# Is it possible to spread signal using sum of more than one orthogonal code

I was wondering if we can spread the signal using more than one spreading code. Assume we have the Walsh code used to spread the transmitted signal, the Walsh code is, for example, gotten based on Hadamard matrix:

V = [1  1  1  1
1 -1  1 -1
1  1 -1 -1
1 -1 -1  1]


where every column of matrix $$V$$ represents one spreading code we can choose and they are all orthogonal. where, $$V_1$$ = [1 1 1 1], $$V_2$$ = [1 -1 1 -1], $$V_3$$ = [1 1 -1 -1] and $$V_4$$ = [1 -1 -1 1]. So, if I have $$V_{21} = V_1 + V_2$$, what's the advantages and disadvantages of using $$V_{21}$$ as spreading code since it's orthogonal also on all codes except $$V_1$$ and $$V_2$$

thank you

• Hm, why should we come up with advantages of a scheme you devised? I mean, you didn't randomly say "hey, let's combine these row vectors"; you did that for a reason, is my guess. So, tell us what you were hoping to achieve? – Marcus Müller May 26 at 11:19

The disadvantage is that the signal V21 = V1 + V2 = [2, 0, 2, 0] disappears every other chip interval which makes maintaining carrier and phase synchronization more difficult. Also, while the total energy in V21 is equals to the sum of the energies of V1 and V2, V21 uses 4 times the instantaneous power needed by either V1 or V2 and so the transmitter needs to have greater power-handling capacity which increases the cost. Also, one problem that received a great deal of attention forty years ago was the "near-far" problem which had to do with the fact that different spread-spectrum users received with different power levels caused problems when synchronization was not perfect and the strict orthogonality used in the OP's question was not quite valid; practical stuff that modern engineers don't need to deal with in their MATLAB programs.