The radio interface EDGE (Enhanced Data rates for Global Evolution) is currently being standardized as an evolutionary path from GSM and TDMA-IS136 for third-generation high-speed data wireless systems. For the EDGE system with multiple antennas, spatial-temporal equalization (STE) can reduce intersymbol interference and co-channel interference, thereby increasing the capacity and range. In this paper, we propose two new techniques to improve the performance of a previously proposed STE: a fast timing recovery algorithm for a selective time-reversal equalizer and a two-stage soft-output equalizer. The new timing recovery algorithm determines the estimated burst timing and processing direction by computing the minimum mean-square error (MMSE) for decision feedback equalizers in both the forward and reverse time directions. The two-stage soft-output equalizer is the cascade of a delayed decision-feedback sequence estimator (DDFSE) and maximum a posteriori probability (MAP) estimator. The DDFSE provides better noise variance estimation and channel truncation for the following MAP. The performance of the new STE is evaluated for the EDGE. At 10% block error rate, the two-branch receiver requires a 3-7-dB lower signal-to-interference ratio (SIR) than the previous approach. Compared with the one-branch receiver, the two-branch receiver requires a 4-dB lower SNR with noise only, and a 10-27-dB lower SIR with a single interferer.

We propose a new 2-stage soft-output equalizer (TSSOE) structure for spatial-temporal processing in EDGE. The TSSOE is the cascade of a delayed decision-feedback sequence estimator (DDFSE) and maximum a posteriori probability (MAP) estimator. The TSSOE uses the final-decision symbols from the DDFSE to estimate the noise variance and truncates the channel memory for the following MAP estimator. Compared with the soft-output DDFSE, the TSSOE reduces both the feedback symbol errors and the noise variance estimation error. At a 10% block error rate and 20 dB signal-to-noise ratio, the TSSOE requires about 10 dB lower signal-to-interference ratio than the soft-output DDFSE for the GSM typical urban channel profile.

The Godard (1980) or the constant modulus algorithm (CMA) is an effective technique for blind receiver design in communications. However, due to the complexity of the constant modulus (CM) cost function, the performance of the CM receivers has primarily been evaluated using simulations. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function. The following question, while resolvable numerically for a specific example, remains unanswered in a generic manner. In the presence of channel noise, where are the CM local minima and what are their mean-squared errors (MSE)? In this paper, a geometrical approach is presented that relates the CM to Wiener (or minimum MSE) receivers. Given the MSE and the intersymbol/user interference of a Wiener receiver, a sufficient condition is given for the existence of a CM local minimum in the neighborhood of the Wiener receiver. The MSE bounds on CM receiver performance are derived and shown to be tight in simulations. The analysis shows that, while in some cases the CM receiver performs almost as well as the (nonblind) Wiener receiver, it is also possible that, due to its blind nature, the CM receiver may perform considerably worse than a (nonblind) Wiener receiver.

The constant modulus algorithm (CMA) is an effective technique for blind receiver design in practice. Treating CMA as a linear estimation problem, effects of noise and channel conditions are investigated. For the class of channels with arbitrary finite impulse responses, an analytical description of locations of constant modulus receivers and an upper bound of their mean squared errors (MSE) are derived. We show that, with proper initializations, CMA can achieve almost the same performance as the (nonblind) minimum mean square error (MMSE) receiver. Our analysis reveals a strong relationship between the (blind) constant modulus and the (nonblind) MMSE receivers. It also highlights the significance of initialization/reinitialization schemes. The approach developed in this paper also applies to CMA blind beamforming in array signal processing.

The proper initialization of the constant modulus algorithm (CMA) is a critical problem that has not been solved. This paper presents a new reinitialization scheme for CMA. The proposed scheme searches in the channel space for the constant modulus equalizer with minimum mean-square error by exploiting the structure of the minimum mean square error (MMSE) equalizer and connections between the constant modulus and the MMSE equalizers.

Equalization based on blind channel estimation using the second-order statistics has a rapid convergence rate and is potentially attractive in digital wireless communications. The asymptotic behavior of this type of approach is investigated. In particular, the achievable lower bounds of the asymptotic mean-square error (MSE) are derived to serve as benchmarks for a class of blind equalization algorithms using second-order statistics. It is shown that the convergence rate of these equalizers suffers when channels are ill-conditioned. Applying this analysis to systems using antenna arrays, the performance gain of multiple receivers over single receiver is evaluated analytically.