# Reliable Positioning and mmWave Communication via Multi-Point Connectivity +
## 2 System Model
### Performance Metrics
#### 2.3.2 Effective Throughput
Assuming perfect-CSI of the equivalent channel at the output of the analog beamformers, the effective rate for \(k\)th user, \(R_{k}\) is then computed as  
\[R_{k}=B_{d}\Big{(}1-\frac{T_{t}}{T_{f}}\Big{)}log_{2}\Big{(}1+\gamma_{k}( \mathcal{B})\Big{)}\, \tag{9}\]  
where signal-to-interference-plus-noise ratio (SINR) \(\gamma_{k}(\mathcal{B})\) for user \(k\)\(\forall k\) is obtained as  
\[\gamma_{k}(\mathcal{B}) =\frac{|\mathbf{f}_{k}^{\rm H}\tilde{\mathbf{h}}_{k}|^{2}P_{k}}{ \sum_{k^{\prime}\in\mathcal{K}\backslash k}|\mathbf{f}_{k}^{\rm H}\tilde{ \mathbf{h}}_{k^{\prime}}|^{2}P_{k^{\prime}}+\|\mathbf{f}_{k}\|^{2}\sigma^{2}}\] \[=\tilde{\mathbf{h}}_{k}^{\rm H}\Big{(}\sigma^{2}\mathbf{I}+\sum_ {k^{\prime}\in\mathcal{K}\backslash k}P_{k^{\prime}}\tilde{\mathbf{h}}_{k^{ \prime}}\tilde{\mathbf{h}}_{k^{\prime}}^{\rm H}\Big{)}^{-1}\tilde{\mathbf{h}} _{k}P_{k}\, \tag{10}\]  
assuming linear MMSE receiver, \(\mathbf{f}_{k}\) is computed as  
\[\mathbf{f}_{k}=\Big{(}\sigma^{2}\mathbf{I}+\sum_{k^{\prime}\in\mathcal{K} \backslash k}P_{k^{\prime}}\tilde{\mathbf{h}}_{k^{\prime}}\tilde{\mathbf{h}}_ {k^{\prime}}^{\rm H}\Big{)}^{-1}\tilde{\mathbf{h}}_{k}P_{k}\, \tag{11}\]  
where \(P_{k}\) is the maximum uplink transmit power of user \(k\) and \(\sigma^{2}=N_{o}B_{d}\) is the noise power over the signal bandwidth. In the reference scenario without BS cooperation (or digital post-combiner), each user is only assigned to the closest BS and served with the best matching analog beamformer \(\mathbf{w}_{b}^{(k)}\), whereas all other users are treated as interference. In this case, the corresponding SINR is given by  
\[\gamma_{k}=\frac{|\mathbf{w}_{b}^{(k)}{}^{\rm H}\mathbf{h}_{b,k}|^{2}P_{k}}{ \sum_{k^{\prime}\in\mathcal{K}\backslash k}|\mathbf{w}_{b}^{(k)}{}^{\rm H} \mathbf{h}_{b,k^{\prime}}|^{2}P_{k^{\prime}}+\|\mathbf{w}_{b}^{(k)}\|^{2} \sigma^{2}}\,\ \forall k,\ \forall b. \tag{12}\]  
From the above explanation, we can observe the impact of full-cooperation on achievable user-rate and system reliability. For example, use of fully-coordinated multi-point reception will improve system reliability, as all the active users will be connected to all coordinating BSs. However, this will result in lower estimate of the received SINR, because of the compromised receive beam at each BS, which intends to collects signal from all active users rather than focusing the beam towards a specific user at a time. However, the reduced analog beamforming gain can be compensated by efficient joint decoder at the common BBU. Conversely, the non-cooperation scenario, where each BS serves only one closest user for uplink data reception, provides relatively higher estimate of the received SINR because of full analog beamforming gain. However, overall system will be more vulnerable to outage, because of the single point connection. Clearly, there is tension between achievable analog beamforming gain and reliable connectivity for each user. Our goal here is to understand and quantify this trade-off and provide its affect on the localization accuracy.