Device and method for compensating crosstalk in transmission links

[0001] An embodiment of the invention relates to transmission links and in particular embodiments to hard-wired transmission lines.

[0002] Telecommunication and broadband services are usually provided to customer premises via twisted pairs of wires. The twisted pairs are often grouped in close proximity into binder groups. Data transmission in these settings may suffer from interference arising from electromagnetic coupling between neighboring twisted pairs, referred to as crosstalk interference.

[0016] In the following embodiments of the invention are described with reference to the drawings, wherein like reference numerals are generally utilized to refer to like elements throughout, and wherein the various structures are not necessarily drawn to scale. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more aspects of embodiments of the invention. It may be evident, however, to one skilled in the art that one or more aspects of the embodiments of the invention may be practiced with a lesser degree of these specific details. In other instances, known structures and devices are shown in block diagram form in order to facilitate describing one or more aspects of the embodiments of the invention. The following description is therefore not to be taken in a limiting sense, and the scope of the invention is defined by the appended claims.

[0017] Referring to FIG. 1, a schematic diagram of a network of a plurality of transmission lines L₁ to L_M is shown. The transmission lines L₁ to L_M are bundled together within a cable C over a length l₀. The network has a central office CO containing a plurality of transceivers LT₁ to LT_M coupled to the respective ends of the transmission lines L₁ to L_M. At the subscriber premises transceivers RT₁ to RT_M are coupled to the other respective ends of the transmission lines L₁ to L_M. The transceivers RT₁ to RT_M may, for example, be modems. Data transmission from the central office CO to a subscriber is called downstream data transmission, whereas data transmission from a subscriber to the central office CO is called upstream data transmission.

[0018] While the transmission lines L₁ to L_M may have all the same length, it is to be noted that they may also have different lengths. In the network shown in FIG. 1 the length of a transmission line L_i is the sum of the length l₀ and a length l_i (i=1, . . . M). The length l₀ is the length over which the transmission lines L₁ to L_M are bundled together and occupy the same cable C. The length l_i is the length from the end of the cable C to the transceiver RT_i. Each of the transmission lines L₁ to L_M may, for example, be a pair of twisted wires.

[0019] Furthermore, it is to be noted that the cable C may comprise transmission lines L_ext, which are not coupled to the central office CO.

[0020] The transmission lines L₁ to L_M may form a telecommunication channel. Since voice telephony uses only a small fraction of the bandwidth usually available on the transmission lines L₁ to L_M, the remaining fraction of the available bandwidth may be used for transmitting data. For data transmission there are a number of services available, such as ISDN (Integrated Services Digital Network) or ADSL (Asymmetric Digital Subscriber Line) or VDSL (Very high bit-rate Digital Subscriber Line) or VDSL2 (Very high bit-rate Digital Subscriber Line 2) or other services.

[0021] In systems such as the system shown in FIG. 1, due to the proximity of the transmission lines L₁ to L_M within the cable C of the length l₀, crosstalk interference between different neighboring transmission lines L₁ to L_M exists. Depending on the location where the crosstalk is introduced, two types of interference are distinguished which are explained in the following: near-end crosstalk (NEXT) and far-end crosstalk (FEXT).

[0022] NEXT refers to interference between neighboring transmission lines L₁ to L_M that arises when signals are transmitted in opposite directions. If the neighboring transmission lines L₁ to L_M carry the same type of service, then the interference is called self-NEXT.

[0023] FEXT refers to interference between neighboring transmission lines L₁ to L_M that arises when signals are transmitted in the same direction. If the neighboring transmission lines L₁ to L_M carry the same type of service, such as VDSL, then the interference is called self-FEXT.

[0024] Furthermore, noise can be coupled to the transmission lines L₁ to L_M that is generated by other sources than neighboring transmission lines L₁ to L_M. This noise is called alien noise and may, for example, be generated by the transmission lines L_ext.

[0025] If different frequency bands are used for downstream data transmission and upstream data transmission which is, for example, the case in VDSL, NEXT does not affect the transmission quality. However, FEXT causes more serious problems.

[0026] The frequency band used for transmitting signals in downstream direction may be different from the frequency band used for transmitting signals in upstream direction. As a consequence, self-NEXT can be excluded as a source of interference in this case, however self-FEXT must be considered.

