A Semi-Linear Approximation of the First-Order Marcum Q-function with Application to Predictor Antenna Systems

Hao Guo, Behrooz Makki, Mohamed-Slim Alouini, Tommy Svensson
2021 IEEE Open Journal of the Communications Society  
First-order Marcum Q-function is observed in various problem formulations. However, it is not an easy-to-handle function. For this reason, in this article, we first present a semi-linear approximation of the Marcum Q-function. Our proposed approximation is useful because it simplifies, e.g., various integral calculations including Marcum Q-function as well as different operations such as parameter optimization. Then, as an example of interest, we apply our proposed approximation approach to the
more » ... ion approach to the performance analysis of predictor antenna (PA) systems. Here, the PA system is referred to as a system with two sets of antennas on the roof of a vehicle. Then, the PA positioned in the front of the vehicle can be used to improve the channel state estimation for data transmission of the receive antenna that is aligned behind the PA. Considering spatial mismatch due to the mobility, we derive closed-form expressions for the instantaneous and average throughput as well as the throughput-optimized rate allocation. As we show, our proposed approximation scheme enables us to analyze PA systems with high accuracy. Moreover, our results show that rate adaptation can improve the performance of PA systems with different levels of spatial mismatch. INDEX TERMS Backhaul, channel state information (CSI), integrated access and backhaul (IAB), linear approximation, Marcum Q-function, mobility, mobile relay, outage probability, predictor antenna, rate adaptation, spatial correlation, throughput, vehicle communication, V2X, V2I. ∞ 0 x z−1 e −x dx represents the Gamma function. Reviewing the literature, Marcum Q-function, which finds 1. To simplify the analysis, our paper concentrates on the approximation of the first-order Marcum-Q function. However, our approximation technique can be easily extended to the cases with different orders of Marcum Q-function. its roots in radar study [2] , has appeared in solving different kinds of problems such as statistics, non-coherent/coherent signal detection [3] , and in the performance analysis of different digital communication setups such as temporally correlated channels [4], spatially correlated channels [5], free-space optical (FSO) links [6], relay [7] and spectrum sharing [8] networks, as well as cognitive radio and radar systems [9]-[29]. The presence of Marcum Q-function, however, makes the mathematical analysis challenging, because it is difficult to manipulate with no closed-form expressions especially when it appears in parameter optimizations and integral calculations. For this reason, several methods have This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 2, 2021 273 HAO GUO (Student Member, IEEE) received the bachelor's degree in electrical engineering from Nankai University and Tianjin University, Tianjin, China, in 2015, and the master's degree in communication engineering from Chalmers University of Technology, Gothenburg, Sweden, in 2017, where he is currently pursuing the Ph.D. degree with the Communication Systems Group, Department of Electrical Engineering. His current research interests include millimeter wave communications, V2X, integrated access and backhaul, and moving relays. He serves as a reviewer for IEEE WIRELESS COMMUNICATIONS LETTERS and IEEE COMMUNICATIONS LETTERS, and he is selected as one of the exemplary reviewers for IEEE WIRELESS COMMUNICATIONS LETTERS, 2020. BEHROOZ MAKKI (Senior Member, IEEE) received the Ph.D. degree in communication engineering , as a Professor of Electrical Engineering in 2009. His current research interests include the modeling, design, and performance analysis of wireless communication systems. TOMMY SVENSSON (Senior Member, IEEE) received the Ph.D. degree in information theory from Chalmers University of Technology, Gothenburg, Sweden, in 2003. He is a Full Professor in Communication Systems with the Chalmers University of Technology, where he is leading the Wireless Systems Research on air interface and wireless backhaul networking technologies for future wireless systems. He has worked with Ericsson AB with core networks, radio access networks, and microwave transmission products. He was involved in the European WINNER and ARTIST4G Projects that made important contributions to the 3GPP LTE standards, the EU FP7 METIS and the EU H2020 5GPPP mmMAGIC and 5GCar projects toward 5G and currently Hexa-X and RISE-6G toward 6G, as well as in the ChaseOn antenna systems excellence center with Chalmers targeting mm-wave and (sub)-THz solutions for 5G/6G access, backhaul/fronthaul and V2X scenarios. He has coauthored five books, 93 journal papers, 129 conference papers, and 53 public EU projects deliverables. His research interests include design and analysis of physical layer algorithms, multiple access, resource allocation, cooperative systems, moving networks, and satellite networks. He is the Chairman of the IEEE Sweden Joint Vehicular Technology/ Communications/ Information Theory Societies Chapter, the Founding Editorial Board Member and an Editor of IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Series on Machine Learning in Communications and Networks, has been an Editor of IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, IEEE WIRELESS COMMUNICATIONS LETTERS, an guest editor of several top journals, organized several tutorials, and workshops at top IEEE conferences, and served as the coordinator of the Communication Engineering Master's Program, Chalmers.
doi:10.1109/ojcoms.2021.3056393 fatcat:kmtj2whzebh4pp2hpcyajmrgvm