On VDSL Performance and Hardware Implications for Single Carrier Modulation Transceivers

Transcription

1 On VDSL Performance and ardware Implications for Single Carrier Modulation Transceivers S. AAR, R.ZUKUNFT, T.MAGESACER Institute for Integrated Circuits - BRIDGELAB Munich University of Technology Arcisstr. 1 D-8090 München GERMANY Sven.aar@ei.tum.de Abstract: In this paper the performance of evolving Very high rate Digital Subscriber Line (VDSL) is evaluated based on a Single Carrier Modulation (SCM) transceiver model meeting needs for flexible band allocation and low implementation complexity. An analytical approach to performance evaluation of finite-length Minimum Mean Square Error (MMSE) equalizers is applied which takes into account equalizer s number of taps, oversampling factor, and sampling phase. By this means it is shown that for typical VDSL loops symbol-spaced equalizers will perform almost as well as fractionally-spaced ones, when neglecting the influence of the Analog Front End (AFE). Furthermore, performance results for two typical VDSL test loops are presented. Key-Words: Single Carrier Modulation, VDSL, Finite-Length MMSE DFE, Equalization, Digital Interpolation, Asynchronous Sampling 1 Introduction In recent years copper twisted-pair access has proven to be a suitable technique to solve the last mile problem by exploiting existing Plain Old Telephone Service (POTS) infrastructure. As xdsl evolution steadily proceeds towards higher rates and enhanced flexibility of services, a new xdsl system will reach market entry in the near future: Very high rate Digital Subscriber Line (VDSL). In the beginning, VDSL transceivers will replace older lower-performant siblings of the xdsl family. Later on, a new hybrid infrastructure of fiber and copper - still to be installed - is supposed to allow an even higher-speed access. This will be achieved by bringing fiber from Central Office (CO) to Cabinet, and thus lowering copper channel s line-length dependent channel attenuation. VDSL will be used by business customers, interested in symmetrical services, and as well by private users, favoring asymmetrical services. As a result a VDSL transceiver, suitable for mass market, has to meet a large variety of needs besides low implementation costs. igh flexibility in reaches, rates and services also sets constraints on transceiver s architecture, as analyzed in this paper later on. Question arises what reaches and rates VDSL will be able to offer, dependent on transceiver s implementation complexity. At the present point of time two different modulation schemes have been agreed on by standardization committees ANSI and ETSI: QAM based Single Carrier Modulation and Discrete Multi-Tone modulation (DMT) [1][]. Now, that also frequency band allocation and Power Spectral Density (PSD) masks have been fixed by the standardization process, it makes sense to evaluate likely VDSL system capabilities as a function of the transceiver s structure. In this paper we describe an analytical approach to evaluate finite-length MMSE equalizer structures and their performance for VDSL application, taking into account the number of taps, oversampling factor, and sampling phase. The paper is organized as follows: In Section we present a VDSL transceiver model meeting needs for flexibility and low costs. On this base an analytical approach to performance evaluation by means of the Wiener equation is described in Section 3. Thereafter, in Section 4, hardware needs effects on VDSL performance are evaluated. Section 5 shows some performance results for typical VDSL test loops. Finally, Section 6 will draw some conclusions. VDSL System and Transceiver Model For our investigation, we consider a VDSL transceiver model as depicted in Fig. 1. Single Carrier Modulation on base of QAM is employed. The data