[0027] In FIG. 2 an interference channel model is illustrated exhibiting crosstalk interference among the transmission lines L₁ to L_M in either downstream or upstream direction. A signal u_i(k) is provided to the input terminal of a transmission line L_i and a signal y_i(k) is received at the output terminal of the transmission line L_i (i=1, . . . M). Transfer functions H₁ to H_M are the transfer functions of the transmission lines L₁ to L_M, respectively. In particular, each transfer function H_i depends on the attenuation along the corresponding transmission line L_i. Transfer functions Fext₁₁, Fext₁₂, Fext₂₁, . . . , Fext_(M-1)M, Fext_M(M-1) are crosstalk transfer functions, wherein the crosstalk transfer function Fext_ji is the transfer function of the crosstalk channel from the input terminal of the transmission line L_j to the output terminal of the transmission line L_i for a specific frequency channel k (j, i=1, . . . , M). In the following, the term Fext_ji is not only associated with the crosstalk transfer function from the input terminal of the transmission line L_j to the output terminal of the transmission line L_i, but also with the corresponding crosstalk channel. Alien noise is not considered in the interference channel model shown in FIG. 2.

[0028] In upstream data transmission the receiving modems, which are the transceivers LT₁ to LT_M, are co-located at the central office CO. This allows joint reception of the signals transmitted over the transmission lines L₁ to L_M, thereby enabling crosstalk cancellation.

[0029] In downstream data transmission the receiving modems, which are the transceivers RT₁ to RT_M, reside within different customer premises so that crosstalk cancellation is not possible. However, since in downstream data transmission the transmitting modems, which are the transceivers LT₁ to LT_M, are co-located at the central office CO, it is possible to employ crosstalk precompensation. In crosstalk precompensation the signal to be transmitted is pre-distorted such that the pre-distortion compensates the crosstalk introduced by the transmission channel.

[0030] If the frequency band used for transmitting signals in downstream direction is different from the frequency band used for transmitting signals in upstream direction, self-NEXT can be excluded as a source of interference, however self-FEXT must be considered. For example, VDSL may be used as services for transmitting data over the transmission lines and DMT (discrete multi-tone) modulation may be used for modulating signals, however the embodiment described in the following is not limited thereto. While the following description is provided with respect to systems using different frequency bands for transmitting in downstream and upstream direction, it is to be noted that according to other embodiments a system may use the same frequency band, but different time slots for downstream and upstream directions.

[0031] Since DMT transmission is employed and interconnections between different frequency channels do not occur, it is possible to model crosstalk independently on each frequency (or tone). In the following the frequency channels are denoted by the index k. For precompensating self-FEXT in downstream data transmission, the signals u₁(k) to u_M(k) to be transmitted are listed in a vector u. The vector u is multiplied by a precompensation matrix P, in which the main diagonal entries are the precompensation values P_i and the entries outside of the main diagonal are the precompensation values P_ji as shown on the left hand side of FIG. 3. This multiplication results in a vector v containing precompensated signals v₁(k) to v_M(k). The precompensated signals v₁(k) to v_M(k) are emitted from the transceivers LT₁ to LT_M, respectively. During transmission over the transmission lines L₁ to L_M, the signals v₁(k) to v_M(k) experience crosstalk interference. On the right hand side of FIG. 3, the interference channel model that was already shown in FIG. 2 is illustrated exhibiting crosstalk interference among the transmission lines L₁ to L_M. At the output terminals of the transmission lines L₁ to L_M signals x₁(k) to x_M(k) are received, respectively.

[0032] FIG. 4 shows crosstalk compensation when signals u₁(k) to u_M(k) are transmitted in upstream direction. In this case, the crosstalk compensation is carried out in the central office CO. For this purpose, the vector v containing the signals v₁(k) to v_M(k) received at the output terminals of the transmission lines L₁ to L_M is multiplied by a compensation matrix C containing compensation values C_ji.

[0033] In FIG. 5, FEXT precompensation in downstream direction is summarized. The signals generated at the central office CO are first precompensated and then transmitted over the transmission lines L₁ to L_M and received at the customers premises CPE. Signals received at the output terminals of the transmission lines L₁ to L_M are fed into frequency equalizers FEQ. The frequency equalizers FEQ multiply the received signals with the inverses 1/H₁ to 1/H_M of the transfer functions H₁ to H_M, respectively. If the frequency equalizers FEQ are used, the precompensation values P₁ to P_M of the direct transmission channels can be set to a fixed value, for example 1.

