out of the top branch. So, we require that 5. Next, we also want to make sure that the signal SU (t) in r(t) does not make it out of branch 2, branch 3, and branch 4. That means we require that (11.3) Chapter Eleven (11.4) 6. Generally, we can state that we want to make sure that (11.5) for all possible s(k)(t) signals sent. It is easily shown using Fourier transforms that, equivalently, we want to make sure that (stk) "(f)s," (f)df=0 (11.6) In words, we want to make sure that the signal sent by user j is orthogonal to the signal sent by user k. This is the underlying principle of multiple access techniques- making sure that Equation (11.5) or (11.6) is satisfied. If you do that, then you make sure that user j's signal does not appear in the output of a receiver that wants to pick up user k's signal, and vice versa. Recently, engineers have become a more forgiving lot. Some say: "It would be OK if just a tiny bit of user j's signal appeared in user k's receiver, as long as it was such a small amount that it didn't affect the performance of user k's receiver." Mathematically what they are saying is that they want to make sure that (11.7) where E is a very small number. If you decide to build a multiple access system where this is the case, it is called interference-limited, and the signals sent are called pseudo- orthogonal. Example 11.1 Two users set out to share a communication channel. One user sends her binary information as +x(t) (if the bit to send is 1) or -x(t) (if the bit is 0). The second user sends his bit as +y(t) or -y(t). The c(t) and y(t) are shown in Figure E10.1. Determine if these users are able to share the channel without interfering with one another. Solution: The users, we'll call them user 1 and user 2, will be able to share the channel if the signals they send satisfy (E11.1) Multiple Access Schemes: Teaching Telecommunications Systems to Share Now, we know that user 1 sends either + or - x(t) and user 2 sends either + or - y(t). So, plugging this into our requirement leads to (E11.2) Now, 