Nick Letzepis

The Gaussian free space optical MIMO channel with Q-ary pulse position modulation

The main drawback in communicating via the free space optical (FSO) channel is the detrimental effect the atmosphere has on a propagating laser beam. Atmospheric turbulence causes random fluctuations in the irradiance of the received optical laser beam, commonly referred to as scintillation. This paper investigates the use of multiple lasers and multiple apertures to mitigate the effects of scintillation. In particular, the FSO multiple-input multiple-output (MIMO) channel with Q-ary pulse position modulation (QPPM) and transmit repetition under the assumption of non-ideal photodetection is analyzed in terms of its uncoded bit error rate (BER) and ergodic channel capacity. This analysis is based, in part, on the use of irradiance fluctuation samples that were obtained from a laser range experiment that was conducted in the presence of moderate turbulence conditions. Expressions are derived for the log-likelihood ratio (LLR) of a received bit, uncoded BER and ergodic capacity. Using these results it is shown that large gains are possible with the use of MIMO combined with strong coding techniques.

Outage probability of the Gaussian MIMO free-space optical channel with PPM

Atmospheric effects can significantly degrade the reliability of free-space optical communications. One such effect is scintillation, caused by atmospheric turbulence, refers to random fluctuations in the irradiance and phase of the received laser beam. In this paper we investigate the use of multiple lasers and multiple apertures to mitigate scintillation. Since the scintillation process is slow, we adopt a block fading channel model and study the outage probability under the assumptions of orthogonal pulse-position modulation and non-ideal photodetection. Assuming perfect receiver channel state information (CSI), we derive the signal-to-noise ratio (SNR) exponents for the cases when the scintillation is lognormal, exponential and gamma-gamma distributed, which cover a wide range of atmospheric turbulence conditions. Furthermore, when CSI is also available at the transmitter, we illustrate very large gains in SNR are possible (in some cases larger than 15 dB) by adapting the transmitted power. Under a long-term power constraint, we outline fundamental design criteria via a simple expression that relates the required number of lasers and apertures for a given code rate and number of codeword blocks to completely remove system outages.

Outage analysis of the hybrid free-space optical and radio-frequency channel

We study the hybrid free-space optical (FSO) and radio-frequency (RF) channel from an information theoretic perspective. Since both links operate at vastly different carrier frequencies, we model the hybrid channel as a pair of parallel channels. Moreover, since the FSO channel signals at a higher rate than the RF channel, we incorporate this key feature in the parallel channel model. Both channels experience fading due to scintillation, which is slow compared to typical signalling rates. Under this framework, we study the fundamental limits of the hybrid channel. In particular, we analyse the outage probability in the large signal-to-noise ratio (SNR) regime, and obtain the outage diversity or SNR exponent of the hybrid system. First we consider the case when only the receiver has perfect channel state information (CSIR case), and obtain the exponents for general scintillation distributions. These exponents relate key system design parameters to the asymptotic outage performance and illustrate the benefits of using hybrid systems with respect to independent FSO or RF links. We next consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves significant power savings (on the order of tens of dBs) over uniform power allocation. We show that the suboptimal algorithm has the same diversity as the optimal power allocation strategy.

Capacity of the Multiple Spot Beam Satellite Channel With Rician Fading

In this correspondence, the uplink of a multibeam satellite system with Rician fading is analyzed under the framework of Wyners Gaussian cellular multiple access channel. In this framework the received signal at a given multibeam antenna is the sum of signals transmitted by users within that beams cell area plus a factor 0 les alpha les 1 times the sum of the signals transmitted by users from adjacent cells plus ambient Gaussian noise. Both one-dimensional (1-D) linear, and 2-D hexagonal cellular arrangements are considered. In addition, we consider a modified version of the 1-D linear arrangement whereby users from cells further than adjacent cells contribute to intercell interference. It is assumed that the distance between the antenna elements is small compared to the distance between a user and the satellite. Thus when fading is present, a particular users fading coefficient is the same at each multibeam antenna. This is the fundamental difference between the multibeam satellite fading channel and the terrestrial cellular fading channel, in which each user experiences independent fading at each base station. Using a Haar measure approximation we derive closed form approximations for the capacity of the satellite fading channel for the scenarios when optimal joint decoding and linear minimum mean square error filtering is employed at the ground station. These approximations are shown to be in close agreement to Monte Carlo simulation results for large dimensional systems. It is shown that fading causes a loss in capacity compared to the nonfading channel. Furthermore, at high signal-to-noise ratio (SNR) this loss is independent of the intercell interference and topology of the system, but is dependent on the distribution of the fading coefficients and the number of users per beam.

