Far-end crosstalk severely degrades upstream rates in mixtures of vectored and non-vectored Very high-speed Digital Subscriber Loops (VDSL). As replacement of non-vectored VDSL systems by vectored VDSL systems is expected to be gradual, a crucial problem is the upstream rate optimization of vectored lines while maintaining the rate targets of non-vectored lines. To address this problem, this paper describes an algorithm that selects suitable Upstream Power Back-Off parameters for the vectored and the non-vectored lines. The algorithm has much lower computation requirements compared to Optimal Spectrum Balancing (OSB), yet simulation results show that the achievable vectored rates are very close to the OSB theoretical limits.

This letter presents a linear crosstalk precoder for very-high-speed digital subscriber lines (VDSL) that has a low run-time complexity. A lower bound on the data rate of the precoder is developed, and guarantees that the precoder achieves near-optimal performance in 99% of VDSL channels

Crosstalk is a serious problem in next-generation DSL systems, such as VDSL. Several non-linear crosstalk cancelers and pre-compensators have been proposed to address this. Unfortunately, they all suffer from high complexity, DFE error propagation and/or require modification of CPE. We propose the use of a simple linear zero-forcing crosstalk canceler in upstream transmission and a simple linear diagonalizing crosstalk precoder in downstream transmission. Certain properties of DSL channels ensure that these simple linear designs lead to near-optimal performance. We formulate a bound on the performance of these schemes and show that in 99% of upstream DSL channels, the linear zero-forcing canceler achieves 97% of the theoretical channel capacity. Similarly, in 99% of downstream DSL channels, the linear diagonalizing precoder achieves 91% of the theoretical channel capacity.

Crosstalk is the major source of performance degradation in next generation DSL systems such as VDSL. In downstream communications, transmitting modems are co-located at the central office. This allows crosstalk precompensation to be employed. In crosstalk precompensation, the transmitted signal is pre-distorted such that the pre-distortion destructively interferes with the crosstalk introduced by the channel. Existing crosstalk precompensation techniques either give poor performance or require modification of customer premises equipment (CPF). This is impractical since there are millions of legacy CPE modems already in use. We present a novel crosstalk precompensation technique, based on a diagonalization of the crosstalk channel matrix. This technique does not require modification of CPE. Furthermore, certain properties of the DSL channel ensure that this diagonalizing precompensator achieves near-optimal performance.

In certain communication channels, such as short copper twisted pairs, it is theoretically possible to perform transmission with very high spectral efficiency using a very wide bandwidth. However, current analog-to-digital converter (ADC) technology limits the allowable sampling rate and resolution, thus severely constraining the transmission speeds. This paper proposes the partitioning of the available bandwidth into multiple bands, each employing an independent ADC. The benefit of such a scheme is the reduction of the sampling rates of the ADCs. An increase in the dynamic range is allowed, thus offering the potential to realize very high spectral efficiencies. An analysis of transmission under ADC constraints is performed, where an expression for the achievable data rate is derived, based on an empirical rule for the tradeoff between the ADC sampling rate and resolution. A bandwidth-partitioning problem is formulated, where the objective is the maximization of the data rate, and the optimization parameters are the frequency-band assignments. Then, a practical example of transmission over category (CAT)-5 cable is considered. The possible impairment factors are outlined, and the essential system elements are described. Using the previously given algorithm, the optimum solution and the corresponding performance are given for two distinct scenarios. These scenarios serve to illustrate the bandwidth-partitioning procedure, and provide useful intuition regarding the application of the proposed method. In particular, it is deduced that it is best to have narrower bands in frequencies where the signal-to-noise ratio (SNR) is relatively high, and wider bands in frequencies where the SNR is relatively low.

We investigate power allocation and crosstalk cancellation for MIMO-DSL (a.k.a. bonded-DSL) systems. Exploiting a property of the DSL channel, namely column-wise diagonal dominance, allows us to simplify the power allocation and crosstalk cancellation problems. This leads to a significant reduction in initialisation and run-time complexity whilst maintaining near-optimal performance. We. develop a bound which relates the deviation of the simplified power allocation to the degree of column-wise diagonal dominance. Reliable transmission at near-capacity data-rates is also demonstrated through simulation.

Space-time block codes from orthogonal designs were proposed in Tarokh et al. (1999) for communication over fading channels with multiple transmit and receive antennas. These codes require no knowledge of the channel at the transmitter, and linear processing at the receiver achieves maximum-likelihood decoding. This paper presents an alternative approach to code design, where the code criterion is such that the transmitter and receiver operations essentially "diagonalize" any arbitrary matrix channel. Such diagonalization greatly simplifies decoding. The transmitter is assumed to have no knowledge of the channel. The desired properties of such a code are derived. It is shown that with some additional constraints, the resulting class of codes is identical to the codes introduced in Tarokh et al. Hence, an alternative interpretation of space-time block codes from orthogonal designs is given. The alternative code construction criteria that are derived may facilitate the design of more general classes of codes.

