Multiple-input Multiple-output Finite Impulse Response Research Articles

Low-complexity blind polarization demultiplexing and frequency domain equalization for coherent passive optical network systems

Algorithmic and architectural options and trade-offs between performance and complexity/power dissipation are necessary to consider in the transfer of coherent technology from long-haul transmission to short-reach application. An adaptive equalization algorithm cascading polarization demultiplexing and frequency domain equalization is proposed to target passive optical network applications that feature extremely low computational complexity. Three coordinate rotation digital computer-based vector rotators are introduced to realize polarization demultiplexing without performing multiplications. A simplified gradient descent algorithm is proposed to search and trace the state of polarization. A nonbutterfly adaptive equalizer in the frequency domain for each polarization is designed to handle link chromatic dispersion and the imperfection of the transceiver frequency response. The performance of the proposed equalization scheme is experimentally verified by a 32-GBaud dual-polarization Nyquist quadrature phase-shift keying system over 20-km standard single-mode fiber transmission. With the proposed method, the number of hardened multipliers for field-programmable gate array realization is reduced by ∼85 % compared with a conventional 2 × 2 multiple-input multiple-output finite impulse response filter with the same receiver sensitivity.

Hardware Efficient Adaptive Equalizer for Coherent Short-Reach Optical Interconnects

We propose a novel adaptive equalization (AEQ) algorithm for short-reach coherent optical interconnects targeting intra-datacenter applications. The algorithm consists of 1-tap $2\times 2$ complex-valued multiple-input multiple-output (MIMO) finite impulse response (FIR) filter for polarization division de-multiplexing, four N-tap real-valued FIR filters for digital equalization, and a post three-tap T-spaced $4\times 4$ real-valued MIMO FIR filter for the timing skew mitigation. Up to 8-km standard single-mode fiber (SSMF) transmission experiments with 28-Gbaud PDM-16QAM signals verifies that less than the 1-dB receiver sensitivity penalty can be tolerated in comparison with conventional $4\times 4$ MIMO AEQ, while the number of multipliers can be reduced by ~59% if both algorithms use 25 taps. The tolerance of timing skew and chromatic dispersion for the AEQ algorithm is numerically investigated.

Design of Sparse FIR Decision Feedback Equalizers in MIMO Systems Using Hybrid l₁/l₂ Norm Minimization and the OMP Algorithm.

In this paper, a novel scheme using hybrid l1/l2 norm minimization and the orthogonal matching pursuit (OMP) algorithm is proposed to design the sparse finite impulse response (FIR) decision feedback equalizers (DFE) in multiple input multiple output (MIMO) systems. To reduce the number of nonzero taps for the FIR DFE while ensuring its design accuracy, the problem of designing a sparse FIR DFE is transformed into an l0 norm minimization problem, and then the proposed scheme is used to obtain the sparse solution. In the proposed scheme, a sequence of minimum weighted l2 norm problems is solved using the OMP algorithm. The nonzero taps positions can be corrected with the different weights in the diagonal weighting matrix which is computed through the hybrid l1/l2 norm minimization. The simulation results verify that the sparse FIR MIMO DFEs designed by the proposed scheme get a significant reduction in the number of nonzero taps with a small performance loss compared to the non-sparse optimum DFE under the minimum mean square error (MMSE) criterion. In addition, the proposed scheme provides better design accuracy than the OMP algorithm with the same sparsity level.

Iterative Computation of FIR MIMO MMSE-DFE With Flexible Complexity-Performance Tradeoff

In recent years, single-carrier (SC) communication for intersymbol interference (ISI) channels has enjoyed a revived interest. Its principal advantage over the multi-carrier scheme is its lower peak-to-average power ratio (PAPR). In this paper, we propose a new fast iterative algorithm to obtain the optimal finite impulse response (FIR) minimum-mean-square-error decision feedback equalizer (MMSE-DFE) for multiple-input multiple-output (MIMO) SC communication systems over ISI channels based on the QR decomposition of an augmented Toeplitz channel matrix. The proposed algorithm is not only computationally efficient but also very frugal in its memory usage. The algorithm applies to MIMO systems with any number of transmitting and receiving antennas, either balanced or unbalanced. The iterative nature of the proposed algorithm enables a flexible choice of Nf, the length of the feedforward filter (FFF), which leads to a controllable trade-off between complexity and performance. A conversion from time-domain equalization (TDE) to a hybrid DFE (HDFE) can be used to achieve lower complexity when Nf becomes large. Complexity analysis suggests a significant improvement over the prior art of TDE.

Some further results on blind identification of MIMO FIR channels via second-order statistics

In this paper, we consider the problem of blind multiple-input multiple-output (MIMO) finite impulse response (FIR) channel identification driven by spatially correlated signals. The second-order statistics (SOS) of the input sources are assumed known a priori. It is shown that under certain specified conditions, the MIMO FIR channel can be completely identified using the second-order statistics of the channel output. A SOS-based method is proposed and the proof for the uniqueness of the system solution is provided. As a special case, our proposed method can still entirely identify the MIMO channel even if the input source signals are spatially and temporally uncorrelated, given that the channel orders corresponding to each pair of users are different from each other. Extensive numerical simulation results are included to illustrate the performance of the proposed algorithm.

