A Semi-Linear Approximation of the First-Order Marcum Q-function with Application to Predictor Antenna Systems
Artikel i vetenskaplig tidskrift, 2021

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 paper, 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 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.


Marcum $Q$-function



mobile relay

outage probability

integrated access and backhaul (IAB)

rate adaptation

channel state information (CSI)


linear approximation


vehicle communication

spatial correlation

predictor antenna


Hao Guo

Chalmers, Elektroteknik, Kommunikation, Antenner och Optiska Nätverk

Behrooz Makki

Ericsson AB

Mohamed-Slim Alouini

King Abdullah University of Science and Technology (KAUST)

Tommy Svensson

Chalmers, Elektroteknik, Kommunikation, Antenner och Optiska Nätverk

IEEE Open Journal of the Communications Society

2644125X (eISSN)

Vol. 2 273-286


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