A theoretical relationship between the wavelet transform and the fast fourier transformation(FFT) methods in broadband wireless signal is proposed for solving the direction of arrivals(DOAs) estimation problem. This l...A theoretical relationship between the wavelet transform and the fast fourier transformation(FFT) methods in broadband wireless signal is proposed for solving the direction of arrivals(DOAs) estimation problem. This leads naturally to the derivation of minimum variance distortionless response(MVDR) algorithm, which combines the benefits of subspace methods with those of wavelet, and spatially smoothed versions are utilized which exhibits good performance against correlated signals. We test the method's performance by simulating and comparing the performance of proposed algorithm, FFT MVDR and MVDR with correlated signals, and an improved performance is obtained.展开更多
If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a spec...If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.展开更多
基金supported by the Chinese Natural Science Foundation 61401075Central University Business Fee ZYGX2015J106
文摘A theoretical relationship between the wavelet transform and the fast fourier transformation(FFT) methods in broadband wireless signal is proposed for solving the direction of arrivals(DOAs) estimation problem. This leads naturally to the derivation of minimum variance distortionless response(MVDR) algorithm, which combines the benefits of subspace methods with those of wavelet, and spatially smoothed versions are utilized which exhibits good performance against correlated signals. We test the method's performance by simulating and comparing the performance of proposed algorithm, FFT MVDR and MVDR with correlated signals, and an improved performance is obtained.
基金Supported by the Doctoral programme foundation of National Education Ministry of China
文摘If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.
