ABSTRACT In this paper, we investigate optimal receiver filter design with respect to shot noise in both non‐coherent and coherent fibre optic communication systems. We derive analytical expressions for the moment‐generating function of filter output and the signal‐to‐shot noise power ratio (SSNR) for intensity modulation direct detection (IM/DD) and phase diversity homodyne (PDH) optical fibre communication systems, with arbitrary waveform and receiver filter considerations in the presence of shot noise. Closed‐form formulas are provided for the receiver filter structures that maximise the SSNR. The performance of SSNR is evaluated using return‐to‐zero (RZ) coding with rectangular and Gaussian pulse shapes across various receiver filter structures, including the ideal integrator, the RC model, and the matched filter. Our results indicate that the integrator, or its variations, is either optimal or near‐optimal for diverse IM/DD systems. However, matched filtering to the received pulse power becomes superior when dark current or d.c. bias power is prominent. For coherent PDH systems, matched filtering to the complex received pulse amplitude approaches near‐optimal performance provided the local oscillator (LO) power significantly exceeds the received signal power. When the LO power is much greater than the signal power, such systems can achieve double the SSNR of IM/DD systems, equivalent to twice the number of converted photoelectrons per symbol, thus nearing the quantum‐limit performance considering the photodetector quantum efficiency.

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.

Dirty paper coding (DPC) is a non‐linear transmit scheme in presence of known interference, which is capacity achieving. Unfortunately, the implementation complexity of DPC is usually prohibitive. A sub‐optimal yet practical method to implement DPC in inter‐symbol interference channels is Tomlinson–Harashima precoding (THP). However, THP is not applicable to the constant‐envelope phase shift keying (PSK) modulation. In this study, a modified Tomlinson–Harashima precoder is proposed to implement DPC for PSK modulation. The technique involves design of decision region at the receiver side and an algorithm to select the phase of transmitted symbol optimally at the transmitter side accordingly. Various patterns, namely, striped, checked, hexagonal, and radial are proposed and examined. Simulation results show that by using the proposed equaliser, the error floor is eliminated and significantly smaller bit‐error rate is achieved. Numerical and simulation results show that the striped pattern outperforms other decision region designs. Moreover, its implementation and computational complexities is almost the same as the Tomlinson–Harashima precoder.

The authors study the power spectrum density (PSD) estimation of wideband wide‐sense stationary (WSS) signals with sub‐Nyquist sampling rate. Owing to the large bandwidth, Nyquist rate sampling of such signals needs very high rate analogue‐to‐digital converters. It is important to note that PSD estimation does not necessarily require reconstruction of the original signal. Indeed, the power spectrum can be directly obtained from sub‐Nyquist samples. In this study, a new method for reconstructing the power spectrum in the frequency domain for WSS signals is presented. The main idea is to divide the whole spectrum into N equal‐length segments and calculate the average PSD in each segment using a frequency‐domain representation of sub‐Nyquist samples. In addition, the capability of the proposed method, as a detector of spectrum holes, is studied using receiver operating characteristic (ROC) curves. Then, the analysis of false alarm probability is provided. Simulation results for the additive white Gaussian noise channel and the slowly fading frequency selective channel show that the proposed method considerably outperforms available techniques.

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.

There are two types of crosstalk in digital subscriber line (DSL) systems, namely near-end crosstalk (NEXT) and far-end crosstalk (FEXT). NEXT is usually much stronger than FEXT. Therefore, high-speed DSL systems transmit in preplanned disjoint downstream (DS) and upstream (US) frequency bands to avoid NEXT. Although easy for implementation, such a fixed bandplan can lead to inefficient bandwidth usage, depending on the DS and US bit rate requirements and the loop topology, particularly in so-called vectored DSL systems, which include signal coordination for FEXT cancellation. In dynamic bandplanning (DBP), each frequency band is allocated to either DS, US, or to both directions depending on the aforementioned parameters. In this paper, we consider optimal DBP for vectored DSL with linear as well as with nonlinear transmitter/receiver structures. We propose an optimal DBP algorithm for systems with disjoint DS and US bands. For systems with overlapping bands, the problem of finding the optimal transmitter/receiver filters is nonconvex and we propose two iterative algorithms based on recent optimum spectrum balancing schemes from the literature. We also study the effect of echo and US NEXT cancellation on the system performance. Finally, simulation results are provided to demonstrate that our algorithms can indeed significantly increase the achievable bit rates.

