  In this paper, we study the target tracking problem in wireless sensor
networks (WSNs) using quantized sensor measurements under limited bandwidth
availability. At each time step of tracking, the available bandwidth $R$ needs
to be distributed among the $N$ sensors in the WSN for the next time step. The
optimal solution for the bandwidth allocation problem can be obtained by using
a combinatorial search which may become computationally prohibitive for large
$N$ and $R$. Therefore, we develop two new computationally efficient suboptimal
bandwidth distribution algorithms which are based on convex relaxation and
approximate dynamic programming (A-DP). We compare the mean squared error (MSE)
and computational complexity performances of convex relaxation and A-DP with
other existing suboptimal bandwidth distribution schemes based on generalized
Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm and greedy search.
Simulation results show that, A-DP, convex optimization and GBFOS yield similar
MSE performance, which is very close to that based on the optimal exhaustive
search approach and they outperform greedy search and nearest neighbor based
bandwidth allocation approaches significantly. Computationally, A-DP is more
efficient than the bandwidth allocation schemes based on convex relaxation and
GBFOS, especially for a large sensor network.
