Abstract-The purpose of this paper is to analyze the properties of indoor power line communications channels when they are used for broadband transmission. It will be shown that these channels exhibit a short-term variation, due to the fact that high-frequency parameters of electrical devices depend on the instantaneous amplitude of mains voltage. This phenomenon leads to a channel model proposal based on a linear periodically time-varying system and cyclostationary random noise. A measurement system, designed to capture these time variations in real power networks, and some of the most significant results obtained with it, are presented. In addition, a statistical analysis of the measurements performed in several indoor power line scenarios is included, so that the relevance of time variations in actual channels can be evaluated.Index Terms-Broadband communication, cyclostationary noise, frequency response, home appliances measurement, linear periodically time-varying (LPTV) systems, power line communication (PLC), time-varying channels.

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We review in this paper several classical equalizers for data transmission and show that they are especial cases of a general time delay neural net, TDNN. The main point of this paper is t o show that the solution to the deconvolution problem for many transmission channel types, including linear and non-linear distortions, can be solved by mean of TDNN. Alternativelly TDNN can be seen as a generalization o f currently used equalizers and as tools for discovering new ones. _-INTRODUCTIONIntersymbol interference, ISI. i n h i g h speed data communication is one of the main factors which limitate the data throughput. the other one is the noise Usually, the receivers deal with the first impairment by mean of adaptive filters which cancel IS1 trying at the same time to maintain the noise at enough low level) These filters can operate at symbol rate, the T equalizers, in both ronfigurations teed forward or feed-back, or f r a c t i o d l y spaced equalize*\ operating at a fraction of the symbol 'ate Alternativelly. the impulse response of the channel model is known, it is alw possible to use the Viterbi's receiver which do n o t invert the channel neither cancel intersymbol interferences This algorithm basically search, in an optimum way, the sequence of symbols which generated the received signal closest to the received one 191.All of these receivers are based on the important fact that the channel behaviour is linear. When non-linear effects are present and consequently non-linear intersymbol interference, different systems have t o be used, for instance those based on Volterra seriesJ11, [21 In this paper we are going t o study neural nets [31. [41, based equalizers Inputs t o these nets are signals and i t s delayed samples, we call to this nets, following [lo], time delay neural nets, TDNN Theses equalizers WIII be used for both linear and non-linear channels Let a(n) be the sequence of transmited symbols, a(n) in the unidimensional case are the set o f the 2M symbols:{ f 1, f 2, f 3, ? M) In this paper we are going to consider only the case of M = 1 From the receiver end the channel is characterized, aftef sampling at baud rate, as a combination of linear and non-linear filters A n example of channel model t o be considered is that one characterized by two linear filters with a non-linear filter without memory in betweek Special cases will include only linea filters or a linear filter and the non-linear one. See Figure 1 This work was supported by the PLANICYT under the Project "Tratamiento Avanzado de la Informaci6n". General channel model I l a(") = f ? 1, ' 2 , . ' M } a(n) AR TDNN Figure 1. Problem definition In the proposed equalizer the signal x(n) and its time delayed samples are processed by a neural net. Then, the input t o this net i s t h e set of samples x(n-L). x ( n -L + l ) , . . . x(n),x(n + 1).x(n + L l when the symbol n has to be estimated L I S selected in accordance wmth the channel memory Dete,.+ed symbols can be used as addnllonal inputs tr the net We are going to consider several class~rdl ...

The use of digital signal processors (DSP) to equalize coherent optical communication systems based on spatial division multiplexing (SDM) techniques is widespread in current optical receivers. However, most of DSP implementation approaches found in the literature assume a negligible mode-dependent loss (MDL). This paper is focused on the linear multiple-input multiple-output (MIMO) receiver designed to optimize the minimum mean square error (MMSE) for a coherent SDM optical communication system, without previous assumptions on receiver oversampling or analog front-end realizations. The influence of the roll-off factor of a generic pulse-amplitude modulation (PAM) transmitter on system performance is studied as well. As a main result of the proposed approach, the ability of a simple match filter (MF) based MIMO receiver to completely eliminate inter-symbol interference (ISI) and crosstalk for SDM systems under the assumption of negligible MDL is demonstrated. The performance of the linear MIMO fractionally-spaced equalizer (FSE) receiver for an SDM system with a MDL-impaired channel is then evaluated by numerical simulations using novel system performance indicators, in the form of signal to noise and distortion ratio (SNDR) loss, with respect to the case without MDL. System performance improvements by increasing the transmitter roll-off factor are also quantified.

SUMMARYIn this paper, the topic of timing error estimation for baseband discrete multitone modulation is addressed in the context of high-speed digital subscriber line applications. To the authors' best knowledge, this problem is sparsely and not in depth treated in the literature. In this study the modified Cramer-Rao lower bound is derived, two conventional estimators are considered and a new one is proposed. Behavior of these estimators is evaluated in terms of bias, variance and computational complexity in a wide variety of scenarios, concluding that the proposed estimator appears to be superior in all instances.