In this letter, we derive formulas for optimal discrete-time pulse shaping for communications in multiband channels. Furthermore, we propose a technique for extending a short signal segment for the purpose of power spectral estimation using the available information about the signal stopbands. The later technique can be also used for minimizing the energy leakage into stopbands of a signal, e.g., as in windowing for orthogonal frequency division modulation (OFDM). Simulation results show that when the pulse duration is long enough, the stopband energy can be practically reduced to zero using the proposed technique. The proposed power spectral estimation technique can improve the resolution and reduce the energy leakage from signal passbands into adjacent stopbands. Moreover, it can reduce the out-of-band power leakage significantly when used for windowing in OFDM.

Different precoder and equalizer structures have been proposed in literature for vectored digital subscriber lines (DSLs). In this paper, we assess the relative merit of advanced complex precoders and equalizers in practical DSL scenarios. Using extensive computer simulations, the achievable bit rates are investigated in the presence of alien crosstalkers, assuming a beta distribution model for crosstalk couplings. Vectoring in conventional as well as phantom mode (PM) VDSL2 transmission is considered. Vectoring techniques at the access-node (AN) are studied such as the zero-forcing equalizer (ZFE), ZF generalized decision feedback equalizer (ZF-GDFE), linear minimum mean squared error (MMSE), and MMSE-GDFE for upstream (US) scenarios and zero-forcing precoder (ZFP) for downstream (DS) scenarios. Vectoring is also considered at the customer premises (CP) in PM transmission. The results show that when there are no alien crosstalkers, the low-complexity ZFE allows reaching crosstalk-free rates in US direction. However using an MMSE-GDFE and if the noise spatial covariance information is assumed static, considerably higher bit rates can be achieved for long loops in the presence of alien crosstalkers. This rate increase comes at the expense of increased delay. In DS direction, the ZFP can achieve crosstalk-free rates in the absence of alien crosstalkers. The results also show that the use of vectoring techniques at the CP in PM transmission does not increase the achievable bit rates in US or DS direction when vectoring is already employed at the AN.

In this paper, we consider optimal dynamic spectrum management (DSM) for a downstream (DS) DSL scenario in which users are divided into a few separate groups, where vector encoding based signal coordination can be applied in each group and spectrum coordination is possible for all users. This can be seen as a mixed interference/broadcast channel (IF/BC) scenario. We investigate several candidates for vector encoding the signals inside the groups, including the linear zero-forcing (ZF) pre-compensator, ZF Tomlinson-Harashima pre-coder (THP), optimal linear pre-compensator (OLP), and THP with optimal transmit filters. The calculation of the optimal transmit filters (for both the linear pre-compensator and THP) is a non-convex problem. To resolve this problem, we develop a generalized duality between the IF/BC and IF/multiple-access channel (MAC). In order to achieve the highest data rates, optimal spectrum balancing (OSB) is applied to all users on top of the vector encoding inside the groups. Simulation results show that the grouped THP with optimal transmit filters achieves considerably higher bit rates than the other schemes. The resulting algorithm is referred to as the IF/BC-OSB algorithm, and encompasses the OSB (i.e., IF-OSB) and the earlier developed BC-OSB algorithm as special cases.

In this paper, we investigate joint level 2 and 3 dynamic spectrum management (joint DSM 2/3) for downstream (DS) DSL. We consider a DS scenario in which users are divided into a few separate groups, where vector encoding based signal coordination can be applied in each group and spectrum coordination is possible for all users. This can be seen as a mixed interference/broadcast channel (IF/BC) scenario. In order to obtain the optimal transmitter structure, we develop a generalized duality between the vector broadcast and multiple-access channel (MAC) for scenarios in which partial signal coordination is available among users. This theory together with optimal spectrum balancing (OSB) is exploited to calculate the jointly optimal filters and transmit powers for non-linear vector dirty paper coding structures (in the form of Tomlinson-Harashima precoder (THP)) in the groups. The proposed scheme is compared to several other joint DSM 2/3 algorithms for DS DSL. Simulation results show that the proposed scheme (referred to as the IF/BC-OSB algorithm) achieves considerably higher bit rates than the other schemes. IF/BC-OSB encompasses the earlier developed BC-OSB algorithm as a special case. A simplified version of IF/BC-OSB avoiding exhaustive search with near-optimal performance is also proposed.

