On a fading channel with no channel state information at the receiver, calculating true log-likelihood ratios (LLR) is complicated. Existing work assume that the power of the additive noise is known and use the expected value of the fading gain in a linear function of the channel output to find approximate LLRs. In this work, we first assume that the power of the additive noise is known and we find the optimum linear approximation of LLRs in the sense of maximum achievable transmission rate on the channel. The maximum achievable rate under this linear LLR calculation is almost equal to the maximum achievable rate under true LLR calculation. We also observe that this method appears to be the optimum in the sense of bit error rate performance too. These results are then extended to the case that the noise power is unknown at the receiver and a performance almost identical to the case that the noise power is perfectly known is obtained.
Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance losses compared to true LLRs.
A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes,…
In this paper, for a fading decode-and-forward full-duplex relay channel, we analytically derive optimum power allocations. Individual power constraints for the source and the relay are assumed and the related optimization problem is analyzed for two scenarios. First, optimization is taken over the source power, the relay power, and the correlation coefficient between the transmitted signals of the source and the relay. Then, for a fixed value of correlation coefficient, the optimization problem is analyzed. It is also proven that the optimization problems are convex for these two scenarios. F…
Accurate fading characterization and channel capacity determination are of paramount importance in both conventional and emerging communication systems. The present work addresses the nonlinearity of the propagation medium and its effects on the channel capacity. Such fading conditions are first characterized using information theoretic measures, namely, Shannon entropy, cross entropy and relative entropy. The corresponding effects on the channel capacity with and without power adaptation are then analyzed. Closed-form expressions are derived and validated through comparisons with respective r…
This paper is concerned with the error performance analysis of binary differential phase shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. Space antenna diversity reception is assumed. The diversity branches are independent, but have nonidentically distributed statistics. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case …
This paper studies the performance of antenna array processing in distributed multiple access networks without power control. The interference is represented as a Poisson point process. Desired and interfering signals are subject to both path-loss fading (with an exponent greater than 2) and to independent Rayleigh fading. Using these assumptions, we derive the exact closed form expression for the cumulative distribution function of the output signal-to-interference-plus-noise ratio when optimum combining is applied. This results in a pertinent measure of the network performance in terms of th…
The optimization of the pilot overhead in single-user wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the…
We propose an Iterative Detection and Decoding (IDD) scheme with Low Density Parity Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems for block-fading $F = 2$ and fast fading Rayleigh channels. An IDD receiver with soft information processing that exploits the code structure and the behaviour of the log likelihood ratios (LLR)'s is developed. Minimum Mean Square Error (MMSE) with Successive Interference Cancellation (SIC) and with Parallel Interference Cancellation (PIC) schemes are considered. The soft \textit{a posteriori} output of the decoder in a block-fading channel wi…
This paper evaluates the performance of reliability and latency in machine type communication networks, which composed of single transmitter and receiver in the presence of Rayleigh fading channel. The source's traffic arrivals are modeled as Markovian processes namely Discrete-Time Markov process, Fluid Markov process, and Markov Modulated Poisson process, and delay/buffer overflow constraints are imposed. Our approach is based on the reliability and latency outage probability, where transmitter not knowing the channel condition, therefore the transmitter would be transmitting information ove…
This paper studies the tradeoff between channel coding and ARQ (automatic repeat request) in Rayleigh block-fading channels. A heavily coded system corresponds to a low transmission rate with few ARQ re-transmissions, whereas lighter coding corresponds to a higher transmitted rate but more re-transmissions. The optimum error probability, where optimum refers to the maximization of the average successful throughput, is derived and is shown to be a decreasing function of the average signal-to-noise ratio and of the channel diversity order. A general conclusion of the work is that the optimum err…
This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $ε$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. Fo…
Spectral efficiency of low-density spreading non-orthogonal multiple access channels in the presence of fading is derived for linear detection with independent decoding as well as optimum decoding. The large system limit, where both the number of users and number of signal dimensions grow with fixed ratio, called load, is considered. In the case of optimum decoding, it is found that low-density spreading underperforms dense spreading for all loads. Conversely, linear detection is characterized by different behaviors in the underloaded vs. overloaded regimes. In particular, it is shown that spe…
