Method and apparatus for adaptive direction estimation of radio waves

A direction estimation method for coherent signals in an environment of spatially correlated additive noise, where a specified number (=p<M/2) of coherent signals are received by a uniform linear array with multiple (=M) antenna elements, and the length of the spatial correlation of the noise is assumed to be q (0≦q≦M−1), in which when the correlation between the noise wi(n), wj(n) included in the signals received at the ith and jth antenna elements can be expressed by;

• E{wi(n) wj*(n)}≠0(|i-j|≦q)
• E{wi(n) wj*(n)}≠0(|i-j|≦q),
• said direction estimation method comprising:
• calculating (M−q−1) instantaneous cross-correlations r1M(n), r2M(n), . . . rM−q−1,M(n) at time n between a signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n) and a (M−2p−q)×p lower matrix Φf2(n);
• moreover, by calculating (M−q−1) number of instantaneous cross-correlations rq+2,1(n), rq+3,1(n), . . . rM1(n) at time n between a signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n), and a (M−2p−q)×p lower matrix Φf2(n);
• furthermore, calculating (M−q−1) number of instantaneous cross-correlations r1,q+2(n), r1,q+3(n) . . . r1,M(n) at time n between a signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p−q)×p lower matrix Φb2(n);
• moreover, by calculating (M−q−1) instantaneous cross-correlations rM1(n), rM2(n) . . . rM,M−q−1(n) at time n between signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p−q)×p lower matrix Φb2(n);
• selecting one group from the four groups of instantaneous cross-correlation matrices
• Φf1(n), Φf2(n);
• Φf1(n), Φf2(n);
• Φb1(n), Φb2(n);
• Φ1(n), Φb2(n) and forming the matrices Φ1(n), Φ2(n), as
• Φ1(n)=Φf1(n), Φ2(n)=Φf2(n) or
• Φ1(n)= Φf1(n), Φ2(n)= Φf2(n) or
• Φ1(n)=Φb1(n), Φ2(n)=Φb2(n) or
• Φ1(n)= Φb1(n), Φ2(n)= Φb2(n);
• calculating a linear operator at time n from these two matrices Φ1(n), Φ2(n), by using an adaptive LMS algorithm with a fixed or time-varying step-size parameter;
• estimating a noise subspace by using this linear operator;
• and
• estimating the direction of coherent signals from the noise subspace at a predetermined time by using Newton approximation.

A direction estimation method for coherent signals in an environment of spatially correlated additive noise, where a specified number (=p<M/2) of coherent signals are received by a uniform linear array with multiple (=M) antenna elements, and a length of a spatial correlation of the noise is assumed to be q (0≦q≦M−1) in which when the correlation between the noise wi(n), wj(n) included in the signals received at the ith and jth antenna elements can be expressed by:

