## Properties of orthogonal symbols

#### The practical interpretation of the orthogonality definition is that if a symbol ai(t) is mixed with a carrier reference equal to the frequency and phase of a second symbol aj(t), and the mixer output is then averaged over a symbol period using a matched filter or integrator, the output will be zero. This means that with orthogonal signalling it is possible to increase the number of symbol states used without affecting the output from an individual coherent detector, and hence without increasing the probability of symbol error for each detector. As we increase the number of orthogonal symbols used for transmission, we can increase the duration of each symbol for a given data information rate, (see section 2.3). The longer the symbol duration, the greater the time for averaging each symbol in the receiver and the better the S/N ratio at the detector output, improving the probability of correct symbol detection. Orthogonal FSK in theory can have any number of orthogonal symbol states, but does so at the expense of ever-increasing occupied bandwidth. |