2 3.1 Channel Model To consider sampling phase s influence, the whole channel prior to the receiver s sampling structure will be modelled as m -times oversampled. So sampling phase step size equals T m, with symbol period T = 1 f T. A set of m transfer functions G i ( f ), 1 i m, describes the sampling structure s input, one for each discrete sampling phase. After sampling, the signal is matched-filtered by a root-raised-cosine Ny -filter W( f). Despite the common way of adding noise already at the receiver s input, noise is added after W( f) -filtering for easier mathematical treatment. The noise, which consists of AWGN, before being W( f) -filtered, and crosstalk, induced by other systems, is modelled sampling phase independent. Crosstalk is generated by averaging the outputs of m FIR filters, each representing one discrete sampling phase. Synchronously modelled crosstalk, as generated without this averaging, is known to cause lower performance degradation be- symbols x k are baseband-modulated by an oversampled root-raised-cosine Ny -filter, resulting in bandwidth ( 1 + r) f T, with roll-off r =0% and symbol rate f T, after modulation to carrier frequency f 0. Then samples are filtered by transmitter s AFE. The signal is distorted by the loop, and noise n k is added, mainly by other systems crosstalk. α k = πk f 0 f Transmitter (TX) S f x k cosα S k Ny IP Ny =: W( f) TX AFE Ny IP sinα k xdsl Loop cosα n k k IP Ny xˆ RX k Equalizer AFE IP Ny sinα f T w ft f k S Receiver (RX) Fig. 1 - SCM VDSL transceiver model The receiver s structure is of major interest for the following performance evaluation. The incoming signal is processed by the receiver s AFE comprising an analog filter for out-of-band-noise suppression. After demodulation and matched- Ny -filtering on high sampling rate f S, the signal is fed through an interpolation (IP) filter. Digital interpolation is applied to meet one of the central objectives for newer generation xdsl transceivers. This is flexibility in band allocation in order to handle a variety of frequency plans. Digital interpolation combined with asynchronous sampling allows, besides fully digital timing recovery, any arbitrary ratio f S f T. This lifts synchronous sampling s constraint of f S f T being an integer. Performance loss due to digital interpolation is known to be negligible even for linear interpolation based on a few number of samples [3][4]. Then, prior to symbol decision, equalization on rate w f T, as examined in further detail in Section 3, is performed. In the following we will restrict our focus to w = 1, implying symbol(t)-spaced equalization, and w =, meaning fractional(t/)-spaced equalization. Please note, that Fig. 1 only shows the system model for a single band of overall four. ETSI and ANSI have both standardized four frequency bands, alternating by downstream (DS) and upstream (US) direction, as shown in Fig.. ETSI has fixed two sets of bands, one set being identical to ANSI s frequency plan [1][] DS1 US1 DS US ETSI: Standard band plan (SP) Symbol rates f T j [Mz]; Assumption: no guard bands ETSI: Reg.-spec. opt. plan (RP) / ANSI DS1 US1 DS US Corner frequencies [Mz] Fig. - VDSL frequency band allocation 3 Analytical Approach to Performance Evaluation VDSL performance is limited by noise, predominantly caused by crosstalk of other systems, and channel distortion, compensated at receiver side by an adaptive equalizer. For pure performance investigation in terms of reach and rate, a widely applied method is to determine the signal-to-noise ratio (SNR) after equalization at the slicer. A constellation size dependent minimum SNR must be achieved to keep the bit error rate below a mandatory level (for xdsl: 10 7 ). Then, usually symbol-spaced equalization at optimum sampling phase is assumed for simple means. In this paper we also want to examine the influence of symbol-spaced vs. fractionally-spaced equalization on performance to determine hardware requirements. Thus our analytical approach must cope with both equalization schemes as a function of sampling phase.

3 cause of its cyclostationary character. Cyclostationary interference can be suppressed substantially by a DFE [5]. The whole communication system, from the transmitter s Ny -filter up to the equalizer s input, can be combined to ( f ) = G i ( f ) W( f), (1) i where index i again represents one of m discrete sampling phases. For further evaluation of equalizer s performance we will switch to a vector/matrix representation with data symbol vector x k, noise vector n k, and vector y k representing the equalizer input which is given by x k x k x y k = k 1 + n k = x k NF υ 1, () each =. (3) y' k ykt ( ) y T kt --- w y kt w T 1 w Eq. already introduces two