Correction Factor for Analysis of MIMO Wireless Networks With Highly Directional Beamforming

In this letter, we reconsider a popular simplified received signal power model with single stream beamforming employed by the transmitter and the receiver in the regime when the beams have high gain and narrow beamwidth. We define the correction factor as the ratio of the average actual received signal power divided by the average received signal power using the popular simplified model. We analytically quantify this factor for LOS and NLOS service and interfering links under some assumptions. The analysis along with simulations using a 3GPP compliant new radio (NR) channel model confirm the importance of incorporating the correction factor in coverage analysis of wireless networks that utilize the popular simplified received power model. I. INTRODUCING THE CORRECTION FACTOR In system level analysis for computing coverage and rate performance of wireless networks on R a popular model to compute the received signal power at X ∈ R from a transmitter (serving/interfering) at Y ∈ R is as follows [1]– [4]. Pr = Pt`(||X − Y ||)hGt(θ)Gr(φ), (1) where Pt is the transmit power, `(.) is the path loss, h is the small scale fading, Gt(θ) is the transmit antenna gain and Gr(φ) is the receive antenna gain. If at all blockage effects are explicitly incorporated in the analysis by differentiating line of sight (LOS) and non-LOS (NLOS) links, then only h and ` are modeled differently for LOS and NLOS [3]. The antenna patterns Gt(.) and Gr(.) are considered to have the same distribution for LOS/NLOS links. In this work, we will show the importance of incorporating an additional blockage dependent factor in the received signal power when the antenna patterns have very narrow beamwidths and large gains – for example, an antenna pattern having 36 dB gain and 12 half power beamwidth in azimuth. Our analytical model shows that if there are large number of antennas at the transmitter and receiver, which employ analog beamforming, then the additional factor (called as the correction factor) is much less than 1 for NLOS service links but is close to 1 for LOS service links, and equal to 1 for NLOS/LOS interfering links. Such a factor cannot be incorporated by modifying either h or `(.) for analyzing signal to interference plus noise ratio (SINR) in highly directional MIMO wireless networks, especially cellular networks, and an example to explain this is given in the Appendix. Email: {mandar.kulkarni@, jandrews@ece.}utexas.edu, eugene. visotsky@nokia− bell− labs.com. M. Kulkarni and J. Andrews are with the UT Austin, TX. E. Visotsky is with Nokia Bell Labs, IL. Last revised on February 2, 2018. Most prior analyses of MIMO wireless networks computing coverage and rate performance with highly directional single user beamforming incorporates a received signal power similar to (1) and do not model a channel with LOS/NLOS dependent rank [2]–[9]1, which gives rise to the needed correction factor as we will show in this work. The purpose of this letter is to make the growing research community using received power model similar to (1) aware of the significance of how different rank of the MIMO channel for LOS and NLOS can affect the effective antenna gain and thus the design insights. We will formally define effective antenna gain in this work. Also we propose a quick way to preserve the existing analyses by multiplication of a LOS/NLOS dependent constant for service links but not the interfering links. The example in Appendix is indicative of how this can be done. The correction factor is especially important for analysis of millimeter wave (mmWave) cellular networks, wherein inclusion of blockage effects is crucial and the beamforming is highly directional [3]. All prior works which studied different system design issues in these networks like [5]–[9] use the received power model in (1) without incorporating the correction factor. In Section V, we discuss key implications on system design resulting from incorporation of such a factor. The analysis in this work is for analog beamforming implementation done at the transmitter and the receiver under consideration. Our analysis along with the simulation results considering a more detailed wideband 3GPP channel model suffice to motivate the inaccuracy of the popular model in (1) when the transmit and receive beams are narrow and with large gains. However, more detailed analysis is needed in the future to estimate the correction factor more accurately.