Generalized Decision Feedback Equalizer Research Articles

Price of Fairness in Digital Subscriber Line Systems Using Dynamic Spectrum Management

Bit rate fairness is an important concern in current G.fast and the forthcoming fifth generation DSL systems where the frequency is extended to hundreds of MHz and crosstalk couplings reach unprecedented levels. In this paper, we study the price of fairness (PoF) in dynamic spectrum management (DSM) enabled DSL systems. We propose optimal low complexity PoF-constrained max-min fairness (MMF), weighted max-min fairness (WMMF), proportional fairness (PF), and (p,α)-PF algorithms. The proposed algorithms inherently provide weight factors which can be used to reduce the computational complexity of user encoding or decoding order optimizing algorithms used in nonlinear vectoring. Our simulation results show that although PoF grows exponentially with the minimum bit rate, fairness can be improved considerably with a relatively small price in DSM level 2 spectrum balancing and particularly in DSM level 3 using minimum mean square error (MMSE) generalized decision feedback equalizer (GDFE). It is also seen that the proposed optimal PoF-constrained MMF algorithm can reach the solutions of PF and (p,α)-PF measures for some PoF. That is, the PoF-constrained MMF or WMMF algorithms can be used instead of the non-linear PF and (p,α)-PF measures, which often result in computationally intensive solutions.

A Practical GDFE Precoder for Multiuser MIMO Systems

Generalized decision feedback equalizer (GDFE) achieves MIMO broadcast channel (BC) capacity but suffers from huge computational complexity and feedback overhead making it unsuitable for practical systems. Much of the complexity is due to the computation of the covariance matrix corresponding to the least favorable noise. Additionally GDFE implementation requires the base stations (BS) to feedback filter coefficients to the users thus increasing overhead. In this paper, we address both the aspects - computational complexity and feedback overhead. We first propose an alternative framework for realizing the GDFE precoder, which avoids the explicit computation of the least favorable noise. We show that, while maintaining capacity optimality of the GDFE precoder, the proposed algorithm has significantly lower complexity. Next, we propose another algorithm which does not require the feedback of filter coefficients from BS to users with minimal loss in achievable capacity. Thus our algorithms are a step towards adopting GDFE precoders in future wireless systems.

Joint Level 2 and 3 Dynamic Spectrum Management for Upstream VDSL

Dynamic spectrum management (DSM) refers to a wide range of techniques for counteracting crosstalk in digital subscriber line (DSL) networks. DSM is categorized into three levels based on the degree of coordination among users. In this article, we investigate optimal joint level 2 and 3 DSM for upstream DSL. We will discuss the difficulties of finding the universally optimal solution and we propose an optimal algorithm, referred to as IF/MAC-OSB, under some practical and implementation assumptions for this problem. Using computer simulations, we show that IF/MAC-OSB is capable of increasing the user bit rates considerably compared to several other DSM techniques. The proposed algorithm involves using the minimum mean squared error (MMSE)-generalized decision feedback equalizer (GDFE) together with Lagrange dual optimization. We address several aspects of the problem including the optimal decoding order in the GDFE receiver, GDFE error propagation, and the computational complexity of the algorithm. We also study effects of channel model randomness and upstream power back-off utilization on the performance of the algorithm.

Design of QR Decomposition Processor for GDFE

This paper presents a QR decomposition processor by exploiting Givens rotation for the GDFE (Generalized Decision Feedback Equalizer). A Givens rotation consists of phase extraction, sine/cosine generation and angle rotation parts. Combining two-stage method (coarse and fine stage) and the fixed-width modified-Booth multiplier, we design an efficient QR decomposition processor. By simulations, it is shown that the proposed QR decomposition processor can be a feasible solution for GDFE.

Optimal Diversity–Multiplexing Tradeoff and Code Constructions of Some Constrained Asymmetric MIMO Systems

In multiple-input-multiple-output (MIMO) communications, the notion of asymmetric channel refers to the situation when the number of transmit antennas is strictly larger than the number of receive antennas. Such channels can often be found in MIMO downlink transmissions. While existing cyclic-division-algebra (CDA)-based codes can still be employed to achieve the optimal diversity-multiplexing tradeoff (DMT) at high signal-to-noise ratio (SNR) regime, such codes cannot be directly decoded using, for example, the pure sphere decoding method. Although other means of decoding methods such as minimum mean square error generalized decision feedback equalizer (MMSE-GDFE) with lattice search and regularized lattice decoding are available, an alternative approach is to constrain the number of active transmit antennas in each channel use to be no larger than the number of receive antennas. The resulting system is coined constrained asymmetric MIMO system. Two general types of asymmetrical channels are considered in this paper, namely, 1) when there are two receive antennas and the number of transmit antennas is arbitrary, and 2) when the number of transmit antennas is one larger than the number of receive antennas. Explicit optimal transmission schemes as well as the corresponding code constructions for such constrained asymmetric MIMO channels are presented, and are shown to achieve the same DMT performance as their unconstrained counterparts.