parameters related to the equalizer s implementation: N F w is the number of feedforward equalizer taps, w is the oversampling factor within the equalizer (here: w = 1 for symbolspaced, w = for fractionally-spaced equalization). Matrix of dimension ( N F w) ( N F + υ) within Eq. is a polyphase subchannel representation of channel ( f ) and can be written as = i h 0 h 1 h υ h 0 h 1 h υ h 0 h 1 h υ......, each =. (4) Although we will omit index i for matrix, please note, that further search of the maximum achievable SNR by calculations has to be done for the set of all i ( f ). The channel s impulse response is truncated to υ symbol periods T for further calculations. The noise is represented by vector n k of length w : N F h k y' k y' k 1 y' k NF + 1 hkt ( ) h T kt --- w h kt w T 1 w n k = n' k n' k 1 n' k NF + 1, each =. (5) 3. Linear Equalization To compensate unknown channel distortion within y k, a linear equalizer (LE) on base of an N F w tap FIR filter, represented by the row vector c of length N F w, is employed, increasing system delay δ : (6) The equalizer s output error yields to =, (7) and the corresponding Mean Square Error (MSE) is σ MSE, LE n' k z k = c y k e k x k δ z k nkt ( ) n T kt --- w n kt w T 1 w (8) The optimum linear Wiener filter c = c opt, whose output is the best mean square approximation to the desired signal, can be determined by means of cross correlation vectors and autocorrelation matrices [6][7]: 1 1 = R yy = r xy R yy (9) (10) (11) where R nn represents the w N normalized noise autocorrelation matrix, thus being equal to identity matrix I for white noise. ε x is the average energy of symbol vector x k. Now Eq. 9 results in, (1) whereas the optimum position of the (sub)set of vectors h k within the first bracket of dimension 1 ( N F w) of Eq. 1 has to be determined by iterative search. Now, the desired Minimum Mean Square Error (MMSE) is given by = E e k = E x k δ c y k c opt r yx r xy r yx E{ x k δ y k } ( E{ x k δ x k }) = = = + E{ x k δ n k } = ε x 0 0 hν h0 0 0 R yy E{ y k y k } ( E{ x k x k }) = = + E{ n k n k } ε x w N 0 = R nn c opt 0 0 hυ h0 0 0 w N 1 0 = ε x h R nn

4 LE = ε x c opt r yx w N w N0 = h 1 δ h ε x h R nn 1 1 δ + 1 (13) where 1 δ + 1 describes an N F + υ element vector of 0 s and a single 1 in column δ + 1. Finally, SNR for unbiased linear equalization can be determined to: = (14) SNR MMSE LE, U ε x, LE Unbiasedness is important for higher than 4QAM constellation sizes [6]. 3.3 Decision Feedback Equalization To eliminate Intersymbol Interference (ISI), caused by channel distortion, more efficiently, we now widen our focus to Decision Feedback Equalization (DFE). In addition to the linear equalizer s symbol- or fractionally-spaced feedforward filter of Eq. 6, a symbol-spaced feedback filter is applied to remove ISI of previously decided-on symbols. Feeding back the decided symbols of the slicer s output actually causes nonlinearity. But with the assumption of all previous decisions having been correct, linear techniques of Section 3. can be used for analysis [6][7]. The MSE, introduced in Eq. 8, then results to σ MSE, DFE = E ẽ k = E x k δ c y k + b x k δ 1 (15) where b is a row vector of N B elements, representing the feedback FIR filter s coefficient set. x k δ 1 is the vector of previously decided-on data symbols in the feedback path. For mathematical convenience, feedforward and feedback coefficient sets are combined: (16) c = c b The DFE input vector can be written as ỹ k = y k x k δ 1. (17) Now cross correlation vectors and autocorrelation matrices, as already given for linear equalization by Eq. 10 and Eq. 11, can be rewritten for decision feedback equalization r ỹx = r yx 0, (18) w N R ỹ ỹ ε x ε x h R nn J δ = J δ, (19) where J δ is a ( N F + υ) N B matrix of 0 s and 1 s. It has the upper δ + 1 rows zeroed, and an identity matrix of dimension min( N B, N F + υ δ 1) with zeros to the right (if N F + υ δ 1< N B ), zeros below (if N F + υ δ 1> N B ), respectively no zeros to the right or below, exactly fitting in the bottom of J δ, if neither inequality holds. The optimum Wiener filter for decision feedback equalization can be determined by applying the tildemarked matrices and vectors of Eq. 16-Eq. 19 to Eq. 9. This will lead us to:. (0) With some algebra the