optical OFDM (SFO-OFDM). It is shown that a necessary and sufficient condition for a band-limited periodic signal to be positive for all time is that the frequency coefficients form an autocorrelation sequence. Instead of sending data directly on the subcarriers, the autocorrelation of the complex data sequence is performed before transmission to guarantee non-negativity. In z-domain, the average optical power is linked to the position of the zeros and used for the design of signal sets. In contrast to previous approaches, SFO-OFDM is able to use the entire bandwidth for data transmission and does not require reserved subcarriers. Using a sub-optimal design technique with 9 subcarriers and 8 bits per symbol, SFO-OFDM has a 0.5 dB gain over ACO-OFDM at a BER of 10−5 and a reduction in peak-to-average ratio of more than 30%.