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Linear equalizers (LEs) have been widely adopted for practical systems due to their low computational complexity. However, it is also well known that LEs provide inferior performance relative to a maximum-likelihood equalizer (MLE) or other near- MLEs, because LEs usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information. More importantly, unlike MLE or near-MLEs, the performance of LEs has not been well quantified. This hinders more general applications of LEs in wireless systems. In this paper, we reveal a fundamental link between a channel parameter-orthogonality deficiency (od) of the channel matrix-and the diversity and capacity of LEs. We identify that when the od of channel matrix has an upper bound strictly less than 1, the same diversity order as that of MLEs is collected by LEs and the outage capacity loss relative to MLEs is also a constant over signal-to-noise ratio (SNR). These results can be applied to designing a framework for hybrid equalizers. Furthermore, by studying the statistical properties of the od and comparing the complexity of different equalizers, we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od. The theoretical analysis is corroborated by computer simulations. [ABSTRACT FROM AUTHOR]

Differential encoding is known to simplify receiver implementation because it by-passes channel estimation. However, over rapidly fading wireless channels, ext!a transceiver modules are necessary to enable differential transmission. Relying on a basis expansion model for time and frequency selective (doubly selective) channels, we derive such a generalized block-differential (BD) codec and prove that it achieves maximum Doppler and multipath diversity gains, while affording low-complexity maximum-likelihood decoding. We further show that existing BD systems over frequency-selective or time-selective channels follow as special cases of our novel system. Simulations using the widely accepted Jakes' model corroborate our theoretical analysis. [ABSTRACT FROM AUTHOR]

Carrier frequency offset (CFO) estimation for orthogonal frequency-division multiplexing (OFDM) has caught attention as OFDM systems have become widely adopted in recent years. In this paper, we design a novel double-differential (DD) codec with low computational complexity. Our design bypasses CFO and channel estimation, and is easy to implement at both transmitter and receiver. It also guarantees full multipath diversity, and reduces the peak-to-average power ratio from the number of subcarriers to the channel order. In addition, it is robust to CFO drifting. The closed form of the performance for our design is derived for OFDM transmissions over frequency-selective channels with CFO. Thorough simulation results corroborate our claims. [ABSTRACT FROM AUTHOR]

Recently, an eigenvector-based algorithm has been developed for multidimensional frequency estimation with a single snapshot of data mixture. Unlike most existing algebraic approaches that estimate frequencies from eigenvalues, the eigenvector-based algorithm achieves automatic frequency pairing without joint diagonalization of multiple matrices, but it fails when there exist identical frequencies in certain dimensions because eigenvectors are not linearly independent anymore. In this paper, we develop an eigenvector-based algorithm for multidimensional frequency estimation with finite data snapshots. We also analyze the identifiability (ID) and performance of the proposed algorithm. It is shown that our algorithm offers the most relaxed statistical ID condition for multidimensional frequency estimation from finite snapshots. More important, we introduce complex weighting factors so that the algorithm is still operational when there exist identical frequencies in one or more dimensions. Furthermore, the weighting factors are optimized to minimize the mean square errors of the frequency estimates. Simulation results show that the proposed algorithm offers competitive performance when compared to existing algebraic approaches but at lower complexity. [ABSTRACT FROM AUTHOR]