From: Opportunistic routing based on partial CSI in MIMO random ad-hoc networks
Parameters | Definition |
---|---|
\(p_{\mathrm {tx}}\) | Transmission probability of the slotted ALOHA MAC. |
\(\lambda\) | Density of nodes [nodes/\(\hbox {km}^2\)] |
\(\Phi\), \(\Phi _T\) | The point process of all the nodes / all the active transmitters. |
N | Number of antennas. |
\(\alpha\) | Path loss exponent. |
\({\mathbf {r}}_i\) | Location vector of the ith node. |
\(\rho\) | Total transmission power. |
\(r_{i,j}, {\mathbf {H}}_{i,j}\) | Distance and channel matrix between the jth transmitter and the ith node, respectively. |
\(K_{j}\) | Number of data streams of the jth transmitter. |
\({\mathbf {F}}_j=[{\mathbf {f}}_{j,1},...,{\mathbf {f}}_{j,K_j} ]\) | Precoding matrix of transmitter j. |
\({\mathbf {w}}_{i,j,k}\) | Receive weight vector at node i for the kth stream of the jth transmitter. |
\({\mathcal {N}}_j\) | The neighborhood of node j (set of node indices). |
\({\mathcal {M}}_j {\scriptstyle =\{ ({\mathbf {r}}_i,{\mathbf {H}}_{i,j}): i \in {\mathcal {N}}_j \}}\) | The local knowledge of node j. |
\(f(\cdot ),\kappa (\cdot )\) | Routing and stream number function (selection of the next hop and the number of streams for transmission). |
B | System bandwidth (in Hertz). |
\(r_{\mathrm{RZ}}\) | Radius of the routing zone. |