William J. Hillery

Downlink Specific Linear Equalization for Frequency Selective CDMA Cellular Systems

We derive and compare several linear equalizers for the CDMA downlink under frequency selective multipath conditions: minimum mean-square error (MMSE), zero-forcing (ZF), and RAKE. MMSE and ZF equalizers are designed based on perfect knowledge of the channel. The downlink specific structure involves first inverting the multipath channel to restore the synchronous multi-user signal transmitted from the base-station at the chip-rate, and then correlating with the product of the desired users channel code times the base-station specific scrambling code once per symbol to decode the symbols. ZF equalization restores orthogonality of the Walsh-Hadamard channel codes on the downlink but often suffers from noise gain because certain channel conditions (no common zeros) are not met; MMSE restores orthogonality only approximately but avoids excessive noise gain. We compare MMSE and ZF to the traditional matched filter (also known as the RAKE receiver). Our formulation generalizes for the multi-channel case as might be derived from multiple antennas and/or over-sampling with respect to the chip-rate. The optimal symbol-level MMSE equalizer is derived and slightly out-performs the chip-level but at greater computational cost. An MMSE soft hand-off receiver is derived and simulated. Average BER for a class of multi-path channels is presented under varying operating conditions of single-cell and edge-of-cell, coded and un-coded BPSK data symbols, and uncoded 16-QAM. These simulations indicate large performance gains compared to the RAKE receiver, especially when the cell is fully loaded with users. Bit error rate (BER) performance for the chip-level equalizers is well predicted by approximate SINR expressions and a Gaussian interference assumption.

Decision feedback equalizers with constrained feedback taps for reduced error propagation

Error propagation is a serious concern when a decision feedback equalizer (DFE) is used in a communication system. This paper describes a method of mitigating the effects of error propagation by constraining the feedback tap coefficients. It is shown that the most natural method of constraining the feedback taps is to constrain the 1-norm of the tap vector. The paper also considers a constraint on the 2-norm of the feedback tap vector. The proposed method is demonstrated using the trellis coded 8-VSB system used by the ATSC terrestrial broadcast standard for digital television. Results show that the constraints do reduce error propagation in the DFE, but the performance is considerably better when a zero delay trellis decoder is used to determine the decisions in the feedback filter.

Structured channel estimation based decision feedback equalizers for sparse multipath channels with applications to digital TV receivers

In this paper, we investigate the performance of channel estimation based equalizers. We introduce two different channel estimation algorithms. Our first channel estimation scheme is a novel structured channel impulse response (CIR) estimation method for sparse multipath channels. The novel CIR estimation method was called blended least squares (BLS) which uses symbol rate sampled signals, based on blending the least squares based channel estimation and the correlation and thresholding based channel estimation methods. The second CIR estimation is called Variable thresholding (VT), and is based on improving the output of the correlation and thresholding based channel estimation method. We then use these two CIR estimates to calculate the decision feedback equalizer (DFE) tap weights. Simulation examples are drawn from the ATSC digital TV 8-VSB system. The delay spread for digital TV systems can be as long as several hundred times the symbol duration; however, digital TV channels are, in general, sparse where there are only a few dominant multipaths.

Conjugate-gradient-based decision feedback equalization with structured channel estimation for digital Television

In this paper, we show how the convergence time of equalizers for 8-VSB based on the conjugate gradient (CG) algorithm can be considerably improved through initialization based on a channel estimate. We derive real and complex minimum mean-square error (MMSE) equalizers and implement them adaptively using the conjugate gradient, recursive least squares (RLS), and least mean squares (LMS) algorithms. We show that both CG and RLS have similar convergence times --- both are much faster than LMS. Since the CG algorithm is easily initialized, we compare several methods of initialization to determine how each affects convergence and then apply the best methods to initialize equalizers using channel estimates. We find that initializing the correlation matrices and filling the feedback taps with training symbols greatly speeds convergence of the CG adaptive equalizer, potentially approaching the rate of convergence when running the algorithm on the matrix equations using the actual channel.

Decision feedback equalizer design for insensitivity to decision delay

In this paper, we use an alternative approach to derive the minimum mean-square error decision feedback equalizer. This derivation yields insight which allows the equalizer to be designed so that its SINR performance is relatively insensitive to variations in the decision delay (also known as the cursor). The design, while generally applicable to the DFE, is illustrated using 8-level vestigial sideband modulation as used in the ATSC digital television standard. We simulate several channels and show that the SINR varies little across a relatively wide band of decision delays.

Finite Impulse Response Cyclic Shift Transmit Diversity for Broadband Mobile OFDM

This paper introduces an open-loop transmit diversity method called finite impulse response cyclic shift diversity (FIR-CSD) for broadband mobile OFDM systems. Ordinary CSD operates in OFDM by cyclically shifting the same time- domain signal by different cyclic shift values on each transmit antenna branch. Unfortunately, in some channels (such as a line of sight channel or a heavily spatially correlated channel), ordinary CSD introduces deep spectral nulls in the composite frequency response seen by the receiver, which results in a performance loss relative to the single transmit antenna case. FIR-CSD is an extension of the CSD concept wherein multiple weighted and circular shifted copies of the time-domain signal are combined and transmitted on each antenna. Each transmit antenna essentially uses a different FIR filter that combines multiple weighted and circularly-shifted copies of the time-domain signal to be transmitted. Careful selection of the circular shift values and weighting factors on each transmit antenna can significantly reduce or eliminate the deep spectral nulls that ordinary CSD would produce in the above mentioned channels. This paper shows that FIR-CSD provides a significant performance improvement over the original cyclic shift diversity method, especially in correlated channels and with high-rate coding.

Computation of a constrained decision feedback equalizer for reduced error propagation

It has been previously shown that the effects of error propagation in a decision feedback equalizer may be reduced by constraining the 2-norm of the feedback filter. This paper describes three algorithms for calculating the constrained equalizer based on a channel estimate. An iteration function is derived for the Karush-Kuhn-Tucker multiplier and the algorithms are designed to quickly find a fixed point of this function. The algorithms include a modified regula falsi algorithm known as the Pegasus iteration, a modified secant algorithm, and a nonlinear fit to the iteration function. At each iteration, the conjugate gradient algorithm is used to solve the resulting linear equations. The algorithms are demonstrated on the 8-VSB terrestrial broadcast digital TV system. While all three algorithms exhibit good convergence characteristics, the nonlinear fit converges the fastest.