an application of Z-matrix in a mobile radio system
The following is an application of Z-matrix in wireless communication called power balancing problem.
Consider pairs of mobile users and receiving antennae. For , mobile user transmits radio signal to antenna . Mobile user transmits at power . The radio channel attenuate the signal and user ’s signal is received at antenna with power , where denote the channel gain. The radio signals also interfere each other. At antenna , the interference due to user has power . The receiver noise power at antenna is denoted by . The signal to interference plus noise at receiver is
To guarantee the quality of received signal, it is required that the signal to interference plus noise ratio is equal to a predefined constant for all . Given , , we want to find such that the above equation holds for . Let be the matrix with zero diagonal and -entry for . We want to solve
where is the power vector and . The matrix is a Z-matrix, since all and are positive constants. The required power vector is if is invertible. We also required that the components of to be positive as power cannot be negative. The resulting power vector has positive components if is a non-negative matrix. In such case, is an M-matrix.
|Title||an application of Z-matrix in a mobile radio system|
|Date of creation||2013-03-22 16:14:16|
|Last modified on||2013-03-22 16:14:16|
|Last modified by||kshum (5987)|