On interference alignment for symmetrically connected interference networks with line of sight channels at finite powers

In this work, interference alignment for a class of Gaussian interference networks with general message demands, having line of sight (LOS) channels, at finite powers is considered. We assume that each transmitter has one independent message to be transmitted and the propagation delays are uniformly distributed between 0 and (L - 1) (L >; 0). If receiver-j, j ∈{1,2,..., J}, requires the message of transmitter-i, i ∈ {1, 2, ..., K}, we say (i, j) belongs to a connection. A class of interference networks called the symmetrically connected interference network is defined as a network where, the number of connections required at each transmitter-i is equal to c_t for all i and the number of connections required at each receiver-j is equal to c_r for all j, for some fixed positive integers c_t and c_r. For such networks with a LOS channel between every transmitter and every receiver, we show that an expected sum-spectral efficiency (in bits/sec/Hz) of at least K/(e+c₁-1)(c_t+1) (c_t/c_t+1)^ct log2 (1+min_{(i, j)∈c}|h_{i, j}|² P/WN₀) can be achieved as the number of transmitters and receivers tend to infinity, i.e., K, J →∞ where, C denotes the set of all connections, h_ij is the channel gain between transmitter-i and receiver-j, P is the average power constraint at each transmitter, W is the bandwidth and N₀ W is the variance of Gaussian noise at each receiver. This means that, for an LOS symmetrically connected interference network, at any finite power, the total spectral efficiency can grow linearly with K as K, J →∞. This is achieved by extending the time domain interference alignment scheme proposed by Grokop et al. for the k-user Gaussian interference channel to interference networks.