IEEE ICC 2012 - Signal Processing for Communications Symposium
Alien Crosstalk Mitigation in Vectored DSL Systems for Backhaul Applications Aditya Awasthi∗† , Naofal Al-Dhahir∗ , Oren E. Eliezer† , and Poras T. Balsara∗ ∗ Department
of Electrical Engineering, The University of Texas at Dallas, Richardson, TX Email:
[email protected],
[email protected],
[email protected] † Xtendwave,
7920 Belt Line Road, Suite 1000, Dallas, TX 75254 USA Email:
[email protected]
Abstract—The performance of digital subscriber line (DSL) systems, such as ADSL and VDSL is limited by crosstalk. Suppression of in-domain far-end self crosstalk using vectoring technology enables very high bidirectional data rates over twisted-pairs of copper wires. However, the performance of vectored DSL systems is severely degraded in the presence of alien or out-of-domain crosstalk that arises from sources that lie outside the vectored DSL system and share the same cable binder. In this paper, we propose a practical, non-iterative, high performance algorithm for alien crosstalk mitigation. Simulation results and complexity analysis corresponding to a vectored VDSL2 system in presence of alien crosstalk are presented to illustrate the significant performance gains of the proposed algorithm and its low implementation complexity.
I. I NTRODUCTION Due to the exponential growth in cellular and access backhaul traffic, particularly in light of the rising popularity of mobile smartphones, cellular and broadband access providers have been overwhelmed by the need for increased backhaul network capacity. Since trenching for new fiber infrastructure is prohibitively costly and time consuming, there is renewed interest in techniques such as common-mode data transmission [1] and crosstalk reduction, which maximize the capacity of the existing copper infrastructure [2]. Recent advances in the suppression of in-domain far-end crosstalk (self-FEXT) [3]– [5] have allowed multi-carrier Digital Subscriber Loop (DSL) systems such as VDSL2 [6] and ADSL2+ [7] to achieve very high bidirectional data rates over twisted-pairs of copper wires. However, the performance of these systems is severely degraded in the presence of out-of-domain crosstalk (also referred to as alien crosstalk in this paper) that arises from sources that lie outside the vectored DSL system. Alien crosstalk can arise from non-coordinated lines within the same binder, lines in adjacent binders, any residual selfFEXT between the coordinated lines, or even external sources such as radio frequency interference (RFI). In the backhaul application, the DSL modems are co-located and usually have multiple coordinated transceivers on both ends. Alien crosstalk This research work was carried out at Xtendwave, 7920 Belt Line Road, Suite 1000, Dallas, TX 75254 USA under NSF SBIR Award #1047336 and NSF Grant #EEC-0946373 to the American Society for Engineering Education.
978-1-4577-2053-6/12/$31.00 ©2012 IEEE
cancellation algorithms [8]–[10] exploit the spatial correlation of alien crosstalk [11] to mitigate its effects by removing the correlated portion of the alien crosstalk across coordinated twisted-pairs in DSL systems. Existing alien crosstalk mitigation algorithms in the literature such as the one in [9], typically use an iterative, suboptimum, and often slowconverging least-mean-square (LMS) algorithm to compute approximate alien crosstalk prediction filter coefficients. A Minimum Mean Squared Error (MMSE) crosstalk canceler is described in [8], which performs a prewhitening operation to decorrelate the alien crosstalk. It was noted in [8] that a decision feedback canceler performs optimally [5], [12]. However, a lower complexity linear MMSE canceler was selected as a good compromise between a low-performance zero-forcing canceler and a high-performance more complex decision feedback canceler. In this paper, we propose a low-latency receiver-based algorithm for alien crosstalk mitigation, based on indirectly estimating the alien crosstalk correlation matrix and noniterative numerically-robust computation of the optimum alien crosstalk prediction filter coefficients. The prediction filter is used to synthesize and cancel the spatially-correlated alien crosstalk. The system model is presented in Section II. Section III describes our approach for alien crosstalk mitigation and discusses various practical considerations. Section IV shows simulation results to illustrate the performance benefits of the proposed algorithm for a VDSL2 system with various alien interference sources. Finally, Section V draws some final conclusions. II. S YSTEM MODEL Algorithms discussed in this paper are applicable to any multiple-input multiple-output (MIMO) discrete multi-tone (DMT) system with coordinated reception including ADSL2+, VDSL2 and “Common-Mode DSL” [1]. It is assumed that the vectored system consists of Lc twisted pairs, and out-ofdomain crosstalk originates from M sources that lie outside the vectored DSL system. Note that the M alien crosstalk sources can be in the same or adjacent binder and the alien crosstalk from any of these M sources can be either far-end crosstalk (alien FEXT) or near-end crosstalk (alien NEXT).