optimum DFE coefficient set in MMSE sense turns out as:, and (1). () Because of the assumption that all decisions are correct, the feedback filter does not effect the MMSE: (3) Please note, that the MMSE is a function to be minimized over δ, e.g. by iterative search. Finally, the SNR for unbiased MMSE DFE is = (4) 4 Impact of ardware 4.1 Finite-Length Equalizer Since we are employing a finite-length DFE ( N F w feedforward and N B feedback taps), we are interested in minimum required DFE size ( N F w, N B ). The challenge is to find the balance between performance loss and implementation complexity. Evaluations based on the approach of Section 3 indicate, that negligible performance loss is guaranteed even for highly distorted channels with a DFE of size ( w =, = 0), as exemplarily shown in Fig. 3 for I N B w N c b ε x ε x h R nn J δ = ε x 1 δ 0 J δ I N B w N0 1 c' opt = 1 δ Jδ J δ ε x h R nn DFE b opt = c' opt J δ = ε x c opt r ỹx = ε x c' opt r yx w N 0 1 = ε x 1 1 δ Jδ J δ ε x h R nn 1 δ N F SNR MMSE DFE, U 30 N B ε x, DFE

5 VDSL6 5 VDSL FEXT Disturbers Band SP DS1 w=1 VDSL1 TP (350m) SP (DS1, US1) N F w = 30 N B = DS1, w= dB Degradation for Band DS1 (w=1) No Degradation for Band US1 19 US1, w= SNR [db] SNR [db] DS1, w= US1, w= No. of Feedforward Taps N F w 10 0 the VDSL6 channel. This test loop of approximately 1000m fixed length consists of 7 segments of underground and arial cable, differing in length and diameter, including a bridged tap. 4. T- vs. T/-Equalization The choice of symbol- vs. fractionally-spaced equalization directly effects receiver s implementation complexity. A T-spaced equalizer has lower implementation effort, because it is running at symbol rate f T, compared to w f T for fractionally-spaced one. For performance comparison the number of required equalizer taps is usually supposed to be equal for both equalization schemes, although a T/-spaced DFE then will cover a shorter channel length. But the choice also effects implementation complexity of all functional units prior to the equalizer. Since asynchronous sampling is employed to meet needs for flexible band allocation, as stated in Section, complexity of the interpolation filter is affected, too. This is of major concern because the IP filter is running on high sampling rate f S. In order to feed a T/-equalizer s input, the filter has to generate its output data at f T. Summarizing, a symbol-spaced equalizer should be applied when aiming at low implementation complexity of the receiver. But on the other hand, T- spaced equalizers are known to show a highly sampling phase dependent performance. The reason for this is, that destructive aliasing can be caused by any amount of excess bandwidth for an unsuitable sampling phase [8]. T/-equalizers performance is almost insensitive to sampling phase because of higher bandwidth usage, avoiding aliasing. A T/-equalizer can even compensate a constantly poor sampling phase [8]. The decision, on which type of equalizer structure No. of Feedback Taps N B Fig. 3 - Effect of DFE s number of taps on maximum SNR VDSL FEXT Disturbers (Distance=Looplength) Sampling phase Fig. 4 - SNR(Sampling phase) for T- and T/ equalization to employ, depends on the common channel characteristics as well. Evaluations for typical VDSL channels by analytical means of Section 3 indicate that the performance loss of symbol-spaced equalization is negligible when compared to fractionally-spaced. Only for the band lowest in frequency (band DS1) a SNR degradation of up to approximately 1dB occurs, as shown exemplarily for a one-segment test loop in Fig. 4. Further examinations, leaving the scope of this paper, have shown that employment of steep analog filters at receiver s input will increase the observed degradation. Another aspect is that the SNR curves of Fig. 4 for T-spaced equalization are quite flat near optimum sampling phase, thus slightly lowering constraints on timing recovery. 5 Performance Evaluation In this section we will exemplarily evaluate standardized VDSL s prospective performance by mathematical means of Section 3. Evaluations will be conducted for ETSI s Standard Band Plan, as depicted in Fig., for two typical test loops. VDSL1-TP represents a one-segment 0.5mm underground cable. VDSL4 represents an arial cable of 3 segments, differing in lengths and diameters. Including two bridged taps, it causes worse signal distortion than the first loop [1]. Channel length for evaluation is υ = 50. Assumptions on constant PSD levels are: PSD TX = 60dBm z, PSD AW GN = 140dBm z. Crosstalk is modelled according to Model A as defined in [1]. The DFE is of size ( N F w = 30, N B = 0). The maximum achievable SNR MMSE, DFE, U (defined in Eq. 4) as a function of looplength is shown for each frequency band in Fig. 5 for both test loops. SNR curves of Fig. 5 are plotted without assuming a channel coding gain or reserving a system margin, as usu-

