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Vector state-scalar observation (VSSO) Kalman channel estimators for doubly-selective OFDM systems (DS-OFDM) result in complexity savings of 90% without any loss of performance, as compared to vector state-vector observation (VSVO) Kalman estimators. In this letter, we present the VSSO Kalman channel estimator for doubly-selective multiple-input multiple-output OFDM (DS-MIMO-OFDM) systems. Unlike the VSSO estimator in a DS-OFDM system, where all the pilot symbols had the same value, the pilot symbols need to be designed in a specific way to enable the feasibility of a VSSO estimator for a DS-MIMO-OFDM system. We derive a sufficient condition called as VSSO Kalman-filter condition (VSSO-KFC) that needs to be satisfied by the pilot-pattern design for the feasibility of the VSSO Kalman estimator. We comment, and compare, the proposed pilot pattern with that of Barhumi's and Dai's pilot pattern. A new scheme is introduced, based on the proposed pilot pattern and VSSO Kalman filter, that increases the spectral efficiency compared to a conventional system.

Vector state-vector observation (VSVO) , and vector state-scalar observation (VSSO) are two types of Kalman estimators that can be used for channel estimation in doubly-selective OFDM systems over wide-sense stationary uncorrelated-scattering (WSSUS) channels. It was shown in that the VSSO Kalman channel estimator resulted in over 90% complexity savings compared to the VSVO Kalman channel estimator and this was achieved without any loss of performance. This inevitably raises the question whether the VSSO and VSVO Kalman channel estimators are computationally equivalent? We attempt to answer this question in this letter and theoretically show the equivalence of the VSSO and VSVO Kalman channel estimator for WSSUS channels.

Subband adaptive filters are preferred in acoustic echo cancellation systems with long echo tail lengths due to speed of convergence and complexity savings. Recently, a new and novel subband affine projection (SAP) algorithm was reported based on the polyphase decomposition of the adaptive filter and noble identities. For good system performance it is important to have a good variable step size (VSS) algorithm as part of an adaptive filter. In this paper, based on the method of delay coefficients (DC), we propose1 a VSS algorithm for the SAP adaptive filter, which is called as delay coefficients based variable step size subband affine projection algorithm (DC-VSS-SAP). We examine in detail the similarities and differences between DC method for the subband and fullband scenarios. Further, we show how the method of DC can be used to detect changes in echo paths and speed up convergence of the adaptive filter.

In orthogonal frequency-division multiplexing (OFDM) systems, parametric channel estimation-based algorithms are known to improve performance when the multipath is sparse in nature. Likewise, subspace-based techniques, that exploit the slowly-varying delay-subspace, are also known to improve the channel estimation performance. However, these methods assumed that the channel is constant over one or many OFDM symbols. In this letter, we present the parametric- and delay-subspace-based algorithms for channel estimation in scenarios where the channel is varying within an OFDM symbol duration. It is also shown that performance considerably improves, when these methods are used in conjunction with a Kalman-based channel-tracking algorithm.

Most existing frequency-invariant (FI) beamformer algorithms design array beampattern response across the entire frequency bands. In this paper, the design of array gain response is extended to both selective frequency and spatial region. The algorithm consists of an objective function that has a two-dimensional constraint. One dimension constraint is on frequency range; this is to ensure a selective frequency invariant region is formed. The second dimension constraint is on spatial direction; this is to maintain the array response of the beamformer constant for a small amount of angle centered at the desired direction. Having such constant gain response over a selective spatial region makes the array beamformer less sensitive to the exact position of the source. Advanced optimization method such as Second Order Cone Programming (SOCP) is used to solve this complex optimization problem with high efficiency and accuracy. Simulation results are compared with other existing algorithms. It demonstrates that the proposed method is able to achieve a constant gain over the specified sector of angle and at the same time having a lower mean square error on the FI performance over the specified frequency region.

The above paper presented a variable regularized affine projection algorithm (VR-APA). A delay coefficients-based variable regularized affine algorithm (DC-VR-APA) was presented in [2], [3]. It was shown in [1, pp. 2103, (39)] that DC-VR-APA is an equivalent and alternate manifestation of the VR-APA when the affine projection order is equal to 1. However, results pertaining to input speech signals and presence of near-end speech activity 1 were not reported in. For the same set of parameters, this letter 2 shows that DC-VR-APA is more robust to the above conditions than the VR-APA. Motivated by some of the explanations in, we present the reasons for the robustness of DC-VR-APA in the above conditions.

Equations (17), (18) and (19) are incorrectly given in the above study. In this study, we give the correct versions of those equations.