# 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? Commented May 26, 2019 at 11:19

## 1 Answer

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.

Advantages? I will let someone else take on the task of enumerating the advantages of the OP's scheme.

• Thank you so much .. please continue explaining the advantages, or provide me a link where I can read about its advantages. .. what you mean by OP ?
– Gze
Commented May 26, 2019 at 2:42
• OP = original poster = person who asked the question. Commented May 26, 2019 at 2:45
• What's about the advantages ?
– Gze
Commented May 26, 2019 at 2:47
• @Gze Be patient. It is Saturday night here (in the US) and the coming Monday is a major holiday in the US. So, someone else will come along (possibly in a few days, not right away) and write an answer enumerating the advantages. But if not, why don't you try to tell us what you think the advantages of your scheme are, and perhaps even explain how the advantages outweigh the disadvantages. Be sure to file a patent application before doing so, though. Commented May 26, 2019 at 2:53
• Also, I frankly fail to see any advantages. Commented May 27, 2019 at 7:11