SUMMARY: Learning underlying correlation patterns in data is a central problem across scientific fields. Maximum entropy models present an important class of statistical approaches for addressing this problem. However, accurately and efficiently inferring model parameters are a major challenge, particularly for modern high-dimensional applications such as in biology, for which the number of parameters is enormous. Previously, we developed a statistical method, minimum probability flow-Boltzmann Machine Learning (MPF-BML), for performing fast and accurate inference of maximum entropy model parameters, which was applied to genetic sequence data to estimate the fitness landscape for the surface proteins of human immunodeficiency virus and hepatitis C virus. To facilitate seamless use of MPF-BML and encourage more widespread application to data in diverse fields, we present a standalone cross-platform package of MPF-BML which features an easy-to-use graphical user interface. The package only requires the input data (protein sequence data or data of multiple configurations of a complex system with large number of variables) and returns the maximum entropy model parameters. AVAILABILITY AND IMPLEMENTATION: The MPF-BML software is publicly available under the MIT License at https://github.com/ahmedaq/MPF-BML-GUI. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We derive an asymptotic outage probability expression for multiple-input multiple-output maximum-ratiocombining (MIMO-MRC) systems considering Rician fading channels with both transmit and receive spatial correlation. This result is facilitated by a new asymptotic expression which we obtain for the cumulative distribution function of the maximum eigenvalue of a noncentral quadratic form in complex Gaussian matrices. Based on our analysis, we demonstrate that for a rank-1 line-of-sight (LoS) path, the interaction with the correlation matrices may yield improved or degraded performance. The relative effect depends largely on the geometric alignment of the LoS path with the eigenvectors of the correlation matrices. Generally speaking, when the LoS path aligns with the weak eigenvectors (i.e., those corresponding to the smallest eigenvalues), both a stronger LoS component, characterized by a higher Rician K factor, and a higher correlation lead to improved performance. In contrast, when the LoS path aligns with the strong eigenvectors, we demonstrate that there exists distinct regions for which increasing the Rician K factor has a beneficial or deleterious effect. Our results, in general, provide novel insight into how the mutual interactions of LoS and spatial correlation components impact the performance of MIMO-MRC systems.

We consider multiple-antenna signal detection of primary user transmission signals by secondary user receivers in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary users. We first derive exact expressions for the moments of the generalized likelihood ratio (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate, which is used to obtain a simple design rule for the signal detection threshold.

In this paper, the impact of interferers that are not synchronized in frequency is investigated in multi-antenna OFDM systems. Exact closed-form expressions for the outage probabilities are derived for two spatial linear receivers: the matched-filter (MF) receiver and the linear minimum-mean-square-error (LMMSE) receiver, assuming correlated frequency-selective Rayleigh fading channels and carrier frequency offsets (CFOs) between each interferer and the receiver. It is found that the CFOs have a negligible impact on the performance of the MF receiver, but a non-negligible impact on the performance of the LMMSE receiver for a range of realistic parameters. This theoretical analysis reveals valuable insights into practical implementation of such systems, and enables system designers to quantify the impact of the CFOs on the performance of the MF receiver and the LMMSE receiver.

Deployment of low-power low-cost small access points such as femtocell access points (FAPs) constitute an attractive solution for improving the existing macrocell access points' (MAPs) capacity, reliability, and coverage. However, FAP deployment faces challenging problems such as interference management and the lack of flexible frameworks for deploying the FAPs by the service providers (SPs). In this paper, we propose a novel solution that jointly associates the user equipment (TIE) to the APs, and allocates the FAPs to the SPs such that the the total satisfaction of the TIEs in an uplink OFDMA network is maximized. We model the competitive behaviors among the TIEs, FAPs, and SPs as a dynamic matching game and we propose distributed algorithms to find the optimal TIE association and FAP allocations. We show analytically that the matching algorithms converge to the optimal and stable outcomes after a small number of iterations. Simulations and analytical results show the proposed mechanism is arbitrarily close to the global optimal solution by setting a design parameter (step number) but has significantly reduced overhead and complexity over the centralized algorithm.

In this paper, we investigate a new polynomial pricing function based demand side management scheme for future smart grid, where the consumers are charged based on their instantaneous load. A non-cooperative game is formulated, where each consumer aims to minimize their total energy cost based on the given pricing function. By casting this game in the variational inequality framework, we present sufficient conditions for the uniqueness of the optimal solution. We then propose a distributed and simultaneous algorithm to achieve the optimal solution. Sufficient conditions for the geometrical convergence of our algorithm are also provided and proved. Numerical results reveal that our proposed algorithm converges very quickly, and is effective in encouraging consumers to shift their energy usage from peak to non-peak times.