Coding and Decoding for the Dynamic Decode and Forward Relay Protocol

We study the dynamic decode-and-forward (DDF) protocol for a single half-duplex relay, single-antenna channel with quasi-static fading. The DDF protocol is well known and has been analyzed in terms of the diversity-multiplexing tradeoff (DMT) in the infinite block length limit. We characterize the finite block length DMT and give new explicit code constructions. The finite block length analysis illuminates a few key aspects that have been neglected in the previous literature: 1) we show that one dominating cause of degradation with respect to the infinite block length regime is the event of decoding error at the relay; 2) we explicitly take into account the fact that the destination does not generally know a priori the relay decision time at which the relay switches from listening to transmit mode. Both of the above problems can be tackled by a careful design of the decoding algorithm. In particular, we introduce a decision rejection criterion at the relay based on Forney's decision rule (a variant of the Neyman-Pearson rule), such that the relay triggers transmission only when its decision is reliable. Also, we show that a receiver based on the generalized likelihood ratio test (GLRT) rule that jointly decodes the relay decision time and the information message achieves the optimal DMT. Our results show that no cyclic redundancy check (CRC) for error detection or additional protocol overhead to communicate the decision time are needed for DDF. Finally, we investigate the use of minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding at both the relay and the destination, and show that it provides near-optimal performance at moderate complexity.

A joint channel estimation and data detection receiver for multiuser MIMO IFDMA systems

In this paper, we are interested in the problem of joint channel estimation and data detection for multi-input multi-output (MIMO) interleaved frequency division multiple access (IFDMA) systems. Although IFDMA is free from the multiple access interference (MAI), it suffers from intersymbol interference (ISI). MIMO-IFDMA system suffers from both ISI and multi-stream interference (MSI). The block iterative generalized decision feedback equalizer (BI-GDFE) is an iterative and effective interference cancelation scheme which could provide near maximum likelihood (ML) performance with very low complexity. However, BI-GDFE needs the channel state information (CSI). In this paper, we utilize the soft estimates of the transmitted symbols provided by the BI-GDFE to estimate the channel via an Expectation Maximization (EM)-based algorithm. By doing so, a joint channel estimation and data detection receiver is developed. To evaluate the performance of the proposed channel estimation algorithm, we derive the Cramér-Rao Lower Bound (CRLB). Computer simulations show that the bit error rate (BER) performance of the proposed joint channel estimation and signal detection receiver can reach the performance of the BI-GDFE with perfect CSI.

Doubly iterative receiver for block transmissions with EM-based channel estimation

Cyclic-prefix code division multiple access (CP-CDMA), multicarrier CDMA (MC-CDMA) and single carrier cyclic-prefix (SCCP) transmission are some schemes that could support the increasing demand of future high data rate applications. The linear and nonlinear equalizers used to detect the transmitted signal are always far from the maximum-likelihood (ML) detection bound. The block iterative generalized decision feedback equalizer (BI-GDFE) is an iterative and effective interference cancelation scheme which could provide near-ML performance yet with very low complexity. In order to deploy this scheme, the channel state information (CSI) must be available at the receiver. In practice, this information has to be estimated by using pilot and data symbols. This paper investigates the problem of channel estimation using the expectation maximization (EM) algorithm. The BI-GDFE provides the soft information of the transmitted signals to the EM-based algorithm in the form a combination of hard decision and a coefficient so-called the input-decision correlation (IDC). The resultant receiver becomes a doubly iterative scheme. To evaluate the performance of the proposed estimation algorithm, the Cramer-Rao lower bound (CRLB) is also derived. Computer simulations show that the bit error rate (BER) performance of the proposed receiver for joint channel estimation and signal detection can reach the performance of the BI-GDFE with perfect CSI.

Space–Time Codes From Structured Lattices

We present constructions of space-time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, i.e., when the block length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping. Our codes achieve the optimal diversity-multiplexing tradeoff (DMT) of quasi-static multiple-input multiple-output (MIMO) fading channels for any fading statistics, and perform very well also at practical, moderate values of signal-to-noise ratios (SNR). Then, we extend the construction to the case of large block lengths, by using trellis coset coding. We provide constructions of trellis coded modulation (TCM) schemes that are endowed with good packing and shaping properties. Both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding and a combination of this with a Viterbi TCM decoder for the TCM case. Beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity.

Design of cyclic delay diversity for single carrier cyclic prefix (SCCP) transmissions with block-iterative GDFE (BI-GDFE) receiver

<i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Single</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">carrier</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cyclic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">prefix</i> (SCCP) modulation has been adopted as one of the physical layer air-interfaces for IEEE802.I6 standards due to its less stringent requirement on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">peak-to-average</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ratio</i> (PAPR) than multicarrier modulation. As a single carrier transmission, however, the received SCCP blocks suffer from inter-symbol interference (ISI). The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">block</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iterative</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generalized</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decision</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feedback</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equalizer</i> (BI-GDFE) is an effective interference cancellation scheme which generally shows performance improvement over linear equalizers. However, in order to achieve a significant gain, the channel must contain rich multipath components, and this may not necessarily be true in many systems. In this paper, we propose to apply <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cyclic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diversity</i> (CDD) to a SCCP system so that the possible performance improvement by using a BI-GDFE detector can be enhanced. The asymptotic performance of the proposed system is analyzed using random matrix results. We propose a scheme to determine the optimal delay parameter for CDD. Computer simulations have shown that by incorporating CDD into the transmitter and using a BI-GDFE receiver, the BER performance of the system can approach the MFB within several iterations for high SNR region.

