Abstract

Let $$ X_{n} $$ be $$ n\times N $$ random complex matrices, and let $$R_{n}$$ and $$T_{n}$$ be non-random complex matrices with dimensions $$n\times N$$ and $$n\times n$$ , respectively. We assume that the entries of $$ X_{n} $$ are normalized independent random variables satisfying the Lindeberg condition, $$ T_{n} $$ are nonnegative definite Hermitian matrices and commutative with $$R_nR_n^*$$ , i.e., $$T_{n}R_{n}R_{n}^{*}= R_{n}R_{n}^{*}T_{n} $$ . The general information-plus-noise-type matrices are defined by $$C_{n}=\frac{1}{N}T_{n}^{\frac{1}{2}} \left( R_{n} +X_{n}\right) \left( R_{n}+X_{n}\right) ^{*}T_{n}^{\frac{1}{2}} $$ . In this paper, we establish the limiting spectral distribution of the large-dimensional general information-plus-noise-type matrices $$C_{n}$$ . Specifically, we show that as n and N tend to infinity proportionally, the empirical distribution of the eigenvalues of $$C_{n}$$ converges weakly to a non-random probability distribution, which is characterized in terms of a system of equations of its Stieltjes transform.

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