# Analytical TCP Model for Millimeter-Wave 5G NR Systems in Dynamic Human Body Blockage Environment
## 1 Introduction  
The 5G New Radio (NR) systems operating in a millimeter-wave band (30-100 GHz) are expected to become an enabling technology for various next-generation mobile systems [1; 2]. While their standardization is essentially complete [3], the research focus is shifting towards optimizing the system-level performance.  
The use of 5G NR in dense urban scenarios brings unique challenges to system designers. Dynamic blockage of the line-of-sight (LoS) link between the 5G NR base station (BS) and the user equipment (UE) by the moving crowd around the UE leads to increased dynamics in the received signal strength. These fluctuations have been theoretically and experimentally shown to occur at the sub-second timescales [4] and may result in significant changes in the effective data rate provided over the air interface.  
The system and user-capacity of mmWave 5G NR systems have been intensely investigated so far. Particularly, the study in [5] reports on maximum theoretical capacity provided to users in the dense deployment of 5G NR BSs. In [6], the authors characterized UE capacity in the presence of multi-connectivity operation. The work presented in [7] derives the NR BS system capacity and UE capacity in the presence of both unicast and multicast sessions. End-to-end simulations of 5G NR systems are reported in [8].  
Most of the performance studies so far concentrated on evaluating the system or UE capacity of NR BS deployments. However, it is up to the transport layer protocols to efficiently utilize the resources available. Recent studies have shown that Transmission Control Protocol (TCP) performance over 5G NR systems might be compromised under certain conditions. Utilizing ns-3 system-level simulations, the authors in [9] showed that even though the achieved TCP throughput decreases in the presence of blockage events, no further artifacts are observed, i.e., TCP throughput achieves its theoretical levels in both LoS blocked and non-blocked states. However, the authors in [10] suggested that TCP throughput might degrade dramatically under certain environmental conditions. The work [11] also overviewed this aspect and identified the speed of blockers as the dominant factor behind the performance degradation.  
To the best of the authors' knowledge, no TCP model allowing for an assessment of TCP throughput at the NR air interface has been proposed so far. This paper aims to fill this gap by providing a simple first-order approximation of TCP rate in dynamic blockage conditions under the following assumptions: (i) negligible buffer size compared to the bandwidth-delay product (BDP), (ii) blockage events causing bandwidth drops but no complete outage, and (iii) constant bandwidth available to the TCP session while in the blockage and non-blockage states. To this aim, in this paper, we first propose a simple TCP model in dynamic blockage conditions and then proceed with understanding the effects of radio propagation and environmental parameters on the TCP throughput. The main findings of our work are:  
* TCP fails to achieve its theoretical throughput when the round-trip time (RTT) is comparable to blocked and non-blocked state durations. These conditions are seldom observed in the case of dynamic human-body blockage.
* The speed of blockers plays a key role in TCP throughput degradation: higher blocker speed leads to more frequent UE state changes as well as minimizes their durations by eventually reducing the TCP throughput.  
This paper is organized as follows. In Section 2, we specify our system model. Next, a TCP model is developed and parametrized in Section 3. The numerical assessment is conducted in Section 4. Conclusions are drawn in the last section.