[0034] In FIG. 6, FEXT compensation in upstream direction is summarized. The signals generated at the customers premises CPE are transmitted over the transmission lines L₁ to L_M and are received at the central office CO. At the central office CO, FEXT compensation and frequency equalizing FEQ is carried out. If frequency equalizers FEQ is carried out, the compensation values C₁ to C_M of the direct transmission channels can be set to a fixed value, for example 1.

[0035] FEXT Channel Selection:

[0036] In the embodiment described in the following, a partial crosstalk compensation concept is presented. Instead of compensating all crosstalk channels Fext_ji for FEXT, certain crosstalk channels Fext_ji are selected and FEXT of only these crosstalk channels Fext_ji is compensated or precompensated. While keeping the principle benefits of crosstalk compensation, its complexity can be reduced when performing partial crosstalk compensation. Since the number of crosstalk channels Fext_ji selected to be compensated or precompensated can be varied, the partial crosstalk compensation scheme offers a scalable complexity.

[0037] Before describing a method for selecting a number of crosstalk channels Fext_ji for compensation or precompensation, channel capacities of the transmission lines L₁ to L_M are considered. The channel capacity R_i(k) of the transmission line L_i is the number of bits that can be transmitted per frequency channel k and DMT frame. The channel capacity R_i(k) can be written as follows:

[0038] $\begin{array}{cc}{R}_i\left(k\right)={\log }_2\left(1+\frac{{\mathrm{SNR}}_i\left(k\right)}{\Gamma }\right)& \left(1\right)\end{array}$

[0039] Parameter Γ is a reference signal-to-noise ratio, which depends on the wanted bit error rate, the margins and the coding gain. SNR_i(k) is the signal-to-noise ratio at the output terminal of the transmission line L_i, which is the ratio between the power S of the wanted signal and the power N of the noise. The signal-to-noise ratio SNR_i(k) is given by the following equation:

[0040] $\begin{array}{cc}{\mathrm{SNR}}_i\left(k\right)={\left(\frac{S}{N}\right)}_i=\frac{p_i\left(k\right)·{H_i\left(k\right)}^2}{{{\sigma }_i\left(k\right)}^2+\sum _{j=1,j\ne i}^M{p}_j·{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}& \left(2\right)\end{array}$

[0041] In equation (2), p_i(k) is the power level of the signal u_i(k), and Υ_i(k) is the noise variance. Equation (2) may be rewritten as:

[0042] $\begin{array}{cc}{\mathrm{SNR}}_i\left(k\right)=\frac{p_i\left(k\right)}{\frac{{{\sigma }_i\left(k\right)}^2}{{H_i\left(k\right)}^2}+\sum _{j=1,j\ne i}^M{p}_j·\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}}& \left(3\right)\end{array}$

[0043] According to one embodiment, first values depending on crosstalk among the transmission lines L₁ to L_M are provided. For example, the crosstalk transfer functions Fext_ji(k) or functions of them such as, for example, the terms |Fext_ji(k)|², may be chosen as first values. The selection of the crosstalk channels to be compensated or precompensated depends on the first values. It is to be noted that crosstalk channels are selected rather than transmission lines. It does not necessarily follows that all crosstalk channels interfering with certain transmission lines are selected. For example, it is possible to select only some of the crosstalk channels interfering with certain transmission lines.

[0044] According to a further embodiment, second values specific to the individual transmission lines L₁ to L_M are provided. For example, the transfer functions H_i(k) or functions of them such as, for example, the terms |H_i(k)|², may be chosen as second values. Each transfer function H_i(k) is specific to the corresponding transmission line L_i. According to this embodiment, the selection of the crosstalk channels to be compensated or precompensated depends on the first and second values. For example, quotients

[0045] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
of the crosstalk transfer functions Fext_ji(k) and the transfer functions H_i(k) may be calculated and the selection of the crosstalk channels to be compensated or precompensated may depend on the quotients

[0046] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
or on functions of them.

[0047] For example, the quotients

[0048] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
or functions of them may be listed in a M×M-matrix. Those crosstalk channels Fext_ji are selected for compensation or precompensation the corresponding quotients

[0049] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
of which are maximal. According to equation (3), the crosstalk channels corresponding to these quotients provide a major contribution to interference noise. For example, a pre-determined number of crosstalk channels having the greatest quotients

[0050] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
are selected. Before selecting the quotients

[0051] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2},$
they may alternatively be sorted in order of magnitude. If the quotient

[0052] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
is selected, the crosstalk channel from the input terminal of the transmission line L_j to the output terminal of the transmission line L_i is compensated or precompensated for FEXT.

