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where A = diag { a$_{1}$, · · · , a$_{N}$ } is an amplification diagonal matrix. Thus, 

where S$_{i}$$_{j}$ is the station transmitting to S$_{j}$ under the permutation P (i.e., in row j of P , element i$_{j}$ is one, and all other elements are zero). Define ˆ r = A − $^{1}$r , i.e., station S$_{j}$ divides its received signal by a$_{j}$ . We can rewrite (7) as 

<img src='content_image/296264.jpg'>

<img src='content_image/296265.jpg'>

Suppose that we require the received signal-to-noise ratio (SNR) of each station to be the same. Let h ( − 1) u, ( i,j ) be element ( i, j ) in H − 1 u . Then 

In other words, 

<img src='content_image/296266.jpg'>

<img src='content_image/296267.jpg'>

where σ 2 e is the effective noise power of each station under unit signal power (i.e., the noise-to-signal ratio). 

Substituting (6) into (4), we have 

<img src='content_image/296273.jpg'>

where h ( − 1) d, ( i,j ) is element ( i, j ) in H − 1 d . If we restrict a$_{j}$ ∀ j to be real values, then plugging (10) into (11) 

