ASYMPTOTIC PROPERTIES OF THE EVLP ESTIMATION FOR SUPERIMPOSED EXPONENTIAL SIGNALS IN NOISE

This paper studies the model of superimposed exponential sigdals in noise: Y_f(t)=\sum_i=1^n a_i s \lambda_i+o_g(t), \quad t=0,1, \cdots, n-1, j=1, N whereλ₁,…,λ_q are unknown complex parameters with module 1, λ_q+1,…,λ_p. are unknown complex parameters with module 1, λ_q+1,…,λ_p are unknown complex parameters with module less than 1, λ₁,…,λ_q are assumed distinct, p assumed known and q unknown. a_ky, k=1,…p, j=1, …, N are unknown complex parameters. e_j（t）,t=0,l ,…, n-1,j=1,…, N, are i.i.d. complex random noise variables such that E_\sigma_1(0), E\left|\epsilon_\theta_1(0)\right|^2=\sigma^2, 0<\sigma^2<\infty, E\left|\sigma_1(0)\right|^4<\infty and σ² is unknown. This paper gives: 1. A strong consistent estimate of q; 2. Strong consistent estimates of λ₁,…,λ_q, σ² and|a_ky|,k＜q; 3. Limiting distributions for some of these estimates; 4. A proof of non-existence of consistent estimates for λ_k and a_ky k＞q. 5. Adiscussion of the case that N→∞