Transmission links

Abstract

Implementations related to transmission systems are presented herein.

Description

BACKGROUND OF THE INVENTION

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.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 schematically illustrates a network of a plurality of transmission lines L₁ to L_M.

FIG. 2 illustrates a model of a transmission system.

FIG. 3 illustrates an interference channel model showing crosstalk interference among the transmission lines L₁ to L_M.

FIG. 4 illustrates the convergence of an embodiment of an iterative method I.

FIG. 5 illustrates exemplary results of a simulation of an embodiment of the method I.

FIG. 6 illustrates definitions of variables a and b.

FIG. 7 illustrates exemplary results of a simulation of an embodiment of an iterative method II.

FIG. 8 illustrates frequency ranges and frequency channels.

FIG. 9 illustrates a further interference channel model showing crosstalk interference among the transmission lines L₁ to L_M.

FIG. 10 illustrates yet a further interference channel model showing crosstalk interference among the transmission lines L₁ to L_M.

FIG. 11 illustrates an embodiment of a method IV.

FIG. 12 illustrates a further embodiment of the method IV.

FIG. 13 illustrates line attenuations of the shortest and the longest transmission lines.

FIG. 14 illustrates minimum and maximum FEXT attenuations.

FIG. 15 illustrates exemplary results of a simulation of an embodiment of a method III.

FIG. 16 illustrates further exemplary results of the simulation of the embodiment of the method III.

DETAILED DESCRIPTION OF THE INVENTION

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.

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 comprising 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.

While 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.

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.

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).

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).

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.

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.

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.

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

According to one embodiment, the frequency band used for transmitting signals in downstream direction is 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, however self-FEXT must be considered. For example, VDSL or ADSL 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. The embodiment may be also applied to a system which uses the same frequency band, but different time slots for downstream and upstream directions.

The network of the transmission lines L₁ to L_M of the present embodiment is shown in FIG. 1. The transceivers LT₁ to LT_M of the central office CO as well as the transceivers RT₁ to RT_M at the subscriber premises comprise units which allow measurement of the signal-to-noise ratios of signals received over the respective transmission lines L₁ to L_M. The values of the measured signal-to-noise ratios are transferred to a central control unit CCU, which is coupled to the central office CO. The central control unit CCU sets the power levels of the signals transmitted by the transceivers LT₁ to LT_M and RT₁ to RT_M. Special transmission and control channels are provided between the central office CO and the transceivers RT₁ to RT_M in order to exchange data between the central control unit CCU and the transceivers RT₁ to RT_M.

FIG. 2 illustrates a model of the transmission system in one embodiment. The model only considers the transmission lines L₁ to L_M which are coupled to the central office CO. The arrows between the transceivers LT_i and RT_i illustrate the logical connections between the transceivers LT_i and RT_i (i=1, . . . , M). Since it is assumed that there is no crosstalk interference between downstream and upstream directions, the power levels in downstream and upstream directions can be determined separately.

As can be seen from FIG. 2, self-FEXT signals fext and interfering signals r disturb the signals transmitted between the transceivers LT_i and RT_i. The interfering signals r are caused by alien noise which may be due to the transmission lines L_ext, which are not coupled to the central office CO, and other external sources.

In FIG. 3 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 is provided to the input terminal of a transmission line L_i and a signal y_i is received at the output terminal of the transmission line L_i (i=1, . . . , M). A transfer function H_ji is the transfer function of a channel from the input terminal of a transmission line L_i to the output terminal of the transmission line L_j for a specific frequency channel (j=1, . . . , M). The transfer functions H_ii are the transfer functions of the transmission lines L₁ to L_M and the transfer functions H_{ji, i≠j} are the crosstalk transfer functions.

According to the interference channel model shown in FIG. 3, the signal y_i received at the output terminal of the transmission line L_i is as follows:

$\begin{array}{cc}{y}_i=u_i·H_{\mathrm{ii}}+\sum _{j=1,j\ne i}^Mu_j·H_{\mathrm{ji}}+r_i& \left(1\right)\end{array}$

Assuming that the signals transmitted over different transmission lines are not correlated, the signal-to-noise ratio Sn_i 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, is given by the following equation:

$\begin{array}{cc}{\mathrm{Sn}}_i={\left(\frac{S}{N}\right)}_i=\frac{{〈u^2〉}_i·{H_{\mathrm{ii}}}^2}{\sum _{j=1,j\ne i}^M{〈u^2〉}_j·{H_{\mathrm{ji}}}^2+{〈r^2〉}_i}& \left(2\right)\end{array}$

Since many signals have a very wide dynamic range, signal-to-noise ratios are usually expressed in terms of the logarithmic decibel scale. In decibels, the logarithmic signal-to-noise ratio Sndb_i is 10 times the logarithm of the power ratio Sn_i:

$\begin{array}{cc}{\mathrm{Sndb}}_i=10·{\log }_{10}\left({\left(\frac{S}{N}\right)}_i\right)& \left(3\right)\end{array}$

In order to be able to transmit high bit rates, the values of the signal-to-noise ratio Sn_i should be large. The channel capacity R_i of the transmission line L_i, which is the number of bits that can be transmitted per frequency channel and data symbol, is:

$\begin{array}{cc}{R}_i={\log }_2\left(1+\frac{{\mathrm{Sn}}_i}{{\mathrm{Sn}}_{\mathrm{ref}}}\right)\mathrm{bit}& \left(4\right)\end{array}$

Sn_ref is a reference signal-to-noise ratio, which depends on the wanted bit error rate, the margins and the coding gain.