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Receiver Multiple twisted-pair channels
Remove Cyclic Extension
Analog Front End
Alien Crosstalk Mitigation
FFT
Convolutional DeInterleaving
Alien crosstalk canceller
Self-FEXT Canceler
cholesky factors Binary Data
Transmitter
Fig. 1.
Hm Xm + Halien Xalien + Nm m m
=
Hm X m + Z m
(1)
where, m is the tone index (allowed values are governed by either the upstream or downstream band-plans). Xm and Ym are Lc × 1 column vectors containing the transmitted and received symbols for all Lc coordinated lines. Hm is the Lc ×Lc channel matrix which contains the direct-channel as well as is the the in-domain crosstalk (self FEXT) channel. Halien m Lc × M alien crosstalk coupling channel matrix (alien NEXT or alien FEXT). Nm is additive white Gaussian background is M × 1 column vector containing the M noise and Xalien m alien interferes. Zm is the total noise vector, containing the sum of all the alien crosstalk contributions to each line as well as the background noise. It was shown in [4] that the linear zero-forcing (ZF) selfFEXT canceler is near optimal due to the diagonally-dominant structure of the MIMO DSL channel matrix [5] at each tone, which minimizes noise amplification. After applying zeroforcing self-FEXT cancellation to (1), we get ˜m ˜ m = H−1 Ym = Xm + H−1 Zm = Xm + Z (2) Y m
˜ m is the Lc × 1 total noise vector after self-FEXT where Z cancellation, which is correlated across the Lc coordinated −∗ DSL lines with covariance matrix H−1 m Rzz,m Hm where Rzz,m is the covariance matrix of Zm . III. A LIEN CROSSTALK MITIGATION According to [8], [10], [11] alien crosstalk is spatially correlated i.e. alien crosstalk is correlated at the same tone for different twisted pairs. The spatial auto-correlation matrix ˜ m (from Equation (2)) can be computed as of the total noise Z Rm =
Binary Data
Timing Synchronization
Alien crosstalk mitigation blocks and their integration within a DMT-based vectored DSL system
=
m
Descrambler
Spatial correlation estimator
Alien crosstalk mitigation techniques described in this paper are applicable to all the scenarios mentioned above, and the input-output model of the vectored system at the mth frequency tone is described by Ym
Frequency Synchronization
FEC decoder
NT 1 ˜ mZ ˜∗ Z m NT j=1
(3)
where NT is the number of DMT symbols used for reliable correlation computation. The Cholesky (triangular) factorization is defined as follows Rm = Lm Dm L∗m
(4)
where Lm is the cholesky lower-triangular matrix with ones on its main diagonal and Dm is a diagonal matrix. The underlying idea behind our proposed alien crosstalk mitigation algorithm is to exploit this spatial correlation and design prediction filters, which can synthesize and cancel the alien crosstalk using Equation (4), as follows ˜ m,1 Em,1 = Z ˜ m,2 − Em,1 Lm (2, 1) Em,2 = Z .. . ˜ m,L − Em,Lc = Z c
(5) L c −1
Em,i Lm (Lc , i)
i=1
where Em is the uncorrelated prediction error vector with variances given by the diagonal elements of Dm . The triangular structure of Lm utilized in Equation (5) is later used in alien canceller design (as shown in Figure 2). As shown in Figure 1, the top-level implementation block diagram of alien crosstalk mitigation in a MIMO DMT system, which consists of 1) Spatial correlation estimator block, where the spatial correlation of the total noise (alien crosstalk and background noise) is estimated and noise prediction filter coefficients (cholesky factors) are computed. 2) Alien crosstalk canceler block, where the correlation estimates are used to mitigate alien crosstalk. Spatial correlation of the total noise (including alien crosstalk and background noise) across Lc coordinated lines is first estimated during initialization of the vectored DSL system (before data transmission) and the reduction in the total received noise after canceling the spatially-correlated noise is calculated during initialization (training) for each of the Lc coordinated lines. This allows us to load more bits on subcarriers (during bit-loading) and therefore, improves the data rates of the vectored DSL system. During data transmission, the spatial correlation estimates can be updated as alien crosstalk coupling slowly varies over time (e.g. due to temperature variations). Large and sudden changes in the alien crosstalk, e.g. due to alien crosstalk sources becoming active or inactive, usually require re-initialization of the vectored DSL system, and thus the spatial alien crosstalk correlation is reestimated.