[0053] Various methods may be employed to select the crosstalk channels to be compensated or precompensated when the quotients

[0054] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
are listed in a matrix or are sorted in order of magnitude. For example, it may be provided that those crosstalk channels are selected, the corresponding quotients

[0055] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
of which are greater than a pre-determined threshold value. Alternatively, for example, a pre-determined number of FEXT channels having the greatest quotients

[0056] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
are selected.

[0057] It may be provided that the selection of crosstalk channels is carried out such that the bit rates of the longer transmission lines are increased at the cost of reducing the bit rates of the shorter transmission lines. This technique provides relatively high bit rates to all subscribers.

[0058] According to a further embodiment, each of the quotients

[0059] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
may be multiplied with a factor α_i before listed in the square matrix or before sorted in order of magnitude. The factor α_i depends on the transmission line L_i and may, for example, be in the range between 0 and 1. For example, if the factor α_i of the transmission line L_i is small, this may indicate that the subscriber i requires a lower bit rate or subscribed a lower bit rate.

[0060] According to a further embodiment, crosstalk channel selection and crosstalk compensation or precompensation of the selected crosstalk channels may be carried out for all frequency channels k or for selected frequency channels k. For example, only frequency channels k having low carrier frequencies may be selected for compensation or precompensation.

[0061] For crosstalk compensation and precompensation various methods are known in the art. In the present embodiment, FEXT compensation or precompensation of the selected crosstalk channels may be carried out by using any of the methods known to a person skilled in the art.

[0062] Determination of Crosstalk Transfer Functions

[0063] In the following, a method is presented for determining the crosstalk transfer functions Fext_ji(k). The direct transfer functions H_i may be determined by using a common method known to a person skilled in the art. The transfer functions Fext_ji(k) and H_i(k) may be used to calculate the quotients

[0064] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}.$
In case there is no interference between different frequency channels, such as in DMT transmission systems, the crosstalk transfer functions Fext_ji(k) may be determined separately for each frequency channel. In the following the method for determining the crosstalk transfer functions Fext_ji(k) is therefore described for only one frequency channel k, but may be applied to other frequency channels as well.

[0065] The interference channel model shown in FIG. 2 may be extended by adding interfering signals r_i caused by alien noise as well as equalizers EQ₁ to EQ_M and deciders D₁ to D_M as illustrated in FIG. 7. The equalizers EQ₁ to EQ_M multiply the received signals with the inverses 1/H′₁ to 1/H′_M of the direct transfer functions H′₁ to H′_M, respectively. The interference channel model of FIG. 7 may be rearranged by integrating the equalizers EQ₁ to EQ_M into the transfer functions H′_i and Fext′_ji, which results in an interference channel model as shown in FIG. 8. In this interference channel model all direct transfer functions H_i are 1. Further, the power of the interfering signals r caused by alien noise needs to be weighted:

[0066] $\begin{array}{cc}\langle r_i^2\left(k\right)\rangle =\frac{1}{H_i\left(k\right)}·\langle r_i^{\prime 2}\left(k\right)\rangle & \left(4\right)\end{array}$

[0067] According to the interference channel model shown in FIG. 8, the signal y_i received at the output terminal of the transmission line L_i is as follows:

[0068] $\begin{array}{cc}{y}_i\left(k\right)=u_i\left(k\right)+\sum _{j=1,j\ne i}^M{u}_j\left(k\right)·{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)+r_i\left(k\right)& \left(5\right)\end{array}$

[0069] In equation (5) the signals u₁(k) to u_M(k) are the output signals of the deciders D₁ to D_M, respectively.

[0070] For the determination of the crosstalk transfer functions Fext_ji a linear system of equations can be established. For i=1 the following equation is obtained:

[0071] $\begin{array}{cc}\left[\begin{array}{c}{y}_1\left(1\right)-u_1\left(1\right)\\ y_1\left(2\right)-u_1\left(2\right)\\ M\\ y_1\left(L\right)-u_1\left(L\right)\end{array}\right]\left[\begin{array}{cccc}{u}_2\left(1\right)& u_3\left(1\right)& \Lambda & u_M\left(1\right)\\ u_2\left(2\right)& u_3\left(2\right)& \Lambda & u_M\left(2\right)\\ M& M& & M\\ u_2\left(L\right)& u_3\left(L\right)& \Lambda & u_M\left(L\right)\end{array}\right]·\left[\begin{array}{c}{H}_{21}\\ H_{31}\\ M\\ H_{M1}\end{array}\right]& \left(6\right)\end{array}$