We consider the use of physical-layer security in a wireless communication system where multiple jamming nodes assist multiple source-destination nodes in combating unwanted eavesdropping from a single eavesdropper. In particular, we propose a distributed algorithm that matches each source-destination pair with a particular jammer. Our algorithm caters for three channel state information (CSI) assumptions: global CSI, local CSI, and local CSI without the eavesdropper channel. We prove that our algorithm has many desirable properties. First, the outcome of the proposed algorithm results in a stable matching, which is important if the source and jamming nodes are selfish. Second, the secrecy rate of the proposed algorithm converges to the secrecy rate of a centralized optimal solution, if the price step-number is sufficiently small. Third, our algorithm converges only after a small number of iterations, and its overhead is relatively small. Fourth, our algorithm has a significantly lower complexity than a centralized optimal approach.

This paper proposes a distributed multiple-access transmission scheme, designed to support the transmission of a small number of active nodes to a central base station when the total number of nodes is large. To achieve this, we propose the integration of multiple antenna technologies with compressed sensing algorithms. This integration is made possible by new precoding weight designs which utilize the multiple transmit antennas to provide a power-gain. We demonstrate that the use of these multiple transmit antennas increases the received signal power, thus enhancing the performance of the compressed sensing algorithm. We also propose the use of multiple receive antennas, which we show reduces the delay. Finally, we compare our distributed scheme with a carrier sense multiple-access scheme, and show that our scheme achieves a lower average delay for even a small number of active nodes.

We investigate the impact of channel estimation (CE) on the performance of point-to-point transmission schemes in wireless ad hoc networks. We first derive a new closed-form expression for the outage probability when the minimum mean square error estimator is utilized for CE, and show that the training-pilot length should increase as a linear function of the network intensity to maintain a fixed CE quality. Next, we derive the optimal training-pilot length which maximizes the transmission capacity under interference-limited conditions, and show that this optimal length increases with the frame length according to a square-root law.

We propose distributed matching algorithms for an uplink communication network comprised of multiple femtocell access points (FAPs), multiple wireless operators (WOs) which own multiple macrocell access points (MAPs) and multiple final users (FUs) subscribed to these WOs. In particular, we propose two algorithms: the first algorithm matches the FAPs with the final users (FUs), the resultant matchings of which are then used for the second matching to match the FAPs with the WOs. The key idea behind the proposed algorithms is that the FAPs aid the transmission of the FUs belonging to the WOs by (i) increasing the WO's coverage and (ii) reducing the traffic load of the WO's macrocell access points (MAPs), and in exchange, the WOs provide monetary compensation to the FAPs. We prove that both of the proposed algorithms converge to a group stable matching. Numerical analysis also reveal that the proposed distributed algorithms achieves a performance close to a centralized method, with much less overhead.

In wireless communications, the physical layer security is an emerging security research area that explores the possibilities of achieving high secrecy data transmission between source-destination nodes, while malicious eavesdroppers will obtain zero information from the source nodes. In this paper we consider enhancing the security level of a network comprising of multiple source-destination pairs, multiple friendly jammers and a malicious eavesdropper. We propose a distributed algorithm to facilitate secure data transmission from each source to its corresponding destination, through the help of friendly jammers. The key idea behind the proposed algorithm is that the friendly jammers help the source nodes to increase their secrecy rates and in exchange, the source nodes provide monetary compensation to the friendly jammers. We prove that after a limited number of iterations, the proposed algorithm converges to an optimal stable matching. Numerical analysis also reveals that the distributed algorithm can achieve a performance comparable to an optimal centralized solution, but with a significantly less overhead and complexity.

We develop a general framework for the analysis of a broad class of point-to-point linear multiple-input multiple-output (MIMO) transmission schemes in decentralized wireless ad hoc networks. New general closed-form expressions are derived for the outage probability, throughput and transmission capacity. For the throughput, we investigate the optimal number of data streams in various asymptotic regimes, which is shown to be dependent on different network parameters. For the transmission capacity, we prove that it scales linearly with the number of antennas, provided that the number of data streams also scales linearly with the number of antennas, in addition to meeting some mild technical conditions. We also characterize the optimal number of data streams for maximizing the transmission capacity. To make our discussion concrete, we apply our general framework to investigate three popular MIMO schemes, each requiring different levels of feedback. In particular, we consider eigenmode selection with MIMO singular value decomposition, multiple transmit antenna selection, and open-loop spatial multiplexing. Our analysis of these schemes reveals that significant performance gains are achieved by utilizing feedback under a range of network conditions.

