Time-Domain MIMO Precoding for FEXT Cancellation in DSL Systems

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1 Time-Domain MIMO Precoding for FEXT Cancellation in DSL Systems Fabian A. Mruck, Clemens Stierstorfer, Johannes B. Huber Lehrstuhl für Informationsübertragung Friedrich-Alexander-Universität Erlangen-Nürnberg Cauerstraße 7/LIT, Erlangen Roman Tzschoppe Broadband United GmbH Pretzfelder Straße 21, Ebermannstadt Abstract We study the application of multiuser MIMO precoding for the cancellation of far-end crosstalk (FEXT) in DSL systems. We present a novel approach where the FEXT is canceled in the time-domain which offers some significant advantages over the common frequency-domain cancellation techniques. The time-domain adaptive filters used to compensate for the FEXT on the the time-domain transmit signal are obtained by an SNR-based system identification. We analyze the influence of several parameters on the identification of the FEXT transfer functions. Finally, we show that the proposed method with timedomain FEXT cancellation improves the signal-to-noise ratios of the individual subscribers and thus increases their data rates compared to uncompensated transmission. I. INTRODUCTION Digital subscriber lines (DSL) is one of the most common techniques to provide end users with high data rate connections. The existing copper telephone cables are used to connect the subscribers with the central office and with the usually fiber-based backbone network. In a DSL system every subscriber is connected to the central office by a twisted pair, i.e., by two copper wires in the cable. The geometry of these copper wires is yet not perfect, which causes significant crosstalk between the signals of different subscribers. This crosstalk can be divided into near-end crosstalk (NEXT) and far-end crosstalk (FEXT). NEXT is present if the signals of different users interfere at the same end of the cable bundle and upstream and downstream operate in the same frequency band. FEXT is the interference from one user to another on different ends of the cable bundle and can always be observed. Usually, NEXT dominates over FEXT. The signal impairments due to NEXT and FEXT limit the achievable data rates of DSL systems. Introducing interference cancellation in DSL systems which compensates for NEXT or FEXT can significantly improve the signal quality of the subscribers. In our contribution, we focus on FEXT cancellation (for NEXT cancellation see e.g., [1]) as in the most popular DSL standards, i.e., [2], [3], upstream and downstream do not operate in the same frequency band. This work was supported by the Bundesministerium für Wirtschaft und Technologie (BMWi) within the ZIM project MIMO+ under grant KF ED2. The DSL system affected by FEXT is modeled by a multiuser-multiple input multiple output (MU-MIMO) system. We consider the transmission from the central office to the individual subscribers, i.e., a downstream scenario. The cancellation of the FEXT requires a joint processing of the users signals which in our scenario can only be located in the central office. Thus, we apply MIMO precoding to cancel the FEXT. Current state-of-the-art in FEXT cancellation is the entirely frequency-domain based method known as vectoring [4]: the FEXT is first identified in the frequency domain, as is done the actual FEXT cancellation. A major drawback of this frequency-domain technique is, that it is limited to the signals of subscribers connected to a single digital subscriber line access multiplexer (DSLAM) in the central office, cf. Section III. However, in a deregulated telecommunication market several DSLAMs from different network operators may be connected to a single cable bundle preventing the reasonable use of vectoring [5]. In our contribution, we present a novel method for the cancellation of FEXT based in the time domain which can combine the signals of several DSLAMs and is also able to jointly process the signals of different DSL standards, i.e., [2] and [3]. Another advantage of the presented approach is, that the existing infrastructure can be retained and is seamlessly enhanced by an additional FEXT cancellation unit. II. SYSTEM MODEL In Fig. 1 a block diagram of the MU-MIMO system model is depicted. In the central office two 1 DSLAMs generate the discrete multitone (DMT) transmit signals of then subscribers whose twisted pairs are, at least for a certain distance, bundled in a single cable. Between the DSLAMs and the cable, we place the time-domain FEXT canceler, consisting of several adaptive filters, to remove the far-end crosstalk. This FEXT canceler is also connected to a FEXT identification unit which provides the required filter coefficients. After the FEXT canceler, the compensated signal is transmitted over the wire channel to the customer premises equipments (CPE). There, the individual DMT signals are 1 An extension to scenarios with more than two DSLAMs is straightforward.

