Block Transmissions over Doubly Selective Channels: Iterative Channel Estimation and Turbo Equalization

Abstract

Modern wireless communication systems require high transmission rates, giving rise to frequency selectivity due to multipath propagation. In addition, high-mobility terminals and scatterers induce Doppler shifts that introduce time selectivity. Therefore, advanced techniques are needed to accurately model the time-and frequency-selective (i.e., doubly selective) channels and to counteract the related performance degradation. In this paper, we develop new receivers for orthogonal frequency-division multiplexing (OFDM) systems and single-carrier (SC) systems in doubly selective channels by embedding the channel estimation task within low-complexity block turbo equalizers. Linear minimum mean-squared error (MMSE) pilot-assisted channel estimators are presented, and the soft data estimates from the turbo equalizers are used to improve the quality of the channel estimates.

A low complexity approach to equalization for doubly selective channels

“…This advantage of the proposed scheme in terms of a low complexity is further magnified in turbo equalization because the receiver has to iterate on the received signal and the computational savings can accrue over the iterations. Similarly, the proposed scheme has a lower complexity than that of [7,20,21], ¶ This is not taken into account either in the final operation count or in any comparison with existing low complexity equalization schemes. Instead, a complexity of N=2 log N complex MA operations is assumed, which is sufficient to establish a lower complexity than the schemes existing in the literature.…”

“…[2,3]) P 3 =6 where P D .L C L eq C 1/.Q C K Q C 1/ Serial Redesign/no complexity mitigation (see [6]) N.L eq C 1/ 3 =6 C N.L C L eq C 1/.L eq C 1/ 2 C N.L eq C 1/L f Serial redesign with recursive computations (see [5]) 3N.L 2 eq C L eq / C NOE.L eq C 1/.L eq C L C 1/ C N.L eq C 1/L f Exploiting sparsity via LDL T factorization [7,30] NOE4.Q=2/ 2 C 12.Q=2/ C 2 Proposed Algorithm which are block equalizers that seek to limit the complexity of equalization by exploiting the banded structure of the time-varying channel convolution matrix. The approach of [7,20,21] reduces the computational burden associated with the equalization problem by taking advantage of the fact that most of the elements in the channel convolution matrix are zeros, and the non-zeros lie on just a few diagonals thereby permitting a band LDL T factorization. In contrast, the approach presented here takes advantage of the correlations in the time-varying equalizer to help efficiently obtain it through sampling designs at a few time instants and then interpolating those to obtain equalizers for the entire block.…”

“…This first step of the proposed algorithm has widely been advocated as an effective approach to reducing the complexity associated with the turbo equalization of frequency selective channels. This approximation of using the average of the a priori information is also necessary for the recently proposed low complexity turbo equalizers of doubly selective channels in . Like these existing works, the proposed approach also replaces the a priori variance by its mean over the transmit block so that the variation of the equalizer over n is a result of only the channel time variations.…”

“…This advantage of the proposed scheme in terms of a low complexity is further magnified in turbo equalization because the receiver has to iterate on the received signal and the computational savings can accrue over the iterations. Similarly, the proposed scheme has a lower complexity than that of , which are block equalizers that seek to limit the complexity of equalization by exploiting the banded structure of the time‐varying channel convolution matrix. The approach of reduces the computational burden associated with the equalization problem by taking advantage of the fact that most of the elements in the channel convolution matrix are zeros, and the non‐zeros lie on just a few diagonals thereby permitting a band L D L T factorization.…”

“…This sampling and interpolation‐based approach to time‐varying equalizer design results in a computationally efficient equalization of doubly selective channels. The primary motivation for this approach is that the resulting equalization complexity is significantly lower than that of conventional serial equalization and it is even lower than that of the previously proposed low complexity doubly selective channel equalization schemes in the literature such as . Furthermore, low complexity equalization of doubly selective channels is motivated by the fact that the rapidly changing nature of these channels results in a very high equalization complexity unless some complexity reducing measures are adopted .…”