Comment on “ Statistical mechanics of CDMA multiuser demodulation ”
نویسنده
چکیده
In a recent paper [1], Tanaka formulated and solved a model of CDMA multiuser demod-ulation by applying the theory of spin glasses, the replica method in particular. It is shown in the present comment that some of his results can be derived without recourse to the replica method; conclusions from the somewhat tricky replica method are justified rigorously. It also becomes clear that there is no finite-size effect in the internal energy for the MPM demod-ulator and that the structure of the phase space is simple; the latter goes beyond the local stability argument of the AT line analysis. The first of our result is a generalization of the identity m = q for the MPM demodulator derived by Tanaka using the replica method: The functional identity P m (x) = P q (x) will be proved for MPM. Here P m (x) (−1 ≤ x ≤ 1) is the distribution function of the order parameter corresponding to magnetization and P q (x) denotes the distribution of the spin glass order parameter. The proof follows the same line as in the spin glass case [2, 3]. The function P m (x) is defined as P m (x) = 1 2 N p+N β s 2π p/2 η t dr t ξ exp − β s 2 t
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