Time-domain Equalizer Design Methods Research Articles

MIMO Time Domain Equalizer Design for Long Reach xDSL MIMO Channel Shortening

In discrete multi-tone (DMT) transmission based digital subscriber line (DSL) systems, a cyclic prefix (CP) is added to each symbol before transmission, where the length of the CP is larger than the estimated channel impulse response (CIR) length. This ensures the elimination of inter-symbol interference (ISI) and inter-carrier interference (ICI) between the carriers of the same symbol, and allows for single tap frequency domain equalizers and crosstalk cancellation at the receiver. Recently, long reach xDSL (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. With the extended loop lengths, the required CP length increases, in order to match the larger CIR length. The longer CP adds a large overhead and results in overall throughput loss. A more efficient way to deal with extended loop lengths is to use a channel shortening filter - commonly referred as a time domain equalizer (TEQ), to reduce the length of the CIR to the length of CP. This paper focuses on minimum mean square error (MMSE) based multiple input multiple output (MIMO) TEQ design for LR-xDSL MIMO channel shortening. Constraints are applied to the minimization problem to eliminate the trivial solution. This paper proposes two new constraints for the MMSE based MIMO TEQ design for upstream scenarios, which result in a lower complexity and provide better (or similar) performance compared to existing MMSE based MIMO TEQ design methods. Furthermore, a diagonal MIMO TEQ with lower memory requirement and lower computational complexity is presented based on the proposed constraints, which can be applied in upstream as well as downstream scenarios.

A Novel Strategy for Proficient Channel Limitation Equalizer

A time-domain equalizer (TEQ) employed in cascade with the channel yields an actual impulse response that is squatter than the channel impulse response. Time-domain equalization is critical in reducing channel state dimension in maximum likelihood sequence approximation, and inter-carrier and inter-symbol interference in multicarrier systems. This project evaluates two TEQ design methods docile to cost-effective real-time implementation: least mean squared error (LMSE) and extreme shortening SNR (ESSNR) methods. We condense the complexity of computing the matrices in the ESSNR and LMSE designs by a factor of 140 and a factor of 16 (respectively) relative to existing approaches, without degrading performance. We prove that an infinite length ESSNR TEQ with unit norm TEQ constraint is symmetric. A symmetric TEQ halves FIR implementation density, enables parallel training of the frequency-domain equalizer and TEQ, reduces TEQ training complexity by a factor of 4 and doubles the length of the TEQ that can be designed using fixed-point arithmetic, with only a small loss in bit rate. Simulations are presented for designs with a symmetric TEQ or target impulse response.

A multi‐stage IIR time domain equalizer for OFDM systems with ISI

In an orthogonal frequency division multiplexing (OFDM) system, it is known that when the delay spread of the channel is larger than the cyclic prefix (CP) size, intersymbol interference will occur. The time‐domain equalizer (TEQ), designed to shorten the channel impulse response (CIR), is a common device to solve this problem. Conventionally, the TEQ is treated as a finite‐impulse‐response (FIR) filter, and many TEQ design methods have been proposed. However, a wireless channel typically has multi‐path responses, exhibiting FIR characteristics. Thus, the corresponding TEQ will have an infinite impulse response (IIR), and the FIR modeling of the TEQ is inefficient, i.e., the required order for the TEQ will be high. The conventional approach will then suffer from the high computation complexity problem, both in the derivation of TEQ and in the operation of channel shortening. In this paper, we propose a new scheme to overcome these problems. In the derivation of the TEQ, we propose to use a multistage structure, replacing a high‐order TEQ with a cascade of several low‐order TEQs. In the shortening operation, we propose to use an IIR TEQ approximating a high‐order FIR TEQ. Since the ideal TEQ exhibits low‐order IIR characteristics, the order of the IIR TEQ can be much lower than the FIR TEQ. Simulations show that while the proposed method can reduce computational complexity significantly, its performance is almost as good as existing methods.

An Eigen-Based TEQ Design for VDSL Systems

In this paper, we propose an eigen-based semiblind time-domain equalizer (TEQ) design method for VDSL systems. We exploit the fact that the VDSL system is frequency-division duplexing and maximize signal-to-interference ratio in the frequency domain. Unlike earlier eigen-based TEQ designs, the proposed method does not require the channel impulse response nor channel noise statistics. Using properties of the training symbols in VDSL initialization, the TEQ can be obtained by computing an eigenvector of a positive definite matrix that depends only on the averaged received VDSL symbols. The proposed method is referred to as semiblind, as properties of the training symbols are used but the channel impulse response is not known. Examples will be given to demonstrate that the proposed TEQ design method can effectively shorten the channel impulse response and achieve very good bit rates with only a small number of training symbols

Iterative Refinement Methods for Time-Domain Equalizer Design

Commonly used time domain equalizer (TEQ) design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread.

Efficient Channel Shortening Equalizer Design

Time-domain equalization is crucial in reducing channel state dimension in maximum likelihood sequence estimation and inter-carrier and intersymbol interference in multicarrier systems. A time-domain equalizer (TEQ) placed in cascade with the channel produces an effective impulse response that is shorter than the channel impulse response. This paper analyzes two TEQ design methods amenable to cost-effective real-time implementation: minimum mean square error (MMSE) and maximum shortening SNR (MSSNR) methods. We reduce the complexity of computing the matrices in the MSSNR and MMSE designs by a factor of 140 and a factor of 16 (respectively) relative to existing approaches, without degrading performance. We prove that an infinite-length MSSNR TEQ with unit norm TEQ constraint is symmetric. A symmetric TEQ halves FIR implementation complexity, enables parallel training of the frequency-domain equalizer and TEQ, reduces TEQ training complexity by a factor of 4, and doubles the length of the TEQ that can be designed using fixed-point arithmetic, with only a small loss in bit rate. Simulations are presented for designs with a symmetric TEQ or target impulse response.

Equalization for discrete multitone transceivers to maximize bit rate

In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces the intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Current TEQ design methods such as the minimum mean-squared error (MMSE), maximum shortening SNR (MSSNR), and maximum geometric SNR (MGSNR) do not directly maximize bit rate. We develop two TEQ design methods to maximize the bit rate. First, we partition an equalized multicarrier channel into its equivalent signal, noise, and ISI paths to develop a new subchannel SNR definition. Then, we derive a nonlinear function of TEQ taps that measures the bit rate, which the proposed maximum bit rate (MBR) method optimizes. We also propose a minimum-ISI method that generalizes the MSSNR method by weighting the ISI in the frequency domain to obtain higher performance. The minimum-ISI method is amenable to real-time implementation on a fixed-point digital signal processor. Based on simulations using eight different carrier-serving-area loop channels, (1) the proposed methods yield higher bit rates than MMSE, MGSNR, and MSSNR methods; (2) the proposed methods give three-tap TEQs with higher bit rates than 17-tap MMSE, MGSNR, and MSSNR TEQs; (3) the proposed MBR method achieves the channel capacity (as computed by the matched filter bound using the proposed subchannel SNR model) with a five-tap TEQ; and (4) the proposed minimum-ISI method achieves the bit rate of the optimal MBR method.