• E{wi(n) wj*(n)}≠0(|i-j|≦q)
• E{wi(n) wj*(n)}≠0(|i-j|≦q),
• said direction estimation method comprising:
• calculating (M−q−1) instantaneous cross-correlations r1M(n), r2M(n), . . . rM−q−1,M(n) at time n between the signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−p−1) th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n), and a (M−2p−q)×p lower matrix Φf2(n);
• moreover, by calculating (M−q−1) number of instantaneous cross-correlations rq+2,1(n), rq+3,1(n), . . . rM1(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n) and a (M−2p−q)×p lower matrix Φf2(n);
• furthermore, calculating (M−q−1) number of instantaneous cross-correlations r1,q+2(n), r1,q+3(n), . . . r1,M(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p−q)×p lower matrix Φb2(n);
• moreover, by calculating (M−q−1) instantaneous cross-correlations rM1(n), rM2(n), . . . rM,M−q−1(n) at time n between signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p−q)×p lower matrix Φb2(n);
• selecting one group from the four groups of instantaneous cross correlation matrices
• Φf1(n), Φf2(n);
• Φf1(n), Φf2(n);
• Φb1(n), Φb2(n);
• Φ1(n), Φb2(n) and forming the matrices Φ1(n), Φ2(n), as
• Φ1(n)=[Φf1(n), Φf1(n)], Φ2(n)=[Φf2(n), Φf2(n)] or
• Φ1(n)=[Φf1(n), Φb1(n)], Φ2(n)=[Φf2(n), Φb2(n)] or
• Φ1(n)=[Φf1(n), Φb1(n)], Φ2(n)=[Φf2(n), Φb2(n)] or
• Φ1(n)=[ Φf1(n), Φb1(n)], Φ2(n)=[ Φf2(n), Φb2(n)] or
• Φ1(n)=[ Φf1(n), Φb1(n)], Φ2(n)=[ Φf2(n), Φb2(n)] or
• Φ1(n)=[Φb1(n), Φb1(n)], Φ2(n)=[(Φb2(n), Φb2(n)];
• calculating a linear operator at time n from these two matrices Φ1(n), Φ2(n), by using an adaptive LMS algorithm with a fixed or time-varying step-size parameter;
• estimating a noise subspace by using that linear operator;
• and
• estimating the direction of coherent signals from the noise subspace at a time predetermined time by using Newton approximation.

A direction estimation method for coherent signals in an environment of spatially correlated additive noise, where a specified number (=p<M/2) of coherent signals are received by a uniform linear array with multiple (=M) antenna elements, and the length of the spatial correlation of the noise is assumed to be q (0≦q≦M−1) in which when the correlation between the noise wi(n), wj(n) included in the signals received at the ith and jth antenna elements can be expressed by:

• E{wi(n) wj*(n)}≠0(|i-j|≦q)
• E{wi(n) wj*(n)}≠0(|i-j|≦q),
• said direction estimation comprising:
• calculating (M−q−1) instantaneous cross-correlations r1M(n), r2M(n), . . . rM−q−1,M(n) at time n between the signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n), and a (M−2p−q)×p lower matrix Φf2(n);
• moreover, by calculating (M−q−1) number of instantaneous cross-correlations rq+2,1(n), rq+3,1(n), . . . rM1(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n) and a (M1−2p−q)×p lower matrix Φf2(n);
• furthermore, calculating (M−q−1) number of instantaneous cross-correlations r1,q+2(n), r1,q+3(n), . . . r1,M(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M1'p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M1'2p−q)×p lower matrix Φb2(n);
• moreover, by calculating (M−q−1) instantaneous cross-correlations rM1(n), rM2(n), . . . rM,M−q−1(n) at time n between signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p1'q)×p lower matrix Φb2(n);
• selecting one group from the four groups of instantaneous cross-correlation matrices
• Φf1(n), Φf2(n);
• Φf1(n), Φf2(n);
• Φb1(n), Φb2(n);
• Φ1(n), Φb2(n) and forming the matrices Φ1(n), Φ2(n), as
• Φ1(n)=[Φf1(n), Φf1(n), Φb1(n)], Φ2(n)=[Φf2(n), Φf2(n), Φb2(n)] or
• Φ1(n)=[Φf1(n), Φf1(n), Φb1(n)], Φ2(n)=[Φf2(n), Φf2(n), Φb2(n)] or
• Φ1(n)=[Φf1(n), Φb1(n), Φb1(n)], Φ2(n)=[Φf2(n), Φb2(n), Φb2(n)] or
• Φ1(n)=[ Φf1(n), Φb1(n), Φb1(n)], Φ2(n)=[ Φf2(n), Φb2(n), Φb2(n)];
• calculating a linear operator at time n from these two matrices Φ1(n), Φ2(n) by using an adaptive LMS algorithm with a fixed or time—varying step—size parameter;
• estimating a noise subspace by using this linear operator;
• and
• estimating the direction of coherent signals from the noise subspace at a predetermined time by using Newton approximation.