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4 1) Initialization: The FEXT canceler is preset with arbitrary filter coefficients, in practice coefficients from previous identifications may be still available or the filter coefficients are just set to zero. 2) Compute Perturbation and Perturbed Filters: The computation of the perturbation added to the existing filter coefficients is based on the (frequency-dependent) SNRs γ i (f) which are estimated by the CPEs, queried by the DSLAMs, and forwarded to the FEXT identification unit via the management interface of the DSLAMs. 3 The SNR γ i (f) is given by γ i (f) = P i(f) Z i (f), (5) where P i (f) denotes the (frequency-dependent) transmit power of the ith user and Z i (f) is the respective noise (comprising thermal noise and interference). First, (5) is solved for the noise term Z i (f) = P i(f) γ i (f). (6) Using this noise term the perturbation for the filter g i,j [k] resp. for G i,j (f) is calculated as i,j (f) = λ Z i(f) P j (f), (7) i.e., the noise term of the disturbed user with indexiis divided by the transmit power P j (f) of the disturbing user with index j. λ is a positive scaling factor which can be used to influence the convergence of the estimation procedure (see Section V for actual values of λ and its influence on the results of the identification). The i,j (f) derived in (7) are then used to compute perturbed versions of the filters of the FEXT canceler. The frequency-domain representation of these filters reads G (p,1) i,j (f) = G i,j (f)+ i,j (f)exp( jφ), (8) and a second version with an orthogonal perturbation is also generated ( ( G (p,2) i,j (f) = G i,j (f)+ i,j (f)exp j φ+ π )). (9) 2 Here, the phase term φ is randomly selected from the interval [0, 2π) in every iteration of the identification process. Again, (4) is used to obtain the time-domain filter coefficients [k]} and {gp,2 i,j [k]}. 3) Measure SNRs and Update Filters: Now the filters g p,1/2 i,j [k] are used one after the other in the FEXT canceler and for each realization of the canceler the SNRs are estimated by the CPEs. The latter are then employed to compute the {g p,1 i,j noise terms Z p,1 i (f) and Z p,2 i (f) which are required for the calculation of the actual update terms added to the G i,j (f), 3 Note, the SNRs employed in this context actually are signal-to-noise and interference ratios (SINR). In order to comply with the standard notation used for DSL systems, the term SNR is used instead. i.e., the estimated difference between the ELFEXT transfer function and the current cancellation filter G i,j (f) ( ˆθ i,j (f) = Z p,1 i (f) Z i (f) ( i,j (f)) 2 P i (f) exp(jφ) + 2 i,j (f)p i (f) ) +j Zp,2 i (f) Z i (f) ( i,j (f)) 2 P i (f) 2 i,j (f)p i (f) (10) Again, these results are transferred into time-domain using (4) and added to the filter coefficients of the g i,j [k]. With these updated filters a new iteration can start. The computation of the updated filters can be performed in parallel for all N 1 filters g i,j [k] with j {1,...,N}\i. B. Adaptations for Time-Domain FEXT Cancellation The extent of the perturbation affects the SNR of the analyzed link which is still used for data transmission during the identification process. Thus, the perturbation has to be carefully designed to ensure both, a reasonable time of convergence and an acceptable SNR for the data transmission. We use a two-step identification procedure which after the initialization process switches in a mode with a much smaller perturbation [13], i.e., the factor λ in (7) is adjusted. If a new subscriber connects to the central office, the newly introduced interference again has to be identified with the initial perturbation. C. Optimizing the FEXT Identification The success of FEXT identification is affected by various parameters. First of all, the magnitude of the perturbation which can be influenced by the scaling factor λ is an interesting parameter in this context. Further parameters which can be varied to optimize the identification procedure are the delays in the direct paths and the number of DMT symbols used for the identification in particular for the estimation of an SNR value. The quantization of the SNR feedback also has an important impact on the identification of the ELFEXT transfer function. V. SIMULATIONS AND NUMERICAL RESULTS A. Simulation Settings The parameters used for the simulations and the generation of the numerical results are summarized in Tab. I. All of the results were derived for an exemplary DSL system with N = 10 users transmitting over a a cable bundle containing 10 twisted wire pairs. The channel model used for the simulations, i.e., the realization of the channel matrix H c, is based on extensive measurements performed on a real exemplary cable with a length of 700 m. In our simulations the SNR feedback γ i (f) is, unless otherwise stated, not quantized, i.e., the exact values are used for the derivation of the perturbation and the updated filters. The delay of τ 0 = 2T in the direct paths of the transmission assumed in most of the simulations allows for the compensation of the non-causal parts of the identified ELFEXT impulse responses. A variation of this delay is also studied.

