Mehdi M. Molu

Optimal Precoding in the Relay and the Optimality of Largest Eigenmode Relaying with Statistical Channel State Information

An optimal precoding method for a multiple antenna relay node is investigated in order to maximize the achievable rate of the cooperative communication system. It is assumed that only the channel covariance matrices of the relays receive and transmit channels are available to the relay and that the antennas of the relay are correlated. It is shown that the optimal transmission from the relay should be conducted in the direction of the eigenvectors of the channel covariance matrix. Moreover, necessary and sufficient conditions are derived under which the relay transmission achieves capacity by transmitting from the strongest eigenvector only; this method is called Largest Eigenmode Relaying (LER). The exact result contains an expectation operation that needs to be solved numerically; to reduce the computational complexity, novel methods are proposed that lead to closed-form solutions. A lower bound for the optimal region of LER is derived. Moreover, the effect of the number of source antennas on the optimality of LER is investigated asymptotically. The simulation results show very little difference between the regions in which LER is optimal when the source is equipped with a finite or an infinite number of antennas.

Robust MMSE Beamforming for Multiantenna Relay Networks

In this paper, we propose a robust minimum mean square error (MMSE)-based beamforming technique for multiantenna relay broadcast channels, where a multiantenna base station transmits signal to single antenna users with the help of a multiantenna relay. The signal transmission from the base station to the single antenna users is completed in two time slots, where the relay receives the signal from the base station in the first time slot, and it then forwards the received signal to different users based on amplify and forward (AF) protocol. We propose a robust beamforming technique for a sum-power minimization problem with an imperfect channel state information (CSI) between the relay and the users. This robust scheme is developed based on the worst-case optimization framework and the Nemirovski Lemma by incorporating uncertainties in the CSI. The original optimization problem is divided into three subproblems due to joint nonconvexity in terms of beamforming vectors at the base station, the relay amplification matrix, and receiver coefficients. These subproblems are formulated into a convex optimization framework by exploiting the Nemirovski Lemma, and an iterative algorithm is developed by alternatively optimizing each of them with channel uncertainties. In addition, we provide an optimization framework to evaluate the achievable worst-case mean square error (MSE) of each user for a given set of design parameters. Simulation results are provided to validate the convergence of the proposed algorithm.

Statistical Analysis of Multiantenna Relay Systems and Power Allocation Algorithms in a Relay With Partial Channel State Information

The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels, and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied, and closed-form expressions are derived for the asymptotic cases of the fully correlated and noncorrelated scenarios; moreover, the statistical characteristics of the SNR are further studied, and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function, which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm, which we call “proportional power allocation.” The algorithm is explained in detail for the case of two antennas and three antennas at the relay, and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.

Low-Complexity Compute-and-Forward Techniques for Multisource Multirelay Networks

Compute-and-forward (C&F) relaying in a multisource multirelay network is studied in this letter and two novel algorithms are proposed, addressing choice of integer matrix, taking into account the effect of singularity. The first algorithm assumes that there is no co-operation between the nodes for choosing proper integer vectors in the relay nodes; this method is referred to as “blind C&F” and an algorithm is proposed which guarantees that each relay chooses the best integer vector that contains information from at least m source nodes. In the second algorithm that is described as “partially coordinated C&F,” we assume that partial cooperation between the relay nodes and propose to exchange a single variable with which the relays are sorted for transmission. The performance of the proposed algorithm is nearly equivalent with optimal relaying, which requires significant overhead signaling.

Constructing convolutional lattices and its application in Compute and Forward

Constructing lattices from convolutional codes based on Construction A is studied; analogous to Construction A, a single layer code lattice is proposed in this paper which outperforms Construction A. As an application for the proposed convolutional lattices, they are exploited in a multi-user relay network where the relay node employs Compute and Forward as its relaying function. We adopt the BCJR algorithm for lattice decoding convoutional lattices; moreover, as the BCJR algorithm requires the knowledge of the statistical characteristics of modulo lattice additive noise (MLAN), the probability density function of MLAN is derived in closed form.