A direction estimation method for coherent signals in an environment of spatially correlated additive noise, where a specified number (=p<M/2) of coherent signals are received by a uniform linear array with multiple (=M) antenna elements, and a length of a spatial correlation of the noise is assumed to be q (0≦q≦M−1) in which when the correlation between the noise wi(n), wj(n) included in the signals received at the ith and jth antenna elements can be expressed by:

• E{wi(n) wj*(n)}≠0(|i-j|≦q)
• E{wi(n) wj*(n)}≠0(|i-j|≦q),
• said direction estimation comprising:
• calculating (M−q−1) instantaneous cross-correlations r1M(n), r2M(n), . . . rM−q−1,M(n) at time n between the signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n) and a (M−2p1'q)×p lower matrix Φf2(n);
• moreover, by calculating (M−q−1) number of instantaneous cross-correlations rq+2,1(n), rq+3,1(n), . . . rM1(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p1'q)×p Hankel correlation matrix Φf(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φf1(n) and a (M−2p1'q)×p lower matrix Φf2(n);
• furthermore, calculating (M−q−1) number of instantaneous cross-correlations r1,q+2(n), r1,q+3(n), . . . r1,M(n) at time n between the signal received at the first antenna element and the signals received at the (q+2)th, (q+3)th, . . . , Mth antenna elements;
• forming a (M−p1'q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb2(n) and a (M−2p1'q)×p lower matrix Φb2(n);
• moreover, by calculating (M−q−1) instantaneous cross-correlations rM1(n), rM2(n), . . . rM,M−q−1,(n) at time n between signal received at the Mth antenna element and the signals received at the first, second, . . . , (M−q−1)th antenna elements;
• forming a (M−p−q)×p Hankel correlation matrix Φb(n), which is formed by selecting (M−p−q) pairs each of which is consisted of p instantaneous correlations from the (M−q−1) instantaneous cross-correlations and dividing this Hankel matrix into a p×p upper matrix Φb1(n) and a (M−2p1'q)×p lower matrix Φb2(n);
• and forming the matrices Φ1(n), Φ2(n) as
• Φ1(n)=[Φf1(n), Φf1(n), Φb1(n), Φb1(n)],
• Φ1(n)=[Φf2(n), Φf2(n), Φb2(n), Φb2(n)];
• calculating a linear operator at time n from these two matrices Φ1(n), Φ2(n), by using an adaptive LMS algorithm with a fixed or time-varying step-size parameter;
• estimating a noise subspace by using this linear operator;
• and
• estimating the direction of coherent signals from the noise subspace at a predetermined time by using Newton approximation.

A direction estimation apparatus for the coherent, correlated or uncorrelated signals in an environment of spatially correlated additive noise, where a specified number (=p<M/2) of incident signals are received by a uniform linear array with multiple (=M) antenna elements, while a length of a spatial correlation of the noise is assumed to be q (0≦q≦M−1) in which when the correlation between the noise wi(n), wj(n) included in the signals received at the ith and jth antenna elements can be expressed by:

• E{wi(n) wj*(n)}≠0(|i-j|≦q)
• E{wi(n) wj*(n)}≠0(|i-j|≦q),
• said direction estimation apparatus comprising:
• means for calculating M−q−1 instantaneous cross-correlations at time n between the signal received at each antenna element and the signals received at the other antenna elements;
• means for selecting multiple pairs of the cross-correlations, each of which is consisted of p instantaneous cross-correlations from the calculated M−q−1 instantaneous correlations to form a Hankel correlation matrix and dividing this matrix into an upper and lower correlation matrices;
• means calculating a linear operator at time n from these two upper and lower correlation matrices by using an adaptive LMS algorithm with a fixed or time-varying step-size parameter or using an adaptive NLMS algorithm, and estimating a noise subspace by using this estimated linear operator;
• means for estimating a noise subspace by using this estimated linear operator;
• and
• means for estimating the directions of the coherent signals at time n from the estimated u noise subspace by using Newton approximation.