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.

In this study, the authors examine resource allocation in an orthogonal frequency‐division multiple‐access‐based cognitive radio (CR) network which dynamically senses primary users (PUs) spectrum and opportunistically uses available channels. The aim is resource allocation such that the CR network throughput is maximised under the PUs maximum interference constraint and cognitive users (CUs) transmission power budget. This problem is formulated as a mixed‐integer non‐linear programming problem which is 𝔼‐hard in general and infeasible to solve in real‐time. To reduce the computational complexity, the authors decouple the problem into two separate steps. After initial power allocation, in the first step, an adaptive algorithm is employed to assign subcarriers to the CUs toward throughput maximisation by using these initial powers. In the second step, power is allocated optimally to the assigned subcarriers. Simulation results show that the proposed method nearly achieves the optimal solution in a small number of iterations meaning significant reduction in the computational complexity.

Partial feedback in multiple-input multiple-output communication systems provides tremendous capacity gain and enables the transmitter to exploit channel condition and to eliminate channel interference. In the case of severely limited feedback, constructing a quantised partial feedback is an important issue. To reduce the computational complexity of the feedback system, this study introduces an adaptive partial method in which at the transmitter, a set of easy to implement least-square adaptive algorithms is engaged to compute the channel state information. In the proposed method, at the receiver, the time-varying step-sizes of the algorithms are computed and replied to the transmitter via a reliable feedback channel. The transmitter iteratively employs this feedback information to estimate the channel weights. This method is independent of the employed space–time coding schemes and gives all channel components. Complementary solution is given to reduce the computational complexity and simulation examples are given to evaluate the performance of the proposed method.

In this study, we propose a least mean square-partial parallel interference cancellation (LMS-PPIC) method named parallel LMS-PPIC (PLMS-PPIC) in which the normalised least mean square (NLMS) adaptive algorithm with optimised chip time-varying step-size is engaged to obtain the cancellation weights. The former LMS-PPIC method is based on fixed not optimised step-size, which causes propagation of error from one stage to the next one and increases the bit error rate (BER). The unit magnitude of the cancellation weights is the principal property in our step-size optimisation. To avoid computational complexity a small set of NLMS algorithms with different step-sizes are executed. In each iteration the parameter estimate of that NLMS algorithm which the elements magnitudes of its cancellation weight estimate have the best match with unit is chosen. Magnificent decrease in BER is achieved by executing the proposed method. Moreover PLMS-PPIC like former LMS-PPIC method comes to practice only when the channel phases are known. When they are unknown, having only their quarters in (0, 2π), we propose modified versions of LMS-PPIC and PLMS-PPIC to find the channel phases and the cancellation weights simultaneously. Simulation scenarios are given to compare the performance of our methods with that of LMS-PPIC in two cases: balanced channel and unbalanced channel. The results show that in both cases the proposed method outperforms LMS-PPIC, especially for high processing gains.

Parallel least mean square-partial parallel interference cancellation (PLMS-PPIC) is a partial interference cancellation which employs adaptive multistage structure (Shahtalebi et al., 2007). In this algorithm the channel phases for all users are assumed to be known. Having only their quarters in (0, 2pi), a modified version of PLMS-PPIC is proposed in this paper to simultaneously estimate the channel phases and the cancellation weights. Simulation examples are given in the cases of balanced, unbalanced and time varying channels to show the performance of the modified PLMS-PPIC method.

The performance of an adaptive filter is restricted by the statistical behavior of the additive noise. The aim of this paper is to improve the convergence speed and steady state error of the set-membership normalized least mean square (SM-NLMS) algorithm in a colored noise environment. The noise is assumed to follow an auto-regressive (AR) model with bounded excitation uncorrelated samples. Without information about the noise parameters, the traditional SM-NLMS algorithm results in an unsatisfactory performance. A new simple SM algorithm is introduced to estimate the channel and the noise parameters simultaneously. The proposed algorithm efficiently exploits the redundant information of the noise to combat the noise. Theoretical results and simulations illustrate that the proposed algorithm has remarkable performance improvement over the NLMS and the traditional SM-NLMS algorithms. This proposed is successfully applied to a decision-directed algorithm for a QPSK communication scheme over an ISI channel with heavily colored noise environment.

A set-membership (SM) normalized least-mean-square (NLMS) (SMNLMS) algorithm is developed using SM theory in the class of optimal bounding ellipsoid (OBE) algorithms. This signed version of NLMS algorithm requires a priori knowledge of a bound for the error magnitude, which is unknown in most applications. A very simple algorithm is proposed for the case in which the unknown magnitude of the measurement noise is slowly time-varying. The proposed algorithm is able to extract the noise magnitude information and exploit this magnitude to enhance or accelerate the learning process without risk of overbounding or performance loss due to underbounding. The performance of the proposed algorithm is compared with that of SMNLMS using some simulation examples.