We propose a distributed spectrum access algorithm for cognitive radio relay networks with multiple primary users (PU) and multiple secondary users (SU). The key idea behind the proposed algorithm is that the PUs negotiate with the SUs on the amount of time the SUs are either (i) allowed spectrum access, or (ii) cooperatively relaying the PU's data, such that both the PUs' and the SUs' minimum sum-rate requirement are satisfied. We prove that the proposed algorithm will result in a stable matching and is weak Pareto optimal. Numerical analysis also reveal that the distributed algorithm can achieve a performance comparable to an optimal centralized solution, but with significantly less overhead and complexity.

The performance of spatial multiplexing systems with linear minimum-mean-squared-error receivers is investigated in ad hoc networks. We present new exact closed-form expressions for the outage probability and transmission capacity. These expressions reveal that from a transmission capacity perspective, single-stream transmission is preferable over multi-stream transmission.

This paper investigates the performance of open-loop multi-antenna point-to-point links in ad hoc networks with slotted ALOHA medium access control (MAC). We consider spatial multiplexing transmission with linear maximum ratio combining and zero forcing receivers, as well as orthogonal space time block coded transmission. New closed-form expressions are derived for the outage probability, throughput and transmission capacity. Our results demonstrate that both the best performing scheme and the optimum number of transmit antennas depend on different network parameters, such as the node intensity and the signal-to-interference-and-noise ratio operating value. We then compare the performance to a network consisting of single-antenna devices and an idealized fully centrally coordinated MAC. These results show that multi-antenna schemes with a simple decentralized slotted ALOHA MAC can outperform even idealized single-antenna networks in various practical scenarios.

In this paper, we investigate the benefits of providing limited-feedback and using transmit antenna selection (TAS) in ad hoc networks. We find that the TAS scheme can provide throughput gains of up to 50% compared to the non-feedback scheme. We also find that the performance gains of the TAS scheme are more significant for low path loss exponents and single-antenna transmission. Our results are obtained by deriving new closed-form expressions for the network throughput and transmission capacity. Moreover, we also propose design guidelines for TAS to determine the optimal number of antennas used for transmission.

Multiple amplify-and-forward (AF) relays with receive diversity is analyzed over unbalanced hops with independent but not necessarily identically distributed Rayleigh fading. Exact closed-form expressions are derived for the moment generating function of the end-to-end signal-to-noise ratio (SNR) at the destination. Our analysis apply to arbitrary numbers of relays and arbitrary numbers of antennas at the destination. Based on the derived results, we determine the symbol error rate with M-ary phase-shift keying. In addition, we carry out an asymptotic analysis in the high SNR regime. Our results provide fundamental insights into the impact of the number of antennas on the performance of multiple AF relaying. We explicitly reveal that the diversity order is equal to the sum of the number of relays and the number of antennas. Theoretical analysis is verified by simulation.

Multiple fixed gain amplify-and-forward (AF) relays with receive diversity is analyzed for the practical case of unbalanced hops with independent but non-identically distributed (i.n.d.) Rayleigh fading channels. We derive a new exact closed-form expression for the moment generating function (mgf) of the end-to-end signal-to-noise ratio (SNR). Our mgf is valid for the general case of arbitrary numbers of relays and arbitrary numbers of antennas at the destination. Based on this, we determine the exact and approximate symbol error rate (SER) for M-ary phase-shift keying. Our results provide new important insights into the joint impacts of the number of relays and the number of receive antennas on the system performance. Theoretical analysis is verified by simulation.

In this paper, we consider a two hop cognitive radio network where there are multiple primary and secondary users. We propose the design of antenna weights at the source and relay based on zero forcing principles. These antenna weights are designed to cancel the interference among the secondary users while maintaining fairness, and to ensure interference free signals at each primary user. To analyze the performance of our proposed design, we derive new exact expressions for the signal to interference and noise ratio at each secondary user, which are subsequently used to analyze the error performance.