Low-Complexity and Robust Hybrid Beamforming Design for Multi-Antenna Communication Systems

This paper proposes a low-complexity hybrid beamforming design for multi-antenna communication systems. The hybrid beamformer is comprised of a baseband digital beamformer and a constant modulus analog beamformer in the radio frequency (RF) part of the system. As in singular-value-decomposition (SVD)-based beamforming, hybrid beamforming design aims to generate parallel data streams in multi-antenna systems, however, due to the constant modulus constraint of the analog beamformer, the problem cannot be solved similarly. To address this problem, mathematical expressions of the parallel data streams are derived in this paper and desired and interfering signals are specified per stream. The analog beamformers are designed by maximizing the power of desired signal while minimizing the sum-power of interfering signals. Finally, digital beamformers are derived by defining the equivalent channel observed by the transmitter/receiver. Regardless of the number of the antennas or type of channel, the proposed approach can be applied to a wide range of MIMO systems with hybrid structure wherein the number of the antennas is more than the number of the RF chains. In particular, the proposed algorithm is verified for sparse channels that emulate mm-wave transmission as well as rich scattering environments. In order to validate the optimality, the results are compared with those of the state-of-the-art and it is demonstrated that the performance of the proposed method outperforms state-of-the-art techniques, regardless of type of the channel and/or system configuration.

Filtered OFDM Systems, Algorithms, and Performance Analysis for 5G and Beyond

Filtered orthogonal frequency division multiplexing (F-OFDM) system is a promising waveform for 5G and beyond to enable the multi-service system and spectrum efficient network slicing. However, the performance for F-OFDM systems has not been systematically analyzed in the literature. In this paper, we first establish a mathematical model for an F-OFDM system and derive the conditions to achieve the interference-free one-tap channel equalization. In the practical cases (e.g., insufficient guard interval, asynchronous transmission, and so on), the analytical expressions for inter-symbol interference, inter-carrier interference, and adjacent-carrier interference are derived, where the last term is considered as one of the key factors for asynchronous transmissions. Based on the framework, an optimal power compensation matrix is derived to make all of the subcarriers having the same ergodic performance. Another key contribution of this paper is that we propose a multi-rate F-OFDM system to enable low-complexity low-cost communication scenarios, such as narrow-band Internet of Things, at the cost of generating inter-subband interference (ISubBI). Low computational complexity algorithms are proposed to cancel the ISubBI. The result shows that the derived analytical expressions match the simulation results, and the proposed ISubBI cancelation algorithms can significantly save the original F-OFDM complexity (up to 100 times) without significant performance loss.

A Novel Equivalent Definition of Modified Bessel Functions for Performance Analysis of Multi-Hop Wireless Communication Systems

A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver.

On convolutional lattice codes and lattice decoding using Trellis structure

Constructing hypercubic lattices from convolutional codes based on Constructions A and D is investigated in this paper and their error performance in a point-to-point communication system is studied. Moreover, analogous to Construction A/D, single/multilayer code lattices are proposed. As Construction D requires certain minimum Euclidean distance criteria, we propose methods to guarantee the distance requirements of Construction D, which results in a superior lattice construction compared with Construction A. Due to the key role of soft input soft out decoding algorithms in improving the performance of a code, lattice decoding based on the Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm for lattices constructed from convolutional codes is also proposed in this paper. Moreover, as the BCJR algorithm requires knowledge of the statistical characteristics of modulo lattice additive noise (MLAN), the probability density function of MLAN is derived in closed form.

System-level simulation of multihop wireless networks using physical-layer network coding

We discuss the system-level simulation of an ultradense, multi-hop wireless network employing physical layer network coding to increase its throughput and eliminate the effect of interference between links in the network. We describe the network paradigm being developed by the DIWINE project, and the principles of physical layer network coding. The system-level simulator (SLS) operates on a packet level, and determines packet error probability for the network coded data at each relay in terms of the noise power and the signal level from each incoming link. We describe this simulation methodology and the software package used to implement it, and give numerical results for throughput versus load for a simple example network, showing that the approach developed by DIWINE outperforms a simple TDMA baseline scheme under most conditions.