M. Haardt and J. A. Nossek, "Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. on Signal Proc., vol. 43, pp. 1232--1242, May 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Q 2 2 1 2 . J (2)2 J (2)1 29 A unitary left P PP P real matrix of size 2n2n is obtained from the latter one by dropping its central row and central column. Then we compute the K dominant eigenvectors of the covariance matrix of G GG G(X) and form the signal subspace E s . Then it is shown in [16] that the spatial frequencies, related to the parameters of interest, can be obtained by solving the over determined set of equations ( 2 , 1 2 1 = r s r r s r E K E K using a (Total) Least Squares technique. The selection matrices K (r)1 and K (r)2 are obtained from the selection ....

M. Haardt and J. A. Nossek. Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden. IEEE Trans. Signal Processing, 43(5): 1232-1242, May 1995.

....and the estimated channel parameters. and the finite array aperture. The achievable resolution is only limited by the SNR, incorrect model assumptions and limited measurement accuracy (such as remaining calibration errors) Due to its computational efficiency, the Unitary ESPRIT algorithm [3] is chosen for joint multidimensional channel parameter estimation. Figure 1 shows the scenario with the estimated parameters. The DOD (direction of departure at the transmitter) and the DOA (directions of arrival at the receiver) are indicated by the path line orientation at the RX and TX ....

M. Haardt, J.A. Nossek, "Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden," IEEE Transactions on Signal Processing, Vol. 43, pp. 1232-1242, June 1995.

....of MtxMfXMTXMR cross multiplexed impulse responses. Mt is the number of snapshots, Mfthe number of frequency samples across the 120 MHz bandwidth to obtain the averaged impulse response (see Fig. 10) These data were post processed in several ways: by parametric estimation with Unitary ESPRIT [9] or by the conditional maximum likelihood method (see subsection on high speed mobiles) Unitary ESPRIT has proven its suitability for high resolution DOA studies at the mobile station [10] 11] and at the base station [12, 13] ESPRIT is based on a singular value decomposition of the data matrix ....

M.Haardt and J.A.Nossek, "Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden", IEEE Transactions on Signal Processing, 43(5):1232-1242, May 1995

....ARRAY Outline The situation becomesmore interesting if we can assume additional structure on A. Suppose that (i) the array is centro symmetric (see figure 3) and (ii) that there is no multipath. Such assumptions are often made for direction finding algorithms such as (unitary) ESPRIT [14]. The symmetry of the array carries over into a symmetry of the array manifold vectors, under assumption (ii) equal to the columns of A: P A = A ; P= 2 4 0 1 . 1 0 3 5 ; where we have placed the zero phase reference in the center of the array. It follows that X = AS P X = A S so that ....

....collected in a matrix T , after which the beamforming matrix on the original data is given by W =US 1 T . Details The matrix [X P X] can be mapped to a real matrix: there are data independent unitary matrices Q 1 and Q 2 with simple structures such that Q 1 [X P X]Q 2 is real valued [14]. Thus, the computation of the SVD of [X P X] can be carried out in the real domain and T will be real valued without further effort. Since t is real, y = tt can be parametrized by a vector y 0 consisting of 1 2 d(d 1) real parameters. There is a reconstruction matrix J s such that y = J s ....

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M. Haardt and J.A. Nossek, "Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. Signal Proc., vol. 43, no. 5, pp. 1232--1242, May 1995.

....is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array. The parameter estimates are obtained by exploiting the rotational invariance structure of the signal subspace. Among the ESPRIT like estimation schemes, Unitary ESPRIT [7] provides increased estimation accuracy with a reduced computational burden. By exploiting the conjugate symmetric property of the array manifold, Unitary ESPRIT utilizes a unitary transformation to map CentroHermitian matrices into real matrices. This transformation not only reduces computations ....

Haardt, M., and Nossek, J. A., "Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. on Signal Processing, vol. 43, pp.1232-1242, May 1995.

....estimation. Thus, the algorithm is closed form and computationally attractive, and angles and delays are jointly estimated and automatically paired. Many of the tricks developed for ESPRIT and DOA estimation, such as forward backward averaging, spatial smoothing [13] and real processing [12, 14], are readily incorporated into the current algorithm. The number of rays may be larger than the number of antennas, which overcomes a limitation of the non joint 1 D ESPRIT method mentioned in [6] for initialization of a joint iterative ML optimization. A second difference to several other ....