This paper investigates the performance of practical physical-layer network coding (PNC) schemes for two-way relay channels. We first consider a network consisting of two source nodes and a single relay node, which is used to aid communication between the two source nodes. For this scenario, we investigate transmission over two, three or four time slots. We show that the two time slot PNC scheme offers a higher maximum sum-rate, but a lower sum-bit error rate (BER) than the four time slot transmission scheme for a number of practical scenarios. We also show that the three time slot PNC scheme offers a good compromise between the two and four time slot transmission schemes, and also achieves the best maximum sum-rate and/or sum-BER in certain practical scenarios. To facilitate comparison, we derive new closed-form expressions for the outage probability, maximum sum-rate and sum-BER. We also consider an opportunistic relaying scheme for a network with multiple relay nodes, where a single relay is chosen to maximize either the maximum sum-rate or minimize the sum-BER. Our results indicate that the opportunistic relaying scheme can significantly improve system performance, compared to a single relay network.

This paper investigates the performance of practical physical layer network coding (PLNC) schemes for two-way relay channels. We consider a network consisting of two source nodes and a single relay node, which is used to aid communication between the two source nodes. For this scenario, we investigate various transmission schemes, where transmission takes place over two, three or four time slots. We show that the two time slot PLNC scheme offers a higher maximum sum-rate, but a lower sum-bit error rate (BER) than the four time slot transmission scheme for a number of practical scenarios. We also investigate a three time slot PLNC scheme, which we show offers a good compromise between the two time slot PLNC and four time slot transmission schemes, and also achieves the best maximum sum-rate and/or sum-BER in certain practical scenarios. To facilitate comparison, we derive new closed-form expressions for the outage probability, maximum sum-rate and sum-BER.

In this paper, we consider two hop networks with multiple source, relay and destination nodes. In particular, we investigate systems with different processing capabilities at the relay and destination nodes. We derive new closed-form outage probability expressions when zero forcing processing is used at the i) relay, ii) relay and destination and iii) destination nodes only. Our results indicate significant decreases in outage probability for certain node configurations. We confirm our results through comparison with Monte Carlo simulations.

This paper investigates the performance of point-to-point spatial multiplexing with stream control and slotted ALOHA in ad hoc networks. In particular, we derive new closed-form outage probability, network throughput and transmission capacity expressions for spatial multiplexing with maximum-ratio-combining (MRC) and zero forcing (ZF) receivers. From these expressions, we show that the relative throughput of MRC and ZF receivers is dependent on node intensity and SINR threshold levels. In addition, we present a new transmission capacity scaling law for ZF receivers, which shows that increasing the number of transmitted data streams can either increase or decrease the transmission capacity depending on the path loss exponent and number of receive antennas. We also present conditions such that the transmission capacity using spatial multiplexing with ZF receivers is greater than orthogonal space time block codes.

In this paper, we consider a two hop Amplify and Forward (AF) multiple-input multiple-output (MIMO) relay network with antenna correlation, where beamforming is performed at the source and destination. This network consists of a single relay which is used to amplify and forward the signal from the source to the destination. The source and destination are both equipped with multiple antennas, which are correlated in space, while the relay has a single antenna. In this paper, we derive closed form expressions for the outage probability and probability density function of the received signal-to-noise ratio at the destination. We also present exact symbol error rate expressions for the two hop AF MIMO relay network, and show that the full spatial diversity order can be achieved.

This paper analyzes the performance of multiuser optimum combining systems. We consider the practical scenario where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We derive new closed-form expressions for the symbol error rate, ergodic capacity, level crossing rate, and average fade duration. These results are given as either accurate approximations or asymptotic (eg. high signal-to-noise ratio (SNR)) expressions, and are based on new closed-form statistical properties which we derive for the signal-to-interference noise ratio (SINR). Specifically, we derive exact first order expansions and accurate gamma approximations for the SINR distribution, as well as simplified exact expressions for the moments. We also present closed-form expressions for key performance parameters such as the diversity order and array gain, wideband slope, and high SNR power offset, and analyze the impact of the Rician K-factor, which is shown in all cases to yield a performance improvement.

We analyze scheduling algorithms for multiuser communication systems with users having multiple antennas and linear receivers. When there is no feedback of channel information, we consider a common round robin scheduling algorithm, and derive new exact and high signal-to-noise ratio (SNR) maximum sum-rate results for the maximum ratio combining (MRC) and minimum mean squared error (MMSE) receivers. We also present new analysis of MRC, zero forcing (ZF) and MMSE receivers in the low SNR regime. When there are limited feedback capabilities in the system, we consider a common practical scheduling scheme based on signal-to-interference- and-noise ratio (SINR) feedback at the transmitter. We derive new accurate approximations for the maximum sum-rate, for the cases of MRC, ZF and MMSE receivers. We also derive maximum sum-rate scaling laws, which reveal that the maximum sum-rate of all three linear receivers converge to the same value for a large number of users, but at different rates.

