# User Association Performance Trade-Offs in Integrated RF/mmWave/THz Communications
## 3 System Model  
We consider a system with BSs that are subdivided into three BS types: (1) RF (\(k_{1}\)), where \(k_{1}\in\{1,2,3,...K_{1}\}\); (2) mmW (\(k_{2}\)); and (3) THz (\(k_{3}\)). These BS are geographically distributed according to a homogeneous Poisson point process (PPP) [35], \(\phi_{k}\) of density \(\lambda_{k}\). The BS transmission power is \(P_{T_{k}}\), and the minimum allowed distance between any two BSs is \(d_{min}\). Each BS serves \(U\) number of single-antenna users with the same transmit power \(P_{u}\). Note that \(\lambda_{u}\) is the UE density.  
Each BS and user is equipped with an antenna array that can form directional beams via beamforming. Beamforming vectors define the direction and beamwidth of each link. Beamwidths vary by frequency based on array size. Incorporating directional beamforming provides a realistic 5G/6G channel model by capturing aspects such as gain/interference variations due to beams, multi-user MIMO through multi-beam transmission, and 3D propagation characteristics.  
For the RF band, we model the interference-limited coverage probability. Also, UEs, interferers, and blockages are distributed according to a PPP. Blockages are modeled as rectangles with a defined length and width. Links can be either LOS or NLOS depending on whether they are blocked. For the THz system, molecular absorption loss and exponential path loss are used to model propagation loss. System losses are also defined. The total noise consists of thermal noise and molecular noise.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Year** & **Key Advantages** & **Key Limitations** & **Suitability for mmW/THz** \\ \hline SINR-based & 2012 & Simple implementation; associates users to BS with strongest signal & Does not consider load balancing or multi-band characteristics & Not suitable due to variability in bands \\ Biased algorithms & 2015-2017 & Increased capacity and throughput & Optimal bias factor difficult to determine & Marginally improves performance \\ eICIC & 2013–2017 & Reduces interference in HetNets & Complex to apply across technologies & Complexity limits applicability \\ Load-aware & 2019–2020 & Balances SINR and load & Favors RF band due to higher intrinsic SINR & Better than SINR but still biased \\ Blockage-aware & 2021 & Considers propagation effects & Improved but bias toward RF remains & \\ Optimization & 2018–2023 & Maximizes network utility & Complex formulations, high complexity & High complexity limits real-time use \\ Game theory & 2020–2021 & Models user self-interest & High signaling overhead, assumptions & Signaling overhead challenging \\ Reinforcement learning & 2017–2021 & Adapts dynamically & High computational cost; requires extensive training; poor explainability & Applicable but data/complexity concerns \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of previous user association methods.  
For the BS-UE links, we consider a block-fading channel model with large- and small-scale Rayleigh fading [36; 37]. Large-scale fading depends on the distance and path loss, which vary by frequency band. The multi-path small-scale fading coefficients are assumed to be Rayleigh distributed.  
The system is assumed to be open access, where there is no restriction on the association of UEs to a certain BS.  
OFCDM is considered for the BS to UE links (access downlinks), as it outperforms OFDM for high-speed communications. The system uses coded orthogonal channels, where \(N_{b}\) is the number of transmitted bits (each with bit energy \(E_{b}\)). Also, \(N\) and \(F\) are the spreading factors in time and frequency domains, respectively. The transmitted signal is spread with Pseudo Noise (PN) sequences in the time domain with chip energy \(E_{c}\) and chip duration \(T_{c}\), where  
\[E_{c}=E_{b}/(N\times F) \tag{1}\]