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A. Estimation of Alien Crosstalk Spatial Correlation As shown in Figure 1, the spatial correlation estimator block is not on the receiver datapath and it only provides noise prediction filter coefficients (Cholesky factors) to the alien crosstalk canceler block. Although estimation of the spatial crosstalk correlation has no impact on data latency of the vectored DSL system, the accuracy of the correlation estimates has significant impact on the performance of the alien crosstalk canceler. Furthermore, the required accuracy of the alien crosstalk correlation estimates can only be achieved by processing a large number of DMT symbols, which can potentially lead to huge memory requirements. Existing alien crosstalk mitigation algorithms in the literature often assume the total noise covariance matrix to be known [8] or sufficient processing time and hardware resources are assumed to be available (e.g. 500 to 1000 iterations are required per subcarrier in [9]). To illustrate the issues involved, we use the example of downstream transmission on a VDSL2 [6] system (profile 17a). During initialization, spatial correlation estimates can be performed during the “training” and “channel analysis and exchange” phases that are defined in the VDSL2 initialization procedures, where each phase lasts for a maximum of 10 seconds (40,000 DMT symbols). Each DMT symbol, having a typical cyclic prefix length of 640, has a duration of 0.25ms and contains 2885 frequency subcarriers for downstream transmission. Thus, if the datapath word length is 16 bit complex (note that at least 14-bit ADC are typically used in VDSL modems), the total memory required to store one VDSL DMT symbol for all LC = 8 DSL lines is about 90 kilobyte (kB). Thus, to calculate the spatial correlation estimates using 100 DMT symbols simultaneously, about 9 MB of memory is needed just to store inputs for the spatial correlation estimator block in Figure 1. The memory requirements and the computation complexity can be significantly reduced by using our proposed algorithms for reduced finite-precision effects and by performing incremental computations to arrive at final accurate estimates using a minimum number of DMT symbols at any given time. Computing the alien crosstalk covariance matrix in (3) involves multiplication operations which double the required bit precision. In order to improve robustness to finite-precision effects in a fixed-point implementation, we propose to compute the lower-triangular Cholesky factor in (4) indirectly by applying the numerically well-conditioned Householder transformation [13] to the estimated alien crosstalk samples matrix as shown in Algorithm 1. Apart from enhanced robustness to finite-precision effects and lower computation complexity, Householder-based Algorithm 1 also provides a convenient method to incrementally compute the final Cholesky triangular factor matrix. In our proposed algorithm, the new alien crosstalk sample vectors are appended to the existing lower¯ m . Then, Householder reflections are triangular factor matrix L applied to zero out the appended alien crosstalk sample vectors ¯ m,new . and create the updated lower-triangular factor matrix L def def ∗ ∗ ¯ mL ˜ mL ¯ = L ˜ , where Let Am = NT × Rm = NT × L m
Algorithm 1: Estimation of noise correlation ˜ m (output of self-FEXT canceler (Equation 2)), Input: Y Xm (if available e.g. during training) Output: Lm Step 1: Estimate NT alien crosstalk vectors and arrange them in the size Lc × NT matrix for each tone m ˜ m,i − X ˆ m,i ˜ m,i = Y Z
(6)
ˆ m,i can where i = 1 to NT is the DMT symbol index, X be the known training symbol Xm,i (during initialization). For updating correlation estimates during ˆ m,i can be pilot tones (if available), data transmission, X ˜ m,i , or final tentative decisions by applying a slicer to Y decisions after the decoder. ˜m = Z ˜ m,N ˜ m,2 · · · Z ˜ m,1 Z Z T Step 2: Apply orthonormal Householder transformation Qm to the alien crosstalk matrix formed in the previous step ¯m 0 ˜ mQ ˜ m = NT L Z ¯ m is a lower-triangular matrix of size Lc × Lc where L which is related to Lm in (4) as follows 1 ˜ 1 ˜∗ Rz˜z˜,m = ( √ Zm )( √ Z ) NT NT m ∗ ¯m ∗ L ¯ = ( Lm 0 Qm )(Qm ) 0 ¯ ∗m ¯mL = L =
Lm Dm L∗m
(7)
− 12
¯ m Dm , where Lm is a lower-triangular Hence, Lm = L matrix with ones on its main diagonal and Dm is a diagonal matrix.