The performance of beamforming with antenna correlation in a two hop amplify and forward (AF) multiple input multiple-output (MIMO) relay network is analyzed. This network consists of a single relay which is used to amplify and forward the signal from the source to the destination. The source and destination are both equipped with multiple antennas, which are correlated in space, while the relay has a single antenna. In this paper, we derive new closed form expressions for the outage probability and probability density function of the received signal-to-noise ratio (SNR) at the destination. We also present exact symbol error rate expressions for the two hop AF MIMO relay network, and show that the full spatial diversity order can be achieved. Our results also indicate that spatial correlation is detrimental to the outage probability and symbol error rate at high SNR, and beneficial at low SNR.

We analyze the sum capacity achieved by linear receivers in a multiple-input multiple-output broadcast channel. We consider a simple and practical opportunistic scheduling algorithm, based on the signal to interference noise ratio (SINR) feedback from each user. Each transmit antenna sends data to a particular user, selected based on SINR. Under this scheduling scheme, we derive new accurate approximations for the sum capacity, for the cases of maximum ratio combining, zero forcing, and minimum mean-squared error receivers. We also derive capacity scaling laws, which reveal that the capacity of all three linear receivers converge to the same value for a large number of users. Our results are confirmed through comparison with Monte Carlo simulations.

This paper analyzes the performance of adaptive antenna arrays employing linear combining techniques designed to maximize the SINR. In the communications literature, these systems are referred to as optimum combining (OC) systems. We consider the practical case where the desired signal undergoes Rician fading, and is corrupted by Rayleigh-faded interfering signals and noise. We first propose new closed-form gamma approximations for the SINR distribution at the output of the OC combiner, which we show to be remarkably accurate. We then employ these approximations to derive new closed-form expressions for the ergodic capacity and simplified expressions for the high-SNR regime. These results reveal that the capacity improves monotonically with Rician K-factor.

The performance of beamforming in a two hop amplify and forward (AF) relay network is analyzed. This network consists of a single relay which is used to amplify and forward the signal from the source to the destination. The source and destination are both equipped with multiple antennas while the relay has a single antenna. In this paper, we derive closed form expressions for the outage probability and probability density function of the received SNR. We also present exact symbol error rate expressions for the two hop AF relay network and show that full spatial diversity order, which corresponds to the minimum number of antennas at the source and destination, can be achieved. Our analytical results are confirmed through comparison with Monte Carlo simulations.

This paper analyzes the performance of multiuser optimum combining (OC) systems where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We consider the SER and ergodic capacity in asymptotic SNR regimes, and derive new closed-form expressions for key performance parameters such as the diversity order, array gain, and wideband slope. These results clearly reveal the impact of the Rician if-factor, which is shown to be advantageous to performance in all cases.

This paper investigates an important tradeoff in wireless ad hoc networks concerning the allocation of resources to the PHY and MAC layers. We compare two approaches: One which employs a non-coordinated slotted ALOHA MAC with multi-antenna PHY, and one which employs a tightly coordinated MAC and single-antenna PHY. For both cases, we derive new closed-form throughput expressions. Based on these, we show that using simple slotted ALOHA in conjunction with multiple antennas can provide a higher throughput than fully coordinated access protocols in various practical scenarios. Our results are confirmed through comparison with Monte Carlo simulations.

This paper investigates the capacity of multiple- access and broadcast channels with MIMO-MRC systems in spatially correlated environments. We present new capacity approximations which are shown to be accurate. The approximations are based on new simple expansions which we derive for the maximum eigenvalue distribution of correlated Wishart matrices. We then proceed to analyze the affects of correlation and show it is beneficial for capacity. Our results are confirmed through comparison with Monte Carlo simulations.

This paper investigates the performance of spatial diversity techniques in dense ad hoc networks. We derive analytical expressions for the contention density in systems employing MIMO-MRC or OSTBC. In the case of MIMO- MRC the expressions are based on new expansions for the SIR distribution in the high interference regime typical in dense networks. Our results are confirmed through comparison with Monte Carlo simulations.

This paper investigates the capacity of multiuser MIMO-MRC systems in spatially correlated environments. We present new capacity approximations which are shown to be accurate. The approximations are based on new simple expansions which we derive for the maximum eigenvalue of correlated Wishart matrices. We show that for a large number of users there is a capacity offset due to correlation. Through this, we show that correlation is beneficial for capacity. Our results are confirmed through comparison with Monte-Carlo simulations.