This paper determines the optimum secondary user power allocation and ergodic multicast rate of point-to-multipoint communication in a cognitive radio network in the presence of outage constraints for the primary users. Using tools from extreme value theory (EVT), it is first proved that the limiting distribution of the minimum of independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Weibull distribution, when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) $κ-μ$ shadowed fading.…
Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and impli…
This paper is concerned with optimum diversity receiver structure and its performance analysis of differential phase shift keying (DPSK) with differential detection over nonselective, independent, nonidentically distributed, Rayleigh fading channels. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth, but to have distinct, asymmetric fading power spectral density characteristic. Using 8-DPSK as an example, the average bit error probability (BEP) of the optimum diversity receiver is obtained by calculating the BEP for each of the …
Amplitude-coherent (AC) detection is an efficient detection technique that can simplify the receiver design while providing reliable symbol error rate (SER). Therefore, this work considers AC detector design and SER analysis using M-ary amplitude shift keying (MASK) modulation over Rician fading channels. More specifically, we derive the optimum, near-optimum and a suboptimum AC detectors and compare their SER to the coherent, noncoherent and the heuristic AC detectors. Moreover, the analytical SER of the heuristic detector is derived using two different approaches for single and multiple rece…
This paper analyzes the power imbalance issue in power-domain NOMA (PD-NOMA) in the presence of channel correlations, typically encountered on the downlink of cellular systems when the base station antennas have an insufficient separation. In a recent paper, the authors analyzed this issue for a typical uplink scenario with uncorrelated channels, and the study revealed an astounding result that the optimum in terms of average error probability is achieved when the user signals are perfectly balanced in terms of power as in multi-user MIMO with power control. This result led to some questioning…
This paper focuses on studying the fundamental performance limits and linear dispersion code design for the MIMO-ARQ slow fading channel. Optimal average rate of well-known HARQ protocols is analyzed. The optimal design of space-time coding for the MIMO-ARQ channel is discussed. Information-theoretic measures are used to optimize the rate assignment and derive the optimum design criterion, which is then used to evaluate the optimality of existing space-time codes. A different design criterion, which is obtained from the error probability analysis of space-time coded MIMO-HARQ, is presented. Ex…
A network of $n$ wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power $P$ or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate $λ$. An upper bound is derived that shows the number of active links scales at most like $\frac{1}λ \log n$. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of $λ$, the number of supported links by this strateg…
We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish this duality by first deriving exact exponents for lossy coding of a memoryless source P, at distortion D, for a general i.i.d. codebook distribution Q, for both encoding success (R < R(P,Q,D)) and failure (R > R(P,Q,D)). We then turn to maximum likelihood (ML) decoding over a memoryless channel P with an i.i.d. input Q, and show that if we substitute P=QP, Q=…
This paper investigates the performance of wireless systems that employ finite-blocklength channel codes for transmission and operate under queueing constraints in the form of limitations on buffer overflow probabilities. A block fading model, in which fading stays constant in each coherence block and change independently between blocks, is considered. It is assumed that channel coding is performed over multiple coherence blocks. An approximate lower bound on the transmission rate is obtained from Feintein's Lemma. This lower bound is considered as the service rate and is incorporated into the…
Approximate Symbol error rate (SER), outage probability and rate expressions are derived for receive diversity system employing optimum combining when both the desired and the interfering signals are subjected to Rician fading, for the cases of a) equal power uncorrelated interferers b) unequal power interferers c) interferer correlation. The derived expressions are applicable for an arbitrary number of receive antennas and interferers and for any quadrature amplitude modulation (QAM) constellation. Furthermore, we derive a simple closed form expression for SER in the interference-limited regi…
A unified analytical framework for optimum power allocation in the unordered V-BLAST algorithm and its comparative performance analysis are presented. Compact closed-form approximations for the optimum power allocation are derived, based on average total and block error rates. The choice of the criterion has little impact on the power allocation and, overall, the optimum strategy is to allocate more power to lower step transmitters and less to higher ones. High-SNR approximations for optimized average block and total error rates are given. The SNR gain of optimization is rigorously defined and…
This paper is devoted to the design of precoders maximizing the ergodic mutual information (EMI) of bi-correlated flat fading MIMO systems equiped with MMSE receivers. The channel state information and the second order statistics of the channel are assumed available at the receiver side and at the transmitter side respectively. As the direct maximization of the EMI needs the use of non attractive algorithms, it is proposed to optimize an approximation of the EMI, introduced recently, obtained when the number of transmit and receive antennas $t$ and $r$ converge to $\infty$ at the same rate. It…
Massive multiple-input--multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE (EW-MMSE) estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate t…