Blind Equalization of Nonirreducible Systems Using the CM Criterion

We address the blind equalization of finite-impulse-response (FIR) and multiple-input multiple-output (MIMO) channel systems excited by constant modulus (CM) signals. It is known that the algorithms based on the CM criterion can equalize an FIR MIMO system that is irreducible. The irreducible condition is restrictive as it requires all source signals to be received at sensors simultaneously. In this paper, we further show that the CM property of signals can be exploited to construct a zero-forcing equalizer for a system that is nonirreducible. Simulation examples demonstrate the proposed result

Equalization of a MIMO channel using FIR inverses

In the modern method of equalization, the problem of multiple-input multiple-output (MIMO) finite-impulse-response (FIR) channel equalization boils down to finding the MIMO FIR inverses. This correspondence proposes and proves a theorem that states the condition for the existence of these inverses, which are also FIR. A numerical example is provided to illustrate how the FIR inverses can be evaluated and used for equalization of a channel with known channel parameters.

Group decorrelation enhanced subspace method for identifying FIR MIMO channels driven by unknown uncorrelated colored sources

Identification of finite-impulse-response (FIR) and multiple-input multiple-output (MIMO) channels driven by unknown uncorrelated colored sources is a challenging problem. In this paper, a group decorrelation enhanced subspace (GDES) method is presented. The GDES method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace (JDES) method previously reported in the literature. The GDES method has a much better performance than the JDES method. The correctness of the GDES method is proved assuming that 1) the channel matrix is irreducible and column reduced and 2) the source spectral matrix has distinct diagonal functions. However, the GDES method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix. Simulations show that the GDES method yields good results even when the channel matrix is not irreducible, which is not possible at all for the JDES method.

A sequential subspace method for blind identification of general FIR MIMO channels

This correspondence addresses the problem of blindly identifying multiple input multiple output (MIMO) finite impulse response (FIR) channels without the conventional assumption of identical column degrees. A subspace-based algorithm is developed that identifies the channel's columns sequentially from the lowest degree columns to the highest degree ones. Compared with the previous generalized subspace method by Gorokhov and Loubaton (1997), the new method is simpler and more accurate.

Jointly optimized transmitter and receiver FIR MIMO filters in the presence of near-end crosstalk

A theory for jointly optimizing transmitter and receiver finite impulse response (FIR) multiple-input multiple-output (MIMO) filters is developed in the presence of near-end crosstalk and additive channel noise independent of the original signal. The transfer function of the channel is a known MIMO transfer function with finite memory. Near-end crosstalk is included through another MIMO transfer function. The channel input signal is assumed to be power constrained. For a given channel with a maximum allowable average input power, the transmitter and receiver FIR MIMO filters are jointly optimized such that the mean square error (MSE) between the desired and reconstructed signal is minimized. An iterative numerical optimization algorithm is proposed. When compared to the methods available in the literature, the proposed method yields better results due to the joint optimization of the transmitter-receiver pair and is applicable to a more general scenario that may include correlated sources and near-end crosstalk.

Jointly Minimum BER Transmitter and Receiver FIR MIMO Filters for Binary Signal Vectors

A theory is developed for jointly minimizing the bit error rate (BER) between the desired and decoded signals with respect to the coefficients of transmitter and receiver finite impulse response (FIR) multiple-input multiple-output (MIMO) filters. The original signal is assumed to be a vector time-series with equally likely memoryless Bernoulli vector components. The channel model constitutes of a known FIR MIMO transfer function and Gaussian additive noise independent of the original signal. The channel input signal is assumed to be power constrained. Based on the formulas obtained, an iterative numerical optimization algorithm is proposed. When compared with other design methods available in the literature, the proposed method yields better results due to the generality of the model considered and the joint optimization of the transmitter-receiver pair.

Blind MIMO FIR channel identification based on second-order spectra correlations

We consider a problem of identifying a multiple-input multiple-output (MIMO) finite impulse response (FIR) system excited by colored inputs with known statistics. We propose a new, nonlinear optimization-based method that involves the power spectra and cross-spectra of the system output. The proposed algorithm is tested for the case of cyclostationary inputs (CDMA scenario) and stationary inputs (SDMA scenario). Simulation results indicate that the proposed scheme works well, even for large order systems, and is robust to noise and channel length mismatch.

Multi-Channel Multi-Variate Equalizer Design

The polarimetric calibration of synthetic aperture radar (SAR) imagery requires the equalization of a multiple-input, multiple-output (MIMO) distortion system. For wide-band, wide-angle SAR systems, the distortion is frequency and angle dependent and can be accurately modelled as a two-dimensional finite impulse response (FIR) filter bank. This paper presents a design algorithm, using a Grobner basis, to compute a FIR filter bank that exactly inverts the multi-channel distortion. The results presented for polynomial inversion of MIMO FIR systems hold for sampled data signals of arbitrary dimension.

Blind equalization of MIMO-FIR channels driven by white but higher order colored source signals

The goal of the article is to find a minimal amount of statistical information (or a much weaker condition) about source signals for which blind equalization is possible for multiple-input multiple-output finite-impulse response (MIMO-FIR) channels. First, a sufficiently broad framework is set up within which such a theoretical problem is well posed. Within this framework, it is shown that second-order statistics (SOS) alone are not sufficient for blind equalization when the source signals are white. Additional higher order statistics (HOS) are needed. Then we show that the only additional higher order statistical information needed is spatial fourth-order cumulants. Though it has not yet been proved to be minimal, it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture. We then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth-order uncorrelated. Based on this condition, criterion (A) for blind equalization of MIMO-FIR channels is developed by exploiting the temporal fourth-order statistics. Finally, based on this criterion, a new necessary and sufficient condition in terms of cumulants for the blind equalization of MIMO-FIR channels is obtained.