Interference Modelling for mmWave 5G systems
Fifth generation (5G) and beyond wireless systems aim to provide a minimum of 1 Gb/s data rate anywhere with up to 5 Gb/s for high mobility users and 50 Gb/s data rates for pedestrians by employing dense network of base stations and mobile users at mmWave spectrum. Even under beamforming, the high BS and user densities can drive cellular networks to be more interference rather than noise limited. While large adaptive arrays with narrow beams can boost the received signal power and hence reduce the impact of out-of-cell interference, this interference remains an important performance-limiting factor in dense mmWave networks. Modeling and characterization of wireless interference under these scenarios is essential for cellular system analysis and design.
Background and Motivation:
In next generation of wireless networks with a large number of subscribers and dense BSs deployment, interference modeling is an important step towards network realization. Existing works have modeled the interference based on stochastic geometry using the Laplace transform or using moment matching gamma distribution or Gaussian distribution. These models do not apply when some of the interferers are dominant or under heave shadowing as can be the case with mmWave beamforming (see the left figure). Furthermore, the transmission or beamforming technique together with other network-level decisions such as user and base station connections have a strong effect on the interference. We aim to understand the impacts of these techniques on the interference power distribution.
We propose analytical distribution models characterized by only a few parameters, which can be fitted to simple polynomial functions of channel path loss exponent and shadowing variance, and test their fitness against network simulation based on stochastic geometry. To estimate the parameters of the proposed interference models, we use both moment matching and maximum likelihood estimation (MLE) techniques. Specifically, we consider three approaches: analytical moment matching, individual distribution MLE, and mixture distribution MLE. We exploit the iterative expectation maximization (EM) algorithm to estimate the parameters of the mixture MLE model. To evaluate the goodness of each model, we introduce the use of the information-theoretic relative entropy or Kullback-Leibler (KL) divergence as a measure for the relative distance between the modeled distributions and simulated data.
We propose the use of two distributions each characterized by two parameters: the inverse Gaussian (IG) as a light-to-heavy tailed distribution and the inverse Weibull (IW) as a heavy tailed one. Further, we propose a novel model as a mixture of these two distributions with remarkably good fit to simulation data while having only three parameters. Figure 1 shows results for our three proposed models against simulated data as well as representative sample distributions. The proposed mixture model outperforms both the individual IG and IW models by having the best fit with simulated data and the lowest relative entropy distance to the data distribution.
Figure 2. Spectral efficiency per user (left) and distributions of the interference plus noise power (right) under different transmission schemes and user-base station connection assignments.
Since beamforming needs to be performed based on the actual BS-UE connections (associations), the interference structure is also highly dependent on user association. We contrast mmWave interference distributions under beamforming transmission with those under omnidirectional transmission as often considered in the literature for lower frequency (e.g. LTE) networks. We further compare the effect of mmWave channel models on the interference distributions by considering an analytical 3GPP-based channel model (ACM) and the measurement-based channel simulator NYUSIM developed from extensive field measurements in New York City. The results in Figure 2 show that BIM, which employs SVD beamforming technique, results in a higher spectral efficiency under both Max-SINR association and WCS association. It can also be inferred that the WCS algorithm outperforms the Max-SINR scheme when using BIM, while this is not the case for OIM (omnidirectional transmission model).
The right figure shows the distribution of the interference plus noise power, which is much lower when using directional beamforming transmissions compare to omnidirectional transmissions. The vertical line shows the noise floor which is -114 dB for the network bandwidth of 1 GHz. It can be seen that the minimum interference power is -108 dB which is higher than the noise level, making the network interference-limited rather than noise-limited. The figures show that BIM has a superior performance compared to OIM by having the interference plus noise power more concentrated at lower values.
- Alizadeh, M. Vu, and T. Rappaport, “A Study of Interference Distributions in Millimeter Wave Cellular Networks,” biennial IEEE Conf. on Microwaves, Communications, Antennas & Electronic Systems (IEEE COMCAS), Israel, Nov. 2019.
- H. E. Elkotby and M. Vu, “Interference Modeling for Cellular Networks Under Beamforming Transmission,” IEEE Transactions on Wireless Communications, Vol. 16, No. 8, pp. 5201 – 5217, Aug. 2017. (DOI:10.1109/TWC.2017.2706683)
- H. ElKotby and M. Vu, “A New Probabilistic Model for mmWave Cellular Interference Power Distribution”, IEEE Global Conf. on Signal and Information Proc. (GlobalSIP), Dec 2016.
- H. ElKotby and M. Vu, “A New Model for mmWave Cellular Interference Power Distribution,” IEEE Global Communications Conf. (Globecom), Dec. 2016.
This project is supported in part by the National Science Foundation under CNS Grants 1908552.