Impairments baseband model in-phase and quadrature-phase Imbalance (IQI) and Residual hardware impairments (RHI) are two key factors degrading the performance of wireless communication systems (WCSs), particularly when high-frequency bands are employed, as in 5G systems and beyond. The impact of either IQI or RHI on the performance of various WCSs has been investigated exclusively in a separate way. To fill this gap, in this paper, the joint effect of both IQI and RHI on the performance of a WCS subject to the sum of Fox's H-function fading model (SFHF) is investigated. Such a fading model gen…
Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high S…
This paper studies the optimal points in the capacity region of Gaussian multiple access channels (GMACs) with constant fading, multiple antennas and various power constraints. The points of interest maximize general rate objectives that arise in practical communication scenarios. Achieving these points constitutes the task of jointly optimizing the time-sharing parameters, the input covariance matrices and the order of decoding used by the successive interference cancellation receiver. To approach this problem, Carathéodory's theorem is invoked to represent time-sharing and decoding orders jo…
Cooperative communication has been shown to provide significant increase of transmission reliability and network capacity while expanding coverage in cellular networks. The present work is devoted to the investigation of the end-to-end performance and power allocation of a maximum-ratio-combining based regenerative multi-relay cooperative network over non-homogeneous scattering environment, which is the case in realistic wireless communication scenarios. Novel analytic expressions are derived for the end-to-end symbol-error-rate of both $M-$ary Phase-Shift Keying and $M-$ary Quadrature Amplitu…
This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control. Each secondary user executes the derived power control policy in a distributed fashion by using local knowledge of its direct and interference channel gains such that the resulting aggregate (average) interference does not disrupt primary's communication. Then, the tight sum-rate scaling laws are derived as a function of the number of secondary users $N$ under…
This paper studies the structure of downlink sum-rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back. Firstly, it is shown that any sum-rate maximizing selective decentralized feedback policy must be a threshold feedback policy. This result holds for all fading channel models with continuous distribution functions. Secondly, the resulting optimum threshold selection problem is analyzed in detail. This is a non-convex optimization problem over finite dimensional Euclidean spa…
Reliable communication over the discrete-input/continuous-output noncoherent multiple-input multiple-output (MIMO) Rayleigh block fading channel is considered when the signal-to-noise ratio (SNR) per degree of freedom is low. Two key problems are posed and solved to obtain the optimum discrete input. In both problems, the average and peak power per space-time slot of the input constellation are constrained. In the first one, the peak power to average power ratio (PPAPR) of the input constellation is held fixed, while in the second problem, the peak power is fixed independently of the average p…
We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the sec…
Effective Capacity (EC) indicates the maximum communication rate subject to a certain delay constraint while effective energy efficiency (EEE) denotes the ratio between EC and power consumption. In this paper, we analyze the EEE of ultra-reliable networks operating in the finite blocklength regime. We obtain a closed form approximation for the EEE in Rayleigh block fading channels as a function of power, error probability, and delay. We show the optimum power allocation strategy for maximizing the EEE in finite blocklength transmission which reveals that Shannon's model underestimates the opti…
In this paper, we develop optimal energy-bandwidth allocation algorithms in fading channels for multiple energy harvesting transmitters, each may communicate with multiple receivers via orthogonal channels. We first assume that the side information of both the channel states and the energy harvesting states is known for $K$ time slots {\em a priori}, and the battery capacity and the maximum transmission power in each time slot are bounded. The objective is to maximize the weighted sum-rate of all transmitters over the $K$ time slots by assigning the transmission power and bandwidth for each tr…
While first-order channel statistics, such as bit-error rate (BER) and outage probability, play an important role in the design of wireless communication systems, they provide information only on the static behavior of fading channels. On the other hand, second-order statistics, such as level crossing rate (LCR) and average outage duration (AOD), capture the correlation properties of fading channels, hence, are used in system design notably in packet-based transmission systems. In this paper, exact closed-form expressions are derived for the LCR and AOD of the signal at a receiver where maxima…
The point-to-point multiple-antenna channel is investigated in uncorrelated block fading environment with Rayleigh distribution. The maximum throughput and maximum expected-rate of this channel are derived under the assumption that the transmitter is oblivious to the channel state information (CSI), however, the receiver has perfect CSI. First, we prove that in multiple-input single-output (MISO) channels, the optimum transmission strategy maximizing the throughput is to use all available antennas and perform equal power allocation with uncorrelated signals. Furthermore, to increase the expect…
This work is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall $Q{-}$function, the incomplete Toronto function, the Rice $Ie$-function and the incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and the Humbert, $Φ_{1}$, function as well as for specific cases of the Kamp${\it \acute{e}}$ de F${\it \acute{e}}$riet function. These functions can be considered us…