[0072] In equation (6)l=1, . . . , L denotes the FFT (fast Fourier transformation) frame. L symbols are transmitted over each of the transmission lines L₁ to L_M. Equation (6) may be rewritten as:
Δy₁=U₁·H₁  (7)

[0073] This system of linear equations may be solved by using a least mean square algorithm:
H₁=(U₁*^T·U₁)⁻¹·(U₁*^T·Δy₁)=Q⁻¹·b  (8)
Q=(U₁*^T·U₁)  (9)
b=U₁*^T·Δy₁  (10)

[0074] In equation (8) U₁*^T denotes the complex conjugated transpose of the matrix U₁. For calculating the matrix H₁ the square matrix Q is inverted and multiplied by the vector b.

[0075] The elements q_νμ of the matrix Q and b_ν of the vector b have the form:

[0076] $\begin{array}{cc}{q}_{v\mu }=\sum _{k=1}^L{U}_{v+1}^{*}\left(k\right)·U_{\mu +1}\left(k\right)& \left(11\right)\\ b_v=\sum _{k=1}^L{U}_{v+1}^{*}\left(k\right)·\Delta y_1\left(k\right)& \left(12\right)\end{array}$

[0077] The elements q_νμ and b_ν may be calculated recursively, but may also be calculated as follows:
q_νμ(1)=U_ν+1*(1)·U_μ+1(1)  (13)
q_νμ(λ)=q_νμ(λ−1)+U_ν+1(λ)U_μ+1(λ)  (14)
for λ=2, 3, . . . , L and ν, μ=1, 2, . . . , M−1
b_ν(1)=U_ν+1(1)·Δy₁(1)  (15)
b_ν(λ)=b_ν(λ−1)+U_ν+1(λ)Δy₁(λ)  (16)
for λ=2, 3, . . . , L and ν, μ1, 2, . . . , M−1

[0078] During a test interval, the M−1 elements of the first column of a transmission matrix Ĥ comprising the crosstalk transfer functions Fext_ji can be calculated as described above. The other columns of the matrix Ĥ are calculated accordingly. FIG. 9 schematically illustrates the determination of the matrix Ĥ. Signals u are simultaneously transmitted over the transmission lines L₁ to L_M where they are subject to crosstalk interference which is expressed by the matrix H. Signals y are received at the output terminals of the transmission lines L₁ to L_M by the transceivers RT₁ to RT_M. The signals y are provided to a decider D. The decider D estimates which signal u_i is closest to the signal y_i and outputs the difference between the signals y_i and u_i as an error signal Δy_i. Alternatively, the signal u_i may be known at the transceiver RT_i and the error signal Δy_i may then be the difference between the signal y_i and the signal u_i known at the transceiver RT_i. The vector Δy containing the error signals Δy_i as well as the vector u are used to calculate the elements of the matrix Ĥ.

[0079] Simulation Results:

[0080] In the following, simulations are presented which illustrate the methods described above. The simulated network is a VDSL2 network having a frequency range up to 30 MHz and a frequency band allocation as shown in FIG. 10. Different frequency bands are used for data transmission in upstream direction and downstream direction. According to the standard VDSL2, 4096 frequency samples are used at the transmitter and the receiver for a discrete Fourier transformation, wherein the carrier frequencies within the frequency bands shown in FIG. 10 are used for data transmission. The maximum transmit power density of each of the transmission lines is −56.5 dBm/Hz.

[0081] The simulated network includes 20 transmission lines L₁ to L₂₀. The lengths of the transmission lines L₁ to L₂₀ are evenly distributed between 150 m and 300 m. An additional noise signal having a spectral power density of 120 dBm/Hz is added at the receiver's end in order to simulate alien noise.

[0082] FIG. 11 shows the results of the simulations carried out for data transmission in upstream direction (from the transceivers RT₁ to RT₂₀ to the central office CO). The parameter Γ was set to 11 dB. In FIG. 11 the simulated bit rates of the transmission lines L₁ to L₂₀ are shown for four cases. Data illustrated by circles were recorded without any crosstalk compensation. Data illustrated by dots were recorded using full crosstalk compensation meaning all crosstalk channels, i.e., 20×19=380 FEXT channels, were compensated for all frequency channels. Data illustrated by asterisks were recorded using partial crosstalk compensation, wherein 20×4=80 crosstalk channels for each frequency channel were compensated and for the compensation only those crosstalk channels were selected having the highest term Fext_ji(k). Data illustrated by squares were recorded using partial crosstalk compensation, wherein 20×4=80 crosstalk channels for each frequency channel were compensated and for the compensation only those crosstalk channels were selected having the highest quotients

[0083] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}.$

[0084] Table 1 shows the lowest and highest bit rates for the four cases of the simulated network in upstream direction.