An adaptive method is proposed for multiple-input-multiple-output (MIMO) decision feedback equalization (DFE) in the absence of channel knowledge at the receiver and without requiring a training sequence. The zero-forcing (ZF) DFE is shown to consist of an orthogonal matrix (feedforward section) and an upper triangular matrix (feedback section). The feedforward matrix is expressed as the multiplication of Givens rotations terms, where each term is characterized by a rotation angle. An adaptive algorithm is presented for the blind determination of the unknown angles and of the elements of the feedback matrix. The adaptation criteria are decorrelation conditions. Simulation results are included demonstrating the performance of the method.

Time division multiplexing (TDM) must be employed in multi-Gb/s transceivers in order to overcome onchip clock frequency limitations. This paper describes a transmit pre-emphasis filter for a multi-level transceiver making use of TDM. The possible applications of such a transceiver include serial links and chip-to-chip communication. The requirement of very low probability of error in the absence of coding, and the need for an adaptive solution impose a peak transmit power constraint. The TDM system is mapped to a multiple-input-multiple-output (MIMO) system, and the noise sources are analyzed. The design of the pre-emphasis filter is shown to be a non-convex optimization problem, whose optimal solution is very difficult to obtain. Still, sub-optimal solutions are derived in closed form and adaptive implementations are described. Simulation results using parameters obtained from an experimental testbed indicate that these sub-optimal solutions actually achieve very good performance.

This paper describes the "vectored" transmission technique for digital subscriber line (DSL) systems, which utilizes user coordination at the central office or optical network unit. This method exploits the colocation of the downstream transmitters and of the upstream receivers, in order to achieve far-end crosstalk (FEXT) cancellation and perform multiuser transmission optimization. The performance improvements are particularly pronounced in environments with strong FEXT such as in very high-speed DSL. Discrete multitone is employed for each user with additional constraints on the cyclic prefix length and with the assumption of block-synchronized transmission and reception for downstream and upstream transmission correspondingly. Within each tone, upstream crosstalk is removed by multiple-input-multiple-output decision feedback at the receiving side, while downstream crosstalk is eliminated by analogous preprocessing at the transmitting side. Additionally, the issue of transmission energy allocation in frequency and among users is addressed. Assuming frequency-division duplexing, the corresponding optimization problem is formulated and solved via convex programming both for a fixed upstream-downstream band plan and for a dynamically programmable band plan. The case of power backoff as a means to reduce the impact of crosstalk on alien systems is also treated. Interestingly, the performance of the proposed methods is shown to be very close to known information theory bounds.

This paper considers the multiuser power control problem in a frequency-selective interference channel. The interference channel is modeled as a noncooperative game, and the existence and uniqueness of a Nash equilibrium are established for a two-player version of the game. An iterative water-filling algorithm is proposed to efficiently reach the Nash equilibrium. The iterative water-filling algorithm can be implemented distributively without the need for centralized control. It implicitly takes into account the loop transfer functions and cross couplings, and it reaches a competitively optimal power allocation by offering an opportunity for loops to negotiate the best use of power and frequency with each other. When applied to the upstream power backoff problem in very-high bit-rate digital subscriber lines and the downstream spectral compatibility problem in asymmetric digital subscriber lines, the new power control algorithm is found to give a significant performance improvement when compared with existing methods.

This paper shows that under certain conditions the generalized decision feedback equalizer (GDFE) asymptotically converges to the infinite length minimum-mean-square-error decision feedback equalizer (MMSE-DFE), in the sense that both structures perform essentially the same signal processing operations at both the transmitter and the receiver. The GDFE (developed by Cioffi and Forney (1997)) is a multiple-input-multiple-output (MIMO) generalization of the well-known DFE structure, whose special cases include various transmission schemes such as discrete multi-tone (DMT). The proofs are based on a fundamental equivalence theorem holding between the Cholesky factorization of a doubly infinite Toeplitz covariance matrix and the spectral factorization of a stationary sequence. The results extend to the case where the optimum spectrum consists of several disjoint bands (which implies the operation of multiple corresponding independent MMSE-DFEs). The convergence of GDFE to the potentially many MMSE-DFEs requires performing a "generalized resampling" operation, which is equivalent to partitioning the available bandwidth into disjoint bands and eliminating the unused regions.

This paper investigates optimal power control in a frequency selective multiuser interference network. The power control problem is modeled as a non-cooperative game. The existence and uniqueness of a Nash equilibrium in the game is established, and an iterative water-filling algorithm is proposed to reach the Nash equilibrium efficiently. It is shown that the Nash equilibrium point corresponds to a competitively optimal power allocation in the interference network. Based on this result, an adaptive power control algorithm for upstream VDSL power back-off is developed. The power control algorithm takes into account the loop transfer functions and cross-couplings, and allows the loops to negotiate the best use of power and frequency. This new algorithm is found to have a substantial performance improvement when compared to current methods.

This paper describes a modulation scheme achieving far-end crosstalk (FEXT) cancellation, assuming that joint signal processing among the users can be performed at either the receiver or at the transmitter side. The multi-user channel is modeled as a multiple-input-multiple-output (MIMO) system, and the development starts with the zero-forcing generalized decision feedback equalizer (GDFE). Structures are derived, which combine the discrete multi-tone (DMT) transmission technique with either successive cancellation at the receiver or precoding at the transmitter. A promising application of the proposed scheme is in FEXT-limited digital subscriber line (DSL) systems. Computer simulations demonstrate that significant performance improvements can be realized in such scenarios.