In a heterogeneous unreliable multiaccess network, wherein terminals share a common wireless channel with distinctive error probabilities, existing works have showed that a persistent round-robin (RR-P) scheduling policy (i.e., greedy policy) can be arbitrarily worse than the optimum in terms of Age of Information (AoI) under standard Automatic Repeat reQuest (ARQ), and one must resort to Whittle's index approach for optimal AoI. In this paper, practical Hybrid ARQ (HARQ) schemes which are widely-used in today's wireless networks are considered. We show that RR-P is very close to optimum with …
In this paper, a two-hop network in which information is transmitted from a source via a relay to a destination is considered. It is assumed that the channels are static fading with additive white Gaussian noise. All nodes are equipped with a single antenna and the Channel State Information (CSI) of each hop is not available at the corresponding transmitter. The relay is assumed to be simple, i.e., not capable of data buffering over multiple coding blocks, water-filling over time, or rescheduling. A commonly used design criterion in such configurations is the maximization of the average receiv…
This paper considers minimum sum mean-squared error (sum-MSE) linear transceiver designs in multiuser downlink systems with imperfect channel state information. Specifically, we derive the optimal energy allocations for training and data phases for such a system. Under MMSE estimation of uncorrelated Rayleigh block fading channels with equal average powers, we prove the separability of the energy allocation and transceiver design optimization problems. A closed-form optimum energy allocation is derived and applied to existing transceiver designs. Analysis and simulation results demonstrate the…
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 (ST-PR) link, is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels (with continuous probability density function) under average and peak transmit-power constraints and with respect to two different interference constraints: an interference outage constraint and a signal-t…
In this paper, we analytically study the bit error rate (BER) performance of underwater visible light communication (UVLC) systems with binary pulse position modulation (BPPM). We simulate the channel fading-free impulse response (FFIR) based on Monte Carlo numerical method to take into account the absorption and scattering effects. Additionally, to characterize turbulence effects, we multiply the aforementioned FFIR by a fading coefficient which for weak oceanic turbulence can be modeled as a lognormal random variable (RV). Moreover, to mitigate turbulence effects, we employ multiple transmit…
Explicit codes are constructed that achieve the diversity-multiplexing gain tradeoff of the cooperative-relay channel under the dynamic decode-and-forward protocol for any network size and for all numbers of transmit and receive antennas at the relays. A particularly simple code construction that makes use of the Alamouti code as a basic building block is provided for the single relay case. Along the way, we prove that space-time codes previously constructed in the literature for the block-fading and parallel channels are approximately universal, i.e., they achieve the DMT for any fading distr…
We analyze a cooperative wireless communication system with finite block length and finite battery energy, under quasi-static Rayleigh fading. Source and relay nodes are powered by a wireless energy transfer (WET) process, while using the harvested energy to feed their circuits, send pilot signals to estimate channels at receivers, and for wireless information transmission (WIT). Other power consumption sources beyond data transmission power are considered. The error probability is investigated under perfect/imperfect channel state information (CSI), while reaching accurate closed-form approxi…
Effective Capacity defines the maximum communication rate subject to a specific delay constraint, while effective energy efficiency (EEE) indicates the ratio between effective capacity and power consumption. We analyze the EEE of ultra-reliable networks operating in the finite blocklength regime. We obtain a closed form approximation for the EEE in quasi-static Nakagami-$m$ (and Rayleigh as sub-case) fading channels as a function of power, error probability, and latency. Furthermore, we characterize the QoS constrained EEE maximization problem for different power consumption models, which show…
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper. We present an inner bound on the secrecy capacity region for this model. This inner bound is base…
Orthogonal frequency division multiplexing (OFDM) has been considered for visible light communication (VLC) thanks to its ability to boost data rates as well as its robustness against frequency-selective fading channels. A major disadvantage of OFDM is the large dynamic range of its time-domain waveforms, making OFDM vulnerable to nonlinearity of light emitting diodes (LEDs). DC biased optical OFDM (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) are two popular OFDM techniques developed for the VLC. In this paper, we will analyze the performance of the DCO-OFDM and ACO-OFDM signa…
In this paper, we study the trade-off between reliability and latency in machine type communication (MTC), which consists of single transmitter and receiver in the presence of Rayleigh fading channel. We assume that the transmitter does not know the channel conditions, therefore it would be transmitting information over a fixed rate. The fixed rate transmission is modeled as a two-state continuous-time Markov process, where the optimum transmission rate is obtained. Moreover, we conduct a performance analysis for different arrival traffic originated from MTC device via effective rate transmiss…