[0085]

TABLE 1
Upstream direction	lowest bit rate	highest bit rate
without crosstalk compensation	11 MBit/s	78.5 MBit/s
full crosstalk compensation	105 MBit/s	181 MBit/s
partial crosstalk compensation, channel	28.5 MBit/s	94.8 MBit/s
selection according to the term Fextji(k)
partial crosstalk compensation, channel	48.5 MBit/s	77.2 MBit/s
selection
according ⁢ ⁢ to ⁢ ⁢ the ⁢ ⁢ quotient ⁢ ⁢  Fext ji ⁡ ( k )  2  H i ⁡ ( k )  2

[0086] It can be seen from FIG. 11 and Table 1 that if the selection of the crosstalk channels to be compensated depends on the quotients

[0087] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2},$
the bit rates of the longer transmission lines are increased at the cost of reducing the bit rates of the shorter transmission lines compared to the case where the selection of the crosstalk channels to be compensated only depend on the term Fext_ji(k). By increasing the bit rates of the longer transmission lines at cost of reducing the bit rates of the shorter transmission lines it is possible to provide relatively high bit rates to all subscribers.

[0088] FIG. 12 shows the results of the simulations carried out for data transmission in downstream direction (from the central office CO to the transceivers RT₁ to RT₂₀). In FIG. 12 the simulated bit rates of the transmission lines L₁ to L₂₀ are shown for the same four cases as in FIG. 11. Table 2 shows the lowest and highest bit rates for the four cases of the simulated network in downstream direction.

[0089]

TABLE 2
Downstream direction	lowest bit rate	highest bit rate
without crosstalk compensation	58.2 MBit/s	72.9 MBit/s
full crosstalk compensation	123.8 MBit/s	158.0 MBit/s
partial crosstalk compensation, channel	66.2 MBit/s	98.0 MBit/s
selection according to the term Fextji(k)
partial crosstalk compensation, channel	78.4 MBit/s	84.3 MBit/s
selection
according ⁢ ⁢ to ⁢ ⁢ the ⁢ ⁢ quotient ⁢ ⁢  Fext ji ⁡ ( k )  2  H i ⁡ ( k )  2

[0090] It can be seen from FIG. 12 and Table 2 that when the selection of the crosstalk channels to be compensated depends on the quotients

[0091] $\frac{{{\mathrm{Fext}}_{\mathrm{ji}}\left(k\right)}^2}{{H_i\left(k\right)}^2}$
the bit rates of the longer transmission lines in downstream direction are also increased at the cost of reducing the bit rates of the shorter transmission lines compared to the case where the selection of the crosstalk channels to be compensated only depend on the term Fext_ji(k).

[0092] While in the above exemplary embodiments have been described, it is to be understood that many modifications of these embodiments may be provided. For example, the transmission lines L₁ to L_M may be replaced by wireless transmission links. Therefore, when reference is made to transmission lines, the transmission lines may be replaced by wireless transmission links.

[0093] The above exemplary systems may provide an xDSL system as well as a system of other services for transmitting data over the transmission lines L₁ to L_M. In addition, while the transmission system may use different frequency bands for downstream and upstream transmission, it may also use a same frequency band for both, downstream and upstream transmission. The above described embodiments are equally applicable to systems using timeslots for transmission.

[0094] In addition, while a particular feature or aspect of an embodiment of the invention may have been disclosed with respect to only one of several implementations, such feature or aspect may be combined with one or more other features or aspects of the other implementations as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms “include”, “have”, “with”, or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term “comprise”. The terms “coupled” and “connected”, along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements co-operate or interact with each other regardless of whether they are in direct physical or electrical contact, or they are not in direct contact with each other. Furthermore, it should be understood that embodiments of the invention may be implemented in discrete circuits, partially integrated circuits or fully integrated circuits or programming means. Also, the term “exemplary” is merely meant as an example, rather than the best or optimal. It is also to be appreciated that features and/or elements depicted herein are illustrated with particular dimensions relative to one another for purposes of simplicity and ease of understanding, and that actual dimensions may differ substantially from that illustrated herein.