Rm is the current alien crosstalk spatial correlation matrix based on NT DMT symbols at the mth subcarrier. As we process Ns additional DMT symbols Ns ˜ ˜ m,j )∗ (Zm,j )(Z Am,new = Am + j=1 ˜ m,new Z ˜∗ = Am + Z m,new
def
(8)
where the Lc ×Ns new alien crosstalk samples matrix is given ˜ m,new = ˜ m,N +N . ˜ m,N +2 · · · Z ˜ m,N +1 Z by Z Z s T T T From Equation (8) ˜∗ L m ˜ m,new ˜m Z Am,new = L ˜∗ Z m,new
m
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˜ m,new L ˜∗ = L m,new ∗ ˜ L m,new ˜ m,new 0L ×N = L c s 0Ns ×Lc def
Qm
Y~m;1 = Y¹m;1
(9)
+
Σ
Em,i Lm (j + 1, i)
Σ
+
Σ
Y^m;2
dec (.)
¡
¢¢¢ Lm(Lc; 2)
£
¡
+
Y^m;1
Latency critical path Y¹m;2
Lm(Lc; 1)
Fig. 2.
£
Σ
¡
+
Σ
Lm(Lc; Lc ¡ 1)
£
¢¢¢
¡Y¹m;L
+
Σ
c
dec (.)
Y^m;Lc
Functional diagram of alien crosstalk canceler implementation
TABLE I A LIEN CROSSTALK CANCELER IMPLEMENTATION COMPLEXITY Hardware for 8 lines Multipliers:116, Adders:137, Registers:27
(10)
Area @45nm CMOS 12k NAND2 gates
Latency @200 MHz clock 0.18μs per subcarrier
TABLE II S IMULATION PARAMETERS No. of DMT tones: 4096 System margin: 6dB Maximum power: 14.5dBm Background noise: −140dBm/Hz
Tone Width: 4.3125kHz Coding gain: 5dB SNR gap: 10.8dB Cable type: 24 AWG
choice involves a tradeoff between latency and reliability of the decisions. To gain insight into implementation aspects, Verilog code of the alien crosstalk canceler (with no pipelining or custom VLSI architectures) was synthesized via the Synopsys design compiler using 45nm CMOS standard cell library [14], and the latency and area are provided in Table I. The implementation architecture has only one decision block (currently realized as a slicer) which has the major contribution in the overall gate-count of the alien crosstalk canceler block. Note that the hardware resources shared between the Lc DSL lines in our proposed method are almost never idle during alien crosstalk cancellation operation unlike implementations which have dedicated hardware for each DSL line. More than one such alien canceler block can be implemented in parallel to achieve optimized area and latency specifications.
(11)
where dec(.) denotes a decision at the output of a slicer or decoder j
¡
+
Y~m;Lc
˜ m is the output of the self-FEXT canceler, IL where, Y c denotes the size-Lc identity matrix. Since the elements of Em ¯ m. are uncorrelated, an element-wise slicer can be applied to Y Our proposed algorithm to cancel the alien crosstalk at each tone m is given below.
¯ m,j − dec(Y ¯ m,j ) Em,j = Y
Lm(2; 1)
£
...
During data transmission, the latest available prediction filter coefficients Lm are used to cancel the alien crosstalk at each tone m. Using Equations (2) and (5), the output of the alien crosstalk canceler is generated as follows
Algorithm 2: Alien Crosstalk Cancellation ˜m Input: Lm ,Y ¯ Output: Ym ¯ m,1 = Y ˜ m,1 Initial condition: Y for j = 1 to Lc − 1 do
¡
Y~m;2
B. Mitigation of Spatially-Correlated Alien Crosstalk
˜ m + (IL − Lm )Em = Xm + Em ¯m = Y Y c
dec (.)
Em;Lc¡1
Em;2
˜ m,new Z
where Qm is the orthonormal Householder matrix. Revisiting our previous example, if we process only Ns = 2 additional DMT symbols at a time, we would need 90 × Ns = 180 kB of memory (instead of 9 MB) to store inputs while processing all 100 DMT symbols. Note that the Householder block would need to complete 2L2c ( 2L3 c + Ns ) = 939 flops per subcarrier (from [13]) within Ns × 0.25 = 0.5ms to avoid input memory overflow. Thus, the number of additional symbols, Ns , simultaneously processed during each update can be made as small (i.e. lower memory requirements) as the implementation of spatial correlation estimator would allow.