Optimized Resource Allocation for Upstream Vectored DSL Systems With Zero-Forcing Generalized Decision Feedback Equalizer

In upstream vectored DSL systems using zero-forcing generalized decision feedback equalizers (ZF-GDFE), different decoding orders cause performance tradeoffs among the users. In this paper, these tradeoffs are characterized by formulating optimization problems with practical constraints. Lagrange dual decomposition and a two-step algorithm are used to solve the dual problems optimally with the computational complexity linear in the number of DMT tones. However, solving the tonal subproblem, which is shared by all the proposed optimization problems, associates with a high-complexity exhaustive search of orderings, where K is the number of users. Thus, this paper proposes two low-complexity algorithms in order to find suboptimal orderings: successive ordering search (SOS) with complexity O(K4) and modified greedy search (MGA) with complexity O(K3). Numerical results show that MGA performs well enough in finding the achievable rate region. For problems related to feasibility check, SOS is suitable for closely approximating the optimal solution.

Multiple Access Channel Optimal Spectrum Balancing for Upstream DSL Transmission

Upstream DSL transmission suffers from in-domain crosstalk as well as out-of-domain or alien crosstalk. Here, the use of multi-user receiver signal coordination e.g. generalized decision feedback equalization, can lead to spectacular performance gains. This paper presents a transmission scheme, referred to as MAC-OSB, which focuses on the weighted rate sum capacity by joint receiver signal coordination and transmit spectrum coordination. The proposed scheme incorporates per-user total power constraints, spectral mask constraints and discrete bit or power loading constraints. Furthermore a low-complexity scheme, referred to as MAC-ISB, is presented which performs similar to MAC-OSB. Simulations show large performance gains over existing methods especially for scenarios with significant alien crosstalk

Block-iterative generalized decision feedback equalizers for large MIMO systems: algorithm design and asymptotic performance analysis

This paper studies the problem of signal detection for multiple-input multiple-output (MIMO) channels with large signal dimensions. We propose a block-iterative generalized decision feedback equalization (BI-GDFE) receiver to recover the transmitted symbols in a block-iterative manner. By exploiting the input-decision correlation, a measure for the reliability of the earlier-made decisions, we design the feed-forward equalizers (FFEs) and feedback equalizers (FBEs) in such a way that maximized signal-to-interference-plus-noise ratio (SINR) is achieved for each of the iterations. Novel implementations are also introduced to simplify the complexity of the receiver, which requires only one-tap filters for FFE and FBE. The proposed receiver also works when the signal dimension is greater than the observation dimension. The asymptotic performance of the proposed receiver is analyzed and its convergence has been confirmed through numerical evaluations for various parameters. Computer simulations are presented to illustrate the capability of the proposed receiver to achieve single user matched-filter bound (MFB) for large random MIMO channels when the received SNR is high enough.

Adaptive MIMO decision feedback equalization for receivers with time-varying channels

In an attempt to reduce the computational complexity of vertical Bell Labs layered space time (V-BLAST) processing with time-varying channels, an efficient adaptive receiver is developed based on the generalized decision feedback equalizer (GDFE) architecture. The proposed receiver updates the filter weight vectors and detection order using a recursive least squares (RLS)-based time- and order-update algorithm. The convergence of the algorithm is examined by analysis and simulation, and it is shown that the proposed adaptive technique is considerably simpler to implement than a V-BLAST processor with channel tracking, yet the performances are almost comparable.

On the relation between V-BLAST and the GDFE

This letter shows that the receiver processing of the Vertical Bell Labs Layered Space-Time (V-BLAST) architecture may he viewed as a generalized decision feedback equalizer (GDFE) as applied to a multiple-input-multiple-output (MIMO) channel. It is proven that, depending on the criterion chosen to reduce the interference, the receiver operations of the V-BLAST system are fundamentally equivalent to either a zero-forcing (ZF) or a minimum-mean-square-error (MMSE) GDFE.

Generalized decision feedback equalizer for approximate maximum likelihood bit detection of digital signals

A new type of non-linear equalizer which gives the maximum Likelihood (ML) bit estimates approximately is presented and its error rate performance is discussed. The structure of the non-linear equalizer is derived by introducing the idea of the decision feedback to the ML bit estimation. Since it is implemented by simple digital filters and decision slicers, we can greatly reduce this computation and storage required in the ML bit estimation and significantly improve the bit error probability as compared to the conventional decision feedback equalizer.

一般化されたDFEの構成とその特性

一般化されたDFEの構成とその特性