This paper presents two new upper bounds on the probability of error for maximum likelihood decoding in the finite blocklength regime. The first bound applies to fixed channel codes and uses the well-known union bound to express the probability of decoding error in terms of the total variation distance between the conditional transition probabilities. It is shown that this bound is tighter than the Bhattacharyya union bound and its variants. The second bound is an improvement on the Random Coding Union bound. In fact, the only decoding events that render it an upper bound, rather than an equality, are the ties a maximum likelihood decoder resolves in favour of the correct codeword. These bounds are then used to give new results for random spherical codes on the Gaussian channel.

Low probability of detection (or covert) communication refers to the scenario where information must be sent reliably to a receiver, but with low probability of detection by an adversary. Recent works on the fundamental limits of this communication problem have established achievability and converse bounds that are asymptotic in the block length of the code. This paper uses Gallager's random coding bound to derive a new achievability bound that is applicable to low probability of detection communication in the finite block length regime. Further insights are unveiled that are otherwise hidden in previous asymptotic analyses.

Multi-hop relaying is well known to extend the range of wireless communications. However, the end-to-end performance of the multi-hop relaying channel degrades compared to that observed at the first hop. This performance degradation mainly arises due to: 1) half-duplex loss and 2) hopping or relaying loss. In this paper, we analyze the degradation in outage probability and ergodic capacity due to hopping loss in a multiple-input multiple-output (MIMO) dual-hop decode-and-forward relaying network over Rayleigh fading channels. In particular, we characterize analytically the performance degradation by deriving closed-form approximations of ergodic capacity and outage probability in the single-source single-relay single-user, single-source multiple-relay single-user, and single-source single-relay multiple-user topologies. These approximations also provide insights on how to overcome performance degradations due to hopping loss. Moreover, we show that cooperative relaying schemes can recover a significant portion of the hopping loss.

In this paper, we present the performance analysis of a multibeam high throughput satellite (HTS) system with optical feeder link. We consider the forward link, or downlink, with a fixed gain transparent satellite payload, where the optical feeder link, i.e. the link between gateway and satellite, is impaired by turbulence fading and the RF user link, i.e. the link between satellite and user terminals, is degraded by rain fading. In multibeam HTS systems, frequency re-use in the user link creates interbeam interference which needs to be mitigated to avoid performance degradation. For this purpose, we consider our recently proposed novel zero-forcing (ZF) precoder that does not require channel state information at the gateway and compare its performance with the conventional ZF precoder. We derive statistics of the end-to-end signal-to-noise ratio to approximate performance measures including outage probability, average bit error rate and ergodic capacity. These approximations provide valuable insights into the system analysis. Monte Carlo simulations are used to validate the accuracy of our analysis.

It is well-known that relaying can extend the communication range. However, the performance of the relaying network is inferior compared to a single-hop system where the destination is placed hypothetically at the relay. The gap between the single-hop and relay network, dubbed the multi-hopping or relaying loss, is studied in this paper. In particular, we investigate the increase in outage probability and the degradation in ergodic capacity incurred due to the multi-hopping loss in a dualhop multiple-input multiple-output decode-and-forward relaying network operating in the single-source single-relay single-user topology. Moreover, we show that a cooperative relaying scheme, called the best relay scheme, in the single-source K-relays single-user topology can recover a significant portion of the multi-hopping loss. In both topologies, we derive closed-form approximations for the outage probability and ergodic capacity using the well-known Gaussian approximation.

Multibeam satellite communication (SatCom) with full or aggressive frequency re-use is one of the most promising candidates for next-generation high throughput satellite systems. However, frequency re-use creates interbeam interference which needs to be managed using multiuser precoding techniques in the forward link and multiuser detection techniques in the reverse link. This work considers the forward link of multibeam Sat-Com systems and proposes a novel zero-forcing (ZF) precoding technique that makes use of users' physical location and antenna radiation pattern available at the gateway. Contrary to conventional precoding techniques in multibeam SatCom systems, the proposed precoding technique does not require feedback from user terminals. Numerical results show that the proposed ZF precoder achieves higher ergodic capacity than the conventional ZF precoder. We provide a closed-form approximation for the ergodic capacity of the proposed ZF precoder under rain fading. We also provide a closed-form approximation for computing the moments of the rain fading attenuation which enables us to derive high and low signal-to-noise ratio (SNR) expressions of the ergodic capacity in closed-form. Furthermore, an upper bound on the ergodic capacity is obtained. Monte Carlo simulations are used to validate the accuracy of our analysis.

This paper analyses the von Mises approximation for the distribution of the phase angle between two independent complex Gaussian vectors. By upper bounding the Kullback-Leibler divergence, it is shown that when their circular means and variances coincide, the distribution converges to a von Mises distribution both in the low and high signal-to-noise ratio regimes.

