Sensor array and narrowband signal processing

The vast majority of sensor array processing algorithms consider fix emitting sources. This assumption is very questionable when air- and space-surveillance is considered. For this reason the problem of estimating parameters for multiple moving targets was considered in this project. The paper 3 proposed an embedded movement model, using angles and angular rates, that is included in the formulation of the steering vectors. The approach is similar to the idea of track-before detect that is employed in the target tracking field. The deterministic maximum likelihood (DML) method was derived using the embedded movement model, together with the Cramer-Rao Bound (CRB) of the estimation problem. It was shown in the paper 3 that the DML algorithm that exploits the embedded model provides high-resolution also when targets are crossing. As seen in Figure 1, this result is supported by the CRB.

Figure 1: Resolving crossing targets with an embeeded movement model. The targets cross at snapshot 41.

Contributions on narrow band signal processing have also been presented on the estimation of damped sinusoids (5), where the CRB was derived for the problem of estimating multiple, poorly damped sinusoids in noise. Contributions treating estimation of a single sine wave in noise (5), and of harmonic signals (2), have also been presented.

The paper 1 introduces recursive filtering for the construction of the covariance matrix of the channel estimates, with the purpose of computational complexity reduction of a subsequent beamforming problem. A repeated use of the matrix inversion lemma result in a complexity that is reduced from cubic to quadratic in the number of antenna elements of the base station. Figure 2 depicts the computational complexity reduction for mobile stations with 1 (black), 4 (blue), 16 (green) and 64 (red) antenna elements.

Figure 2: Computational complexity for the reference algorithm (dashed) and the

recursively filtered algorithm (solid).

References

1. T. Wigren, "Recursively filtered MIMO transmission with quadratic complexity", IEEE Wireless Comm. Letters, vol. 10, no. 5, pp. 929-933, 2021. DOI 10.1109/LWC.2021.3050388

2. T. Wigren and P. Händel, "Harmonic signal modeling using adaptive nonlinear function estimation", Proc. ICASSP, Atlanta, Georgia, U.S.A., pp. 2952-2955, 1996.

3. T. Wigren and A. Eriksson, "Accuracy aspects of DOA and angular velocity estimation in sensor array processing", IEEE Signal Processing Lett., vol. SPL-2, no. 4, pp. 60--62, 1995.

4. P. Händel, A. Eriksson and T. Wigren, "Performance analysis of a correlation based single tone frequency estimator", Signal Processing, vol. 44, no. 2, pp. 223--231, 1995.

5. T. Wigren and A. Nehorai, "Asymptotic Cramér-Rao bounds for estimation of the parameters of damped sine waves in noise", IEEE Trans. Signal Processing, vol. ASSP-39, no. 4, pp. 1017-1020, 1991.