....: The four original data matrices have now been reduced to equivalent r Theta r data matrices, satisfying ae E xOE = S 0 T E yOE = S 0 PhiT ae E x = S 00 T E y = S 00 ThetaT (14) for certain nonsingular r Theta r matrices S 0 , S 00 , T . D. Real processing Similar as in [12, 14], we can use the structure of H e to do a transformation to a real matrix, which allows to keep the SVD of H e and all subsequent operations in the real domain, with obvious computational and numerical advantages. This is possible because every entry in H e can be VAN DER VEEN et al. JOINT ....

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M. Haardt and J.A. Nossek, "Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden, " IEEE Trans. Signal Processing, vol. 43, pp. 1232--1242, May 1995.

.... use the fact that all q i are on the unit circle along with the centro symmetric structure of the array to augment the data matrix to X e = X; PX T ] where P is the reverseidentity matrix which flips the rows of X T : this will not increase the rank but double the number of observations [25]. Using this structure, it is also possible to transform X e to a real valued matrix, by simple linear operations on its rows and columns [25,34] As mentioned in Section IV D, there are many other direction finding algorithms that are applicable, in particular MODE [22] Although ESPRIT is ....

.... [X; PX T ] where P is the reverseidentity matrix which flips the rows of X T : this will not increase the rank but double the number of observations [25] Using this structure, it is also possible to transform X e to a real valued matrix, by simple linear operations on its rows and columns [25,34]. As mentioned in Section IV D, there are many other direction finding algorithms that are applicable, in particular MODE [22] Although ESPRIT is statistically suboptimal, its performance is usually quite adequate. Its interest to us here is its straightforward generalization to more complicated ....

M. Haardt and J.A. Nossek, "Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. Signal Proc., vol. 43, no. 5, pp. 1232--1242, May 1995.

.... of (2) or a SVD (singular value decomposition) of a data matrix composed of # consecutive vectors (1) the lower dimensional signal and noise subspaces can be identified which may be used to calculate the DOA s via high resolution methods like MUSIC, Unitary ESPRIT or Weighted Subspace Fitting [3, 5]. But finding the subspaces is a high numerical burden, especially if they change with time and therefore have to be computed recurringly which shows the necessity to track them efficiently. Let us now assume a communication system like GSM that uses a TDMA component. Then there is no continuous ....

Haardt, M., Nossek, J.A.: Unitary ESPRIT: How to Obtain Increased Estimation Accuracy with a Reduced Computational Burden, IEEE Transactions on Signal Processing, Vol. 43, pp. 1232-1242, May 1995

....threshold fl can be estimated from the noise level. A simple formula for fl is given in this paper. Recently, there have been efforts to improve the subspace based ESPRIT method using the SVD as the basic tool for the subspace separation task (e.g. total least squares ESPRIT or Unitary ESPRIT [5]) Unitary ESPRIT yields improved parameter estimates at a lower computational cost by taking the unitarity of the phase factors into account. Constraining the phase factors to the unit circle improves the performance significantly, especially if the sources are correlated, cf. section 4. Unitary ....

....some performance degradation compared to the optimal SVD based scheme. Unitary ESPRIT provides a way to compensate for this loss of accuracy by exploiting additional information inherent in the rotational invariance structure of the signal subspace. 3. Unitary Schur ESPRIT Since Unitary ESPRIT [5] includes forward backward averaging, all required decomposition, i.e. the hyperbolic L Theta decomposition as well as the subsequent least squares problem and the final eigendecomposition, can be transformed into real valued decompositions of the same size. This is achieved by constructing ....

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M. Haardt and J. A. Nossek, "Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computationalburden", IEEE Trans. Signal Processing, vol. 43, May 1995, scheduled to appear.

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M. Haardt and J. A. Nossek, "Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. on Signal Proc., vol. 43, pp. 1232--1242, May 1995.

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M. Haardt and J. A. Nossek, "Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden," IEEE Trans. Signal Process, vol. 43, no. 5, pp. 1232--1242, 1995.

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M. Haardt and J. A. Nossek. Unitary ESPRIT: How to obtain increased estimation accuracy with a reduced computational burden. IEEE Transactions on Signal Processing, 43:5:1232--1242, May 1995.

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