Karthik Muralidhar

A Low-Complexity Kalman Approach for Channel Estimation in Doubly-Selective OFDM Systems

In this letter, we propose a vector state-scalar observation (VSSO) Kalman filter for channel estimation in doubly-selective orthogonal frequency division multiplexing (OFDM) systems. Vector state-vector observation (VSVO) Kalman filters have been reported before in the literature for this purpose. The proposed VSSO Kalman filter achieves the same performance as the VSVO Kalman filter and results in 92% complexity savings. The Kalman filter outperforms a recently proposed linear minimum mean square error (LMMSE) estimator and achieves a high spectral efficiency of 93% as compared to the LMMSE estimator of 68%. A key aspect of this paper is that we show how the observed pilot symbol vector can be decorrelated or decoupled into uncorrelated multipath scalars. This aspect (and the proposed Kalman filter) is similar in spirit to that of a quasi-static channel.

Equivalence of VSSO and VSVO Kalman Channel Estimators in Doubly-Selective OFDM Systems—A Theoretical Perspective

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.

Pilot Design for Vector State-Scalar Observation Kalman Channel Estimators in Doubly-Selective MIMO-OFDM Systems

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 Barhumis and Dais 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.

Uniform circular broadband beamformer with selective frequency and spatial invariant region

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.

Iterative Kalman-AR Method for Doppler Spread Estimation in Flat Fading Channels

The knowledge of Doppler spread is very important in many channel estimation (tracking) algorithms for flat fading channels. Recently, doppler spread estimators based on the profile of the power spectral density (psd) have been published. They make use of the fact that there is an abrupt change in the psd around the maximum Doppler frequency. However, this assumption is invalid in low signal-to-noise ratios (SNRs). In this paper, we introduce an iterative Kalman autoregressive (IKAR) estimator which overcomes this drawback. In doing so, we also study the excellent detection properties of the IKAR detector and demonstrate its superiority over some of the conventional detectors. The IKAR estimator performance is studied for two low SNR scenarios.

Delay coefficients based variable step size algorithm for subband affine projection adaptive filters

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.

Generalized vector state-scalar observation Kalman channel estimator for doubly-selective OFDM systems

Recently, we presented a low-complexity vector state-scalar observation (VSSO) Kalman channel estimator for doubly-selective OFDM systems in [1]. In [1], we derived the decoupling equations, where a received pilot symbol vector is decoupled into L scalars, L being the number of multipaths of the channel. This decoupling concept formed the basis of the VSSO Kalman channel estimator. However, in [1], we considered only one observed subcarrier from each pilot cluster. In this paper, we consider more than one observed pilot subcarriers from each pilot cluster and work out a more generalized form of the decoupling equation. This paves way to a more generalized form of the VSSO Kalman estimator. The performance and complexity results are shown compared to an existing vector state-vector observation Kalman estimator. It will be seen that our proposed VSSO method achieves the same performance as the existing vector state-vector observation (VSVO) method [2] and results in more than 90% complexity savings. Results are also presented for a practical system like a digital video broadcasting (DVB-H) system.

Comments on 'optimal training design for linearly time-varying MIMO/OFDM channels modelled by a complex exponential basis expansion'

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

Comments on "Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice

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.