As can be seen from equation (2), the signal-to-noise ratio Sn_i measured at the output terminal of the transmission line L_i depends on the power levels of the signals u₁ to u_M, the transfer function H_ii, the transfer functions H_{ji, j≠1} and the power level of the alien noise interference signal r_i. Two extreme cases may arise:

• • (a) FEXT can be neglected compared to alien noise. In this case the signal-to-noise ratio Sn_i only depends on the transmit power level of the signal u_i. In order to achieve a high signal-to-noise ratio Sn_i, it is favorable to feed the transmission lines L₁ to L_M with signals u₁ to u_M at the highest power level.
  • (b) Alien noise can be neglected compared to FEXT. In this case the signal-to-noise ratio Sn_i depends on the transmit power levels of all signals u₁ to u_M. If the signals u₁ to u_M have equal transmit power levels, shorter transmission lines L_i produce better signal-to-noise ratios Sn_i.

Description of a Method I:

In the following a method I is discussed as an exemplary embodiment, which allows a determination of the transmit power levels p₁ to p_M for signals provided to the input terminals of the transmission lines L₁ to L_M so that the signals received at the output terminals of the transmission lines L₁ to L_M exhibit equal signal-to-noise ratios Sn₁ to Sn_M. As a result the same maximized data rate can be transmitted over the transmission lines L₁ to L_M. The method I is performed either for the downstream or the upstream direction and for a single frequency channel.

The transmit power levels p₁ to p_M of the signals provided to the transmission lines L₁ to L_M, the signal-to-noise ratios Sn₁ to Sn_M measured at the output terminals of the transmission lines L₁ to L_M, and the logarithmic signal-to-noise ratios Sndb₁ to Sndb_M are combined in vectors p, Sn and Sndb, respectively:

$\begin{array}{cc}p=\left[\begin{array}{c}{p}_1\\ p_2\\ ⋮\\ p_M\end{array}\right]& \left(5\right)\\ \mathrm{Sn}=\left[\begin{array}{c}{\mathrm{Sn}}_1\\ {\mathrm{Sn}}_2\\ ⋮\\ {\mathrm{Sn}}_M\end{array}\right]& \left(6\right)\\ \mathrm{Sndb}=\left[\begin{array}{c}{\mathrm{Sndb}}_1\\ {\mathrm{Sndb}}_2\\ ⋮\\ {\mathrm{Sndb}}_M\end{array}\right]& \left(7\right)\end{array}$

According to one embodiment, at the first cycle of the method I, which is denoted with k=1, signals are concurrently provided to the transmission lines L₁ to L_M having the highest transmit power level p_max:

$\begin{array}{cc}p\left(k=1\right)=\left[\begin{array}{c}{p}_{\max }\\ p_{\max }\\ ⋮\\ p_{\max }\end{array}\right]& \left(8\right)\end{array}$

The signal-to-noise ratios Sn(1)₁ to Sn(1)_M of the signals, which are received at the output terminals of the transmission lines L₁ to L_M, are measured. According to a further embodiment, the signal-to-noise ratios Sn(1)₁ to Sn(1)_M measured in the first cycle of the method (k=1) are used for determining the transmit power levels p(k=2) of the second cycle:

$\begin{array}{cc}p\left(k=2\right)=\left[\begin{array}{c}\left(\frac{{p\left(1\right)}_1}{{\mathrm{Sn}\left(1\right)}_1}\right)\\ \left(\frac{{p\left(1\right)}_2}{{\mathrm{Sn}\left(1\right)}_2}\right)\\ ⋮\\ \left(\frac{{p\left(1\right)}_M}{{\mathrm{Sn}\left(1\right)}_M}\right)\end{array}\right]& \left(9\right)\end{array}$

According to one embodiment, the vector p(2) is scaled:

$\begin{array}{cc}\hat{p}\left(2\right)=p\left(2\right)·\frac{p_{\max }}{\max \left(p\left(2\right)\right)}& \left(10\right)\end{array}$

In equation (10) max(p(2)) denotes the maximum component of the vector p(2) of equation (9). The scaling prevents exceeding the maximum power level p_max.

The scaled vector {circumflex over (p)}(2) provides the