MIMO ARQ With Multibit Feedback: Outage Analysis

This paper studies the asymptotic outage performance of incremental redundancy automatic-repeat-request (INR-ARQ) transmission over multiple-input multiple-output (MIMO) block-fading channels with discrete input constellations. We first show that transmission with random codes using a discrete signal constellation across all transmit antennas achieves the optimal outage diversity given by the Singleton bound. The optimal SNR-exponent and outage diversity of INR-ARQ transmission over the MIMO block-fading channel are then analysed. We show that a significant gain in outage diversity is obtained by providing more than one bit feedback at each ARQ round. Thus, the outage performance of INR-ARQ transmission can be remarkably improved with minimal additional overhead. A practical feedback-and-power-adaptation rule is proposed for MIMO INR-ARQ, demonstrating the benefits provided by multibit feedback. Although the rule is sub-optimal in terms of outage performance, it achieves the optimal outage diversity.

Symbol-wise beamforming for MIMO-OFDM transceivers in the presence of co-channel interference and spatial correlation

In MIMO-OFDM communications over channels subject to co-channel interference, beamforming (BF) is conventionally applied independently to all subcarriers. Whilst this approach maximises mutual information, it is highly computationally complex. Symbol-wise BF considerably reduces the complexity by carrying out BF in the time domain. In this paper, we generalise symbol-wise BF to take co-channel interference into account. Maximising the mutual information is infeasible in this case and instead, we propose a novel iterative algorithm that maximises the SINR before OFDM demodulation. Computer simulations show that the performance loss relative to subcarrier-wise BF reduces with decreasing frequency selectivity or increasing spatial correlation.

Outage probability of the MIMO Gaussian free-space optical channel with PPM

The main drawback in communicating via the free-space optical channel is the detrimental effect the atmosphere has on a propagating laser beam. Atmospheric turbulence causes random fluctuations in the irradiance of the received laser beam, commonly referred to as scintillation. We investigate the mitigation of scintillation through the use of multiple lasers and multiple apertures, thereby creating a multiple-input multiple output (MIMO) channel. We adopt a quasi-static block fading model and study the outage probability of the channel under the assumption of orthogonal pulse-position modulation. Non-ideal photodetection is also assumed such that the combined shot noise and thermal noise are considered as signal-independent additive Gaussian white noise. Assuming perfect receiver channel state information (CSI), we compute the signal-to-noise ratio exponents for the cases when the scintillation is lognormal, exponential and gamma-gamma distributed, which cover a wide range of atmospheric turbulence conditions. Furthermore, we illustrate very large gains when CSI is also available at the transmitter.

Information capacity of multiple spot beam satellite channels

In this paper we present an information theoretic analysis of a multiple spot beam multiple access channel. The beam pattern considered consists of a center beam surrounded by a ring of six outer beams. Thus users in any given beam experience multiple access interference (MAI) from users in adjacent beams. For this channel we analyze the capacity region and derive expressions for the sum rate capacity. We found that the sum rate constraint is biting for symmetric rates at high interference and high signal-to-noise ratio (SNR) levels. The effects of the center users power on the capacity region is also examined

Channel measurement and estimation for free space optical communications

Free space optical (FSO) communication links experience different fading for longer terrestrial links, which may result in lognormal, Gamma-Gamma or exponentially distributed signals under weak, modarate and strong turbulence. Channel estimation is also corrupted by background and electrical noise. In this paper, we measure the FSO fading distribution from experimental data collected from a 1550nm, 12 km long terrestrial link. Background and electrical noise statistics are found from collected noise data. We also consider the estimation of unknown parameters from FSO channel samples considering the background and electrical noise which are the sum of fading plus Gaussian noise. We determine the root mean square estimation errors (RMSE) using various methods including the Method of Moments (MOM) and iterative Maximum Likelihood (ML) estimations. We evaluate the Cramer-Rao Bounds (CRB) for these problems. We compare our estimation technique performance with existing methods of estimation which ignore Gaussian noise. The new estimation technique which takes noise into account shows significant performance improvement in the low signal to noise ratio (SNR) region. We also compare the estimation performance under varying number of channel samples. We use a single dimension approach where only one parameter is estimated at once.

Bit error rate estimation for turbo decoding

In this paper we propose a method for on-line estimation of bit error rate during turbo decoding. We model the log-likelihood ratios as a mixture of two Gaussian random variables and derive estimators for the mean and variance of these distributions based on a maximum-likelihood approach. The parameter estimates are then employed to calculate the cross-over area of the Gaussian tails to estimate BER at each decoder iteration. The performance of the BER estimator is analysed and compared.