6 ally done in standardization literature. Maximum data rate and reach can roughly be determined by applying SNR min of Table 1 for Gray-coded QAM to Fig. 5. As signal attenuation increases proportionally to squared frequency, highest SNR is found for band DS1, while band US suffers highest attenuation. Due to the dual band usage for both directions, upper frequency bands DS and US will suffer additional degradation for long loops. The difference of attenuation for bands DS1 and DS, resp. US1 and US, amounts at their carrier frequencies to 35dB for a 1000m VDSL1-TP loop. Even in case of a -40dB out-of-band-level of Ny -filter W( f), steep analog filters must be used for band separation to suppress DS1/US1 s influence. This will degrade performance of T-spaced equalization, as stated in Section 4. The achievable SNR strongly depends on the number of VDSL Far End Crosstalk (FEXT) disturbers for looplengths smaller than 600m. Please note, that the applied FEXT model unrealistically assumes that the distance between each VDSL-FEXT disturber and the examined receiver is equal to looplength. SNR [db] VDSL1 TP ; VDSL4 N F w = 30 N B = 0 w= 0 VDSL FEXT Disturbers (Distance=Looplength) V1 : VDSL1 TP V4 : VDSL4 V1 DS1 V1 US1 V1 DS V1 US V4 DS1 V4 US1 V4 DS V4 US Looplength [m] Fig. 5 - Achievable SNR for loops VDSL1-TP, VDSL4 MQAM Data rate / f T SNR min [db] ( SER 10 7 ) Table 1: Required min. SNR(Gray-coded QAM constell. size) 6 Conclusions An SCM VDSL transceiver must meet needs for a flexible band allocation as well as low implementation costs. A suitable transceiver architecture has been presented as a base for VDSL performance evaluation. Thereafter, an approach has been described which allows to evaluate finite-length MMSE equalizers depending on their number of taps, oversampling factor, and sampling phase. Symbol-spaced equalization will result in lower implementation costs mainly due to the slower clocked equalizer and interpolation filters. On the other hand a T-spaced equalizer shows a sampling phase dependent performance, in contrast to the fractionallyspaced one. Neglecting analog filters influence, for three of four VDSL bands performance loss due to T- spaced equalization is negligible. The remaining band suffers approximately 1dB SNR degradation which will increase for usage of steep analog filters. Without taking into account the AFEs, a DFE of size ( N F w = 30, N B = 0) performs sufficiently. Performance results for typical VDSL loops have been shown. They strongly depend on the applied FEXT scenario. References: [1] T1E1.4, "VDSL Metallic Interface - Part1: Functional Requirements and Common Specification", Draft Trial-Use Standard, Feb. 001 [] ETSI TM, "VDSL - Part1: Transceiver Specification", TS v1.1.3, Sep. 000 [3] F.M. Gardner, "Interpolation in digital modems - Part I: Fundamentals", IEEE Trans. on Comm., Vol. 41, No. 3, Mar. 1993, pp [4] L. Erup, F.M. Gardner, F.A. arris, "Interpolation in digital modems - Part II: Implementation and Performance", IEEE Trans. on Comm., Vol. 41, No. 6, Jun. 1993, pp [5] M. Abdulrahman, D.D. Falconer, "Cyclostationary Crosstalk Suppression by Decision Feedback Equalization on Digital Subscriber Loops", IEEE Trans. on Comm., Vol. 10, No. 3, Apr. 199, pp [6] J.M. Cioffi, G.P. Dudevoir, M. Eyuboglu, G.D. Forney, "MMSE Decision-Feedback Equalizers and Coding - Part 1: Equalization Results", IEEE Trans. on Comm., Vol. 43, No. 10, Oct. 1995, pp [7] N. Al-Dhahir, J.M. Cioffi, "MMSE decision-feedback equalizers and coding - Finite length results", IEEE Trans. Inform. Theory, No. 7, 1995, pp [8] S. Qureshi, "Adaptive Equalization", IEEE Proceedings, Vol. 73, 1985, pp