# MAP Estimation Problem for Frequency Band Occupancy Calculation

Consider designing a wireless communication system. Your communication link is not iso- lated in the environment, there are other similar devices trying to communicate in the same general frequency band. For this reason, you wish to infer which frequency bands are occupied in order to minimize inter-channel interference. Fortunately, each of these devices only occupy a relatively narrow frequency band. Unfortunately, links can hop between frequency bands, start, or stop seemingly randomly. You may consider the sampled received signal to be of the form

$$y[n]= \sum_{i=1}^{n} x_i[n] +w[n]$$ where the number of signals N is unknown and each $$x_i$$ ∈ BL(−Bi,Bi) is an unknown, but approximately bandlimited function of a potentially finite non-zero length. Assume i.i.d. w[n] ∼ N (b, σ ) be a random process comprised of (possibly non-zero) Gaussian noise with variance $$\sigma^2$$ Please design an algorithm given a stream of data attempts to determine the set of frequency bands only using prior data

The question is what should be a proper algorithm that given a stream of data, attempts to determine the set of occupied frequency bands using prior data.

I only have a .wav file to test my algorithm

• So, what's your question? – Marcus Müller Oct 13 '20 at 18:26
• The question is what should be a proper algorithm that given a stream of data, attempts to determine the set of occupied frequency bands using prior data. – ranjana sengupta Oct 13 '20 at 21:58
• that sounds like "any parametric spectral estimator". Try using Yule-Walker equations to fit an autoregressive model if these are actually narrowband things. – Marcus Müller Oct 13 '20 at 23:28
• Would you mind to give a little details? Will the algorithm be only to use the Yule-Walker equations? – ranjana sengupta Oct 14 '20 at 5:39
• Here the coeff are not present. How can I use thr YW eqn? Sorry I am little new to the domain. – ranjana sengupta Oct 14 '20 at 5:47