˜ m,j+1 − ¯ m,j+1 = Y Y
Allows reduction of complexity through hardware re-use
Alien Crosstalk Mitigation block
Em;1
Therefore, we can write ˜ m,new 0L ×N ˜m = L L c s
(12)
i=1
end ¯ m,i depends only on The key observation here is that Y Em,j for 1 ≤ j < i which are already generated using (11). This allows for reuse of the same hardware resources for alien crosstalk cancellation on each of the Lc vectored DSL lines as shown in Figure 2. Cancellation of spatiallycorrelated alien crosstalk impacts the data latency of each of the Lc coordinated lines, according to their decorrelation order in Algorithm 1. Note that the noise on the first coordinated line is not affected by Algorithm 2 and therefore, is treated ¯ m,j ) used in (11) as a “reference line”. The decisions dec(Y can be output of a slicer, inner decoder or outer decoder. This
IV. S IMULATION R ESULTS In this section, simulation results are provided to demonstrate the performance benefits of our proposed algorithm. Our simulations follow the VDSL2 standard [6], profile 17a to simulate performance gains in both the upstream and downstream directions. Our vectored DSL system consists of Lc = 8 twisted pairs, and in-domain crosstalk is assumed to be perfectly canceled using methods described in [3]–[5]. The simulation parameters are summarized in Table II. Figure 3 shows the noise power spectral density (PSD) before and after alien crosstalk mitigation on the second DSL
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−95
160
Line 2 noise before alien crosstalk mitigation Line 2 noise after alien crosstalk mitigation
−100
Aggregate data rate(Mbps)
Noise PSD (dBm/Hz)
−105 −110 −115 −120 −125 −130
120 100 80 60 40 20
−135 −140 0
No self−FEXT or alien interferer present Alien & self−FEXT mitigation Only self−FEXT mitigation No crosstalk mitigation
140
1000
2000 3000 Subcarrier index
4000
0 2
5000
3
4
5 Length(kft)
6
7
8
Fig. 3. Noise PSD before and after alien crosstalk cancellation on 2kft loop with 1 T1-interferer
Fig. 4. Aggregate data rate per twisted-pair in presence of single NEXT source from a T1 transmitter
lines of our vectored system, in presence of a single NEXT source from a T1 transmitter [15], [16]. The alien crosstalk coupling is assumed to be 99% worst case as defined in [16] and simulation results are based on downstream transmission of 100 DMT-symbols on a 2000 feet loop. Note that the noise on the first line (reference) is unaffected by the alien crosstalk cancellation algorithm as shown in Figure 2 and Equation (5). However, the noise on the all other DSL lines including the second line, is significantly mitigated on downstream subcarriers after application of the algorithm. This enables higher bit loading per tone and, thus, higher data rates on the second line. Noise reduction similar to line 2 is experienced on other DSL lines (not shown here for the sake of clarity). Figure 4 shows the aggregate rate improvement (both upstream and downstream combined) in the presence of a single T1 transmitter (NEXT) for different loop lengths. Spatial alien crosstalk correlation was estimated by Algorithm 1 using 100 DMT-training symbols during initialization and tentative decisions from the output of slicer were used for alien crosstalk cancellation (refer to Algorithm 1). As shown in [5], [12] our decision feedback based approach to alien crosstalk mitigation performs better than zero-forcing and linear MMSE solutions especially in DMT systems operating at very low bit error rates. As can be seen in Figure 4, the factor of improvement in aggregate data rates due to our proposed alien crosstalk mitigation algorithm increases with loop length since the strongest alien interferers are NEXT sources which significantly degrade performance at longer loop lengths due to weaker received signal levels.
the significant performance gains and practical implementation feasibility of our solution.
V. C ONCLUSION We proposed a high-performance low-latency alien crosstalk mitigation algorithm for vectored DSL system. A numericallyrobust algorithm for accurate estimation of the alien crosstalk spatial correlation was described to address practical implementation issues such as finite-precision effects, memory usage, and latency. Taking cellular backhaul as a case study, simulation results and gate counts were presented to illustrate
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