On the achievable rates of a secondary link coexisting with a primary multiple access network

An achievable rate region for a primary multiple access network coexisting with a secondary link of one transmitter and a corresponding receiver is analyzed. The rate region depicts the sum primary rate versus the secondary rate and is established assuming that the secondary link performs rate splitting. The achievable rate region is the union of two types of rate regions. The first type is a rate region established assuming that the secondary receiver cannot decode any primary signal, whereas the second is established assuming that the secondary receiver can decode the signal of one primary link. The achievable rate region is determined first assuming discrete memoryless channel (DMC), then the results are applied to a Gaussian channel. In the Gaussian channel, the performance of rate splitting is characterized for the two types of rate regions. Moreover, a necessary and sufficient condition to determine which primary signal the secondary receiver can decode without degrading the range of primary achievable sum rates is provided. When this condition is satisfied by a certain primary user, the secondary receiver can decode its signal and achieve larger rates without reducing the sum of the primary achievable rates as compared to the case in which it does not decode any primary signal. It is also shown that the probability of having at least one primary user satisfying this condition grows with the primary signal-to-noise ratio.