# About length of the signal

In my research work i have the equation y(n) = hx(n)+w(n). My understanding about this equation from MATLAB point of view are:

1. h has to be a single number. (for e.g., rayleigh generated).
2. x(n) , w(n) will be vector because they have n associated with them. So is my understanding correct or is their any other concept. Thanks.

n is indicative of time. It shows how the input and noise impact the received symbol with time n.

If x and w are vectors at time n (let's say of length M), which give the corresponding received vector y, since you take h to be a scalar. Such a system would be a strange MIMO system with only links between transmit and receive antennas pairs and each antenna pair seeing the same fading coefficient. For ex: tx antenna 1 would have a fading coefficient of h towards Rx antenna 1 and complete fade (h=0) towards all the other M-1 antennas at the receiver. Similarly for other tx and Rx antenna pairs

So, n here is represting time and x, w should be scalers for this signal model to make sense given h is scalar

• guy, ok understood completely.... I was thinking that 'n' is length of the signal. can you give an example where time (n) and length (M) of signal both are shown. – charu Jun 5 '20 at 7:13
• $\vec{y}(n) = H(n)\vec{x}(n) + \vec{w}(n)$ , here H is the MxM fading coefficient matrix at time n, y,x,w are received, transmit and noise vectors at time n of length M. This is the general form, all other special use cases can be derived from this, like SIMO, MISO, frqeuency flat fading etc. – Dsp guy sam Jun 5 '20 at 7:19
• @ Dsp guy, got it...but my confusion is, by looking at the equation (for e.g., Y(n) = H(n)x(n)+w(n)) we can see that there is time instant 'n' but we cant see that it is having length 'M'. How do we know that the equation has length 'M'. – charu Jun 5 '20 at 7:23
• If it's written mathematically, there would a vector sign or bold and the size of each entity would be specified in a paper or book. If written in code it would be obvious from the declaration. – Dsp guy sam Jun 5 '20 at 7:29
• @ Dsp guy, can you give an example ( MATLAB statement) of " H is the MxM fading coefficient matrix at time n". Because i am getting confused in time instant and length. – charu Jun 5 '20 at 7:52

I beleive that h can be a vector or scalar .. depends on channel taps i.e. h

y[n] = hx[n] + w[n] -- indicates h convolved with x[n] and then added to noise w[n]