The problem of synchronizing weak user signals in multiuser code-division multiple access systems is addressed. We integrate timing synchronization into an iterative multiuser detection (MUD) framework for the improved synchronization performance of weak users. First, the effect of correctly detected users on the remaining undetected users is suppressed via soft parallel interference cancellation. Then, the time offset (TO) of each undetected user is estimated. To speed up the MUD, interference cancellation is performed after only a few decoder iterations of the detected users, and the TO estimator is designed taking into account the residual multiple access interference. A low-complexity non-data-aided TO estimator that estimates the TO of each undetected user separately is proposed. The proposed technique significantly improves the synchronization performance of weak users under high near-far conditions compared to the full interference case. Assuming Gaussian distributed log-likelihood ratios at the decoder outputs, we directly relate the missed detection probability of a desired user to the root-mean-squared error of the detected user's data sequences. The extrinsic information transfer chart of the decoder is used to analyze the acquisition performance of the desired user with the number of decoder iterations of the detected users. An upper bound for the missed detection probability of the proposed estimator is derived.

This paper focuses on the problem of code acquisition in multiuser CDMA systems in a near-far scenario. A new time offset estimator which iteratively cancels interference from correctly acquired users is proposed. Interference cancellation is accomplished by projecting the received signal into the null space of already acquired users. The proposed technique performs well under low SNR conditions in the presence of high multiple access interference. Analytical expressions for the missed detection probability of the proposed estimator are derived and these agree with the results of Monte-Carlo simulations.

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.

We study hybrid free-space optical (FSO) and radio-frequency (RF) communications, whereby information is conveyed simultaneously using both optical and RF carriers. We consider the case where both carriers experience scintillation, which is a slow fading process compared to typical data rates. A parallel block-fading channel model is proposed, that incorporates differences in signalling rates, power scaling and scintillation models between the two carriers. Under this framework, we study the outage probability in the large signal-to-noise ratio (SNR) regime. First we consider the case when only the receiver has perfect channel state information (CSIR case) and obtain the SNR exponent for general scintillation distributions. Then we 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 the same diversity as the optimal one and provides significant power savings (on the order of tens of dBs) over uniform allocation.

We study the outage diversity of the multiple-input multiple-output (MIMO) Rayleigh block-fading channel when causal channel state information (CSI) is available at the transmitter (CSIT). Within this setting, we consider the optimal power allocation for blocks b = 1, ..., B given perfect CSIT for blocks 1, ..., b-u only, subject to a long-term power constraint. The parameter 0 ≤ u ≤ B is a fixed arbitrary integer that determines the delay in acquiring perfect knowledge of the CSI at the transmitter. Without explicitly solving the optimal power allocation problem, we derive the outage diversity of the system. For general 0 ≤ u ≤ B, we derive a simple recursive expression for computing the outage diversity. For the special case u = 0, it is shown that the outage diversity is infinite, coinciding with previously known results. For 1 ≤ u ≤ B, the outage diversity becomes finite and for the special case of u = 1, 2 it can be expressed in simple closed form.

In communication systems that use orthogonal frequency-division multiplexing and multiple transmit and receive antennas, beamforming (BF) is conventionally carried out on a subcarrier basis. The computational requirements are high as dedicated discrete Fourier transform (DFT) processors are needed for each antenna. Considerable complexity reductions can be achieved by symbol-wise BF, which performs the transmit and receive BF operations in the time domain, and therefore requires only one DFT processor per terminal. In this paper, we investigate symbol-wise BF for the mitigation of co-channel interference on spatially correlated channels, which are modelled with the Kronecker model. We show analytically that symbol-wise BF is the optimal BF scheme when the channel is frequency-flat or fully correlated, and present a novel iterative algorithm for the computation of the optimal antenna weights. Monte-Carlo simulations confirm that the relative performance loss of symbol-wise BF becomes negligible when approaching full correlation.

We consider improving the outage performance of incremental-redundancy automatic repeat request (INR-ARQ) transmission over the multiple-input multiple-output (MIMO) block-fading channel by allowing multi-bit receiver feedback. We show that multi-bit feedback offers significant gain in outage diversity when power adaptation is employed. A suboptimal feedback and power adaptation rule is proposed, illustrating the benefits provided by multi-bit feedback.

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.

We study the asymptotic outage probability of multiple-input multiple-output free-space optical communication with pulse-position modulation. In particular, we consider doubly stochastic scintillation models, lognormal-Rice and I-K distributions. First we consider the case when channel state information is available at the receiver only. Then we consider the case when it is also available at the transmitter.

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.

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.

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.

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.

In this correspondence, the uplink of a multibeam satellite system with Rician fading is analyzed under the framework of Wyner's 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 beam's 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 user's 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.

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.

We derive a closed form expression for the Shannon transform of the product of two arbitrary positive semidefinite random matrices, where at least one of the matrices is unitary invariant. In principle, S-transforms could be directly applied in this scenario, however in many cases of interest this approach leads to an intractable expression. Our alternative approach, based on hypergeometric functions, leads to a tractable asymptotic expression. This result is validated for finite size matrices using Monte Carlo simulations.

The nonGaussian behaviour of extrinsic log-values (L-values) during iterative turbo-decoding process is investigated in this paper. We assess the use of the Pearson system to model the extrinsic L-values nonGaussian behaviour