Skip to main content

Table 1 Definitions of parameters and variables

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.