Lagrange dual optimization technique (LDO) is a powerful tool for solving constrained optimization problems in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing systems (OFDM) and is generally considered to be optimal in the literature. LDO relaxes a constrained problem into an unconstrained dual problem using Lagrange multipliers. To solve the dual problem, the optimal value of the Lagrange multipliers should be found. The Lagrange multipliers are usually determined in an iterative process and reducing the number of iterations is of crucial importance to obtain systems with manageable computational complexity. In this paper, we show that for the LDO to be optimal in optimal spectrum balancing of DSL, the joint rate and power region (JRPR) should be strictly convex. Moreover, we propose a new LDO based algorithm with two basic advantages. Firstly, the computational complexity of the algorithm is logarithmic in the desired precision. Secondly, the algorithm can be used to find the optimal solution even for the cases with non-strictly convex JRPR. Our results can potentially be generalized to a wider range of optimization problems in the context of MIMO-OFDM and other complex separable systems.

Orthogonal spreading codes play an essential role in code-division multiple-access (CDMA) systems by eliminating multiple-access interference (MAI). In this paper, a novel orthogonal spreading code has been proposed for spectrally-encoded (SE) CDMA, a.k.a., spread-time (ST) CDMA with arbitrary pulse shape. It has been shown that it is possible to retain the orthogonality of the code in the presence of tail truncation by time windowing and in a general multipath fading channel in which users experience different frequency selectivity just by modifying the user codewords. Simulation results show that the proposed codes can achieve single user performance when the code length is twice the number of users.

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.

Spectrally encoded (SE) CDMA systems, a. k. a. spread time (ST) CDMA systems, have several advantages over their frequency-time dual, direct-sequence CDMA such as the abilities to shape the transmitted spectrum and to avoid narrow-band interference. However, no orthogonal spreading code has been proposed to efficiently avoid multiple-access interference (MAI). In this paper, we propose a novel orthogonal spreading code for SE-CDMA. We study undesirable channel conditions under which the orthogonality property of the code could be lost. We propose a chip normalizing scheme (CNS) to restore the orthogonality property of the code in these cases. Our simulation results show that the encoded system can achieve the performance of interference-free channels. Furthermore, using our CNS the users can achieve a higher bit rate at the same bit error rate as the unnormalized case.

Line selection (LS), tone selection (TS), and joint tone-line selection (JTLS) partial crosstalk cancellers have been proposed to reduce the online computational complexity of far-end crosstalk (FEXT) cancellers in DMT DSL. However, in contrast to perfect crosstalk cancellers, partial crosstalk cancellers should also provide a low pre-processing complexity when crosstalk profile changes rapidly in time. In this paper, we propose two novel fast classes of JTLS algorithms, namely, a family of sub-sort JTLS algorithms and the Lagrange JTLS. The computational complexity of our algorithms is much lower than that of the optimal greedy algorithm. Simulation results show that the performances of the proposed sub-sort algorithms are very close to the optimal greedy algorithm. More importantly, our Lagrange JTLS algorithm is optimal for the DSL channels we consider.

Loop loss and crosstalk are the main impairments in DSL. Recently, novel crosstalk rejection and reduction techniques have been proposed to achieve the maximum capacity of the DSL channel. The performance of these techniques depends strongly on the degree of coordination among the users. In this paper, we consider maximizing the throughput of DSL when the users are coordinated at different levels. Moreover, we propose a novel centralized power allocation algorithm by generalizing a recently proposed iterative spectrum balancing (ISB) algorithm. Our generalized ISB (GISB) algorithm provides a superior performance to the ISB with polynomial complexity in the number of users. This complexity is much lower than that of the optimal spectral balancing (OSB) algorithm. Moreover, it can be selected adaptively based on the available processing power

A class of generalized optical orthogonal codes (OOCs), namely, frame time-hopping (FTH) patterns with an extremely large cardinality, are studied for implementing multirate and multiservice (MR/MS) optical CDMA (OCDMA) networks. Conventional MR/MS methods, namely variable spreading rate and parallel mapping, are considered. Using FTH patterns, the problem of low OOC code cardinality in conventional MR/MS schemes is removed. Moreover, several new multicode methods, using subcode concatenation scheme, are proposed for MR/MS OCDMA. The proposed multicode schemes present flexibility for supporting MR/MS applications such as lower implementation complexity and cost, less need for service synchronization, and finally lower link power budget. Multiple-access performances of the systems are evaluated using saddle-point approximation methods considering photodetector shot-noise, dark current, and circuit thermal noise. The results show that the conventional parallel mapping outperforms the other schemes in high received powers, and the proposed multicode method, using Walsh subcode along with difference modulation, presents the best performance in low received powers for the cases considered.

A new spreading technique for intensity modulation direct detection fiber-optic code-division multiple-access (FO-CDMA) communication systems is proposed. This new spreading technique is based on generalized optical orthogonal codes (OOC) with large cardinality and minimal degradation in performance when compared with a more optimum system, namely, an optical CDMA system using OOC with autocorrelation and cross-correlation value bounded by one, i.e., OOC (/spl lambda/=1). To obtain the performance of such systems, we use a communication scheme, namely, frame time-hopping (FTH)-CDMA with random coding. Systems with generalized OOC patterns and random time-hopping coding are close in structure and performance. Furthermore, the performance of such systems is near the performance of optical CDMA with optimum but low cardinality OOC (/spl lambda/=1), which further renders the practicality of the proposed technique with very large cardinality. Two new receiver structures for FO-CDMA, namely, chip-level detector with optimum comparator threshold and correlation receiver with an electrical hard limiter, are also proposed. The performance analysis for a binary pulse position FTH-FO-CDMA network is considered for the correlation receiver, chip-level detector, correlation receiver with an optical hard limiter, optimum receiver, and the two newly proposed receiver structures. The results also show that a chip-level detector with optimum comparator threshold is superior to a chip-level detector for received low signal powers, and predict that the performance of the correlation receiver with an electrical hard limiter is superior to all other considered receiver structures, e.g., requiring one third of transmission power to achieve a desired bit error rate when compared with other receiver structures.

An ultra-wide bandwidth time-hopping spread-spectrum code division multiple-access system employing a binary PPM signaling has been introduced by Scholtz (1993), and its performance was obtained based on a Gaussian distribution assumption for the multiple-access interference. In this paper, we begin first by proposing to use a practical low-rate error correcting code in the system without any further required bandwidth expansion. We then present a more precise performance analysis of the system for both coded and uncoded schemes. Our analysis shows that the Gaussian assumption is not accurate for predicting bit error rates at high data transmission rates for the uncoded scheme. Furthermore, it indicates that the proposed coded scheme outperforms the uncoded scheme significantly, or more importantly, at a given bit error rate, the coding scheme increases the number of users by a factor which is logarithmic in the number of pulses used in time-hopping spread-spectrum systems.

In a previous paper by R.A. Scholtz (see Proc. IEEE MILCOM '93, p.447-50, Oct. 1993), an ultrawide bandwidth time-hopping spread-spectrum code division multiple access system employing a binary PPM signaling was introduced, and its performance was obtained based on a Gaussian distribution assumption for the multiple access interference. A coded scheme of this system was proposed by the authors (see Proc. PIMRC '00, vol.2, p.1555-8, Sept. 2000), which showed much better performance in comparison to the uncoded scheme under the above Gaussian assumption. In this paper, we present a more precise performance analysis of the system for both coded and uncoded schemes. Our analysis shows that the Gaussian assumption is not accurate for predicting bit error rates at high data transmission rates.

We propose to use a practical low rate error-correcting code in a time-hopping spread spectrum multiple access system employing a binary PPM signaling. To this end, superorthogonal codes, which are near optimal and have relatively low implementation complexity, are considered. The performance analysis shows that the proposed coded scheme outperforms the uncoded scheme significantly, or more importantly, at a given bit error rate the proposed scheme increases the number of users by a factor which is logarithmic in the number of pulses used in a time-hopping spread spectrum system.