Question

A chosen reference symbol sequence A = [1 0 1] is repeatedly transmitted at regular intervals in a binary digital communication system, for the purpose of performing channel estimation. The channel itself is expected to introduce a single ISI term, so that its discrete-time impulse response will be in the form p = [p₀p₁]ᵀ. At specific iteration, the samples seen at the receiver are r = [0.8 0.2 0.6 0.1]ᵀ

Find the estimation of the channel response p at this iteration, using the least-squares (LS) based method.

Answer 1

To estimate the channel response p using the least-squares (LS) based method, solve the equation AR = r, where A is the transmitted reference sequence and R is the matrix of channel coefficients. The LS estimation of the channel response p in this case is [0.2 0.6]ᵀ.

Step-by-step explanation:

To estimate the channel response p using the least-squares (LS) based method, we can set up a system of equations using the transmitted reference sequence A and the received samples r. The LS estimation can be obtained by solving the equation AR = r, where R is the matrix of channel coefficients.

In this case, the equation becomes [1 0 1] * [p₀ p₁]ᵀ = [0.8 0.2 0.6 0.1]ᵀ. So, the LS estimation of the channel response p would be [p₀ p₁]ᵀ = [0.2 0.6]ᵀ.