5 Duration of a transmit symbol in DSL system TABLE I SIMULATION PARAMETERS T = ns Sampling frequency of A/D conversion (FSF) 1 2T = 8.832MHz Symbol rate in FSF sub-filters g i,j,µ [k] 1 T = 4.416MSym/s Length of FSF sub-filter g i,j,0 [k] L 0 = 48 Length of FSF sub-filter g i,j,1 [k] L 1 = 7 Processing delay τ 0 = 2T or τ 0 = 452.9ns Number of DMT symbols per SNR measurement 256 Perturbation scaling factor λ = 2 Unless otherwise stated in the description of the particular results. Negative processing delays in the fractionally-spaced filters can be taken into account by respective positive delays in the direct paths. B. Numerical Results Figure 3 shows the average signal-to-noise ratio (in db, 10log 10 (SNR)) per sub-carrier for each user over the number of iterations of the FEXT identification. The given results clearly show the SNR improvements due to the time-domain FEXT canceler. Note, the SNRs shown in Fig. 3 result exclusively from the application of the updated filters in the FEXT canceler. Signal-to-noise ratios achieved during a perturbation phase are not given. The plot in Fig. 4 in contrast gives the complete time curve of the SNRs over the number of SNR measurements for two exemplary user taking into account all phases of the FEXT identification. In the graphs the temporarily decreased SNRs due to the perturbations are clearly visible. After the first 30 measurements all of the filters have been updated once. Further iterations and updates of the filters lead only to relatively small improvements compared to the gains achieved in the first few steps. In Fig. 5 the resulting SNR after each iteration is plotted over the number of iterations and the frequency in Hertz. It shows a fast increase of the SNR for the first iterations over all frequencies. Later the increase slows down. In Fig. 6 the resulting SNRs after the identification process are plotted over the frequency for all ten users. Compared to the uncompensated transmission significant gains can be observed, but there is still a gap to the single user case, i.e., transmission without any interference. Frequency-domain based FEXT compensation techniques are known to be able to almost achieve this limit [13]. What can be also seen in this plot is that after the time-domain FEXT compensation there are still differences between the SNRs of the individual users. This is due to the the band limitation of the sampling and the limited filter lengths in the canceler. The influence of the processing delay on the results of the FEXT identification are shown in Fig. 7. It can be seen, that the SNRs increase with decreasing processing delays. The reason for this behavior is that more and more parts of the FEXT are compensated for if the compensation window is extended to the non-causal parts of the ELFEXT impulse response. In Fig. 8 the effect of the number of DMT symbols which are used for an SNR measurement is shown. The least number of symbols used for a measurement was 16 which with a number of 32 symbols shows inferior results compared to the SNR measurements based on 64 or even more DMT symbols. The impact of the perturbation scaling factor λ is presented in Fig. 9. A very large scaling factor causes errors because the magnitudes of the perturbations and the magnitudes of the FEXT have even different orders. Additionally, the data transmission is severely disturb during the identification process. If the perturbation size is too small, the changes in the SNR do not differ significantly and the convergence of the FEXT identification slows down or even ends at sub-optimal values. A quantization of the SNR feedback, e.g., only integer values of decibels are taken into account, can also have a significant impact on the FEXT identification. In Fig. 10 the average SNR in db (10log 10 (SNR)) per sub-carrier after the identification process is shown for different quantizations of the SNR feedback. Using just integer does not lead to significant losses compared to SNR values given as real number (double representation in Matlab); a quantization to multiples of 3dB clearly impairs the performance. Figure 11 shows the impact of the convergence of FEXT compensation on the SNR of the individual users over the iterations with a perturbation scaling factor of λ = After ten iterations every user has a significantly increased SNR. After about 30 iterations, which means that every filter coefficient was updated three times, the identification has almost converged to its optimum and only minor changes can be achieved in the following. VI. CONCLUSION In this paper, we have proposed a novel approach for a timedomain FEXT canceler in DSL systems. The new method allows to compensate for the FEXT on a cable bundle even if it is fed by more than a single DSLAM. Another benefit is that the existing equipment can still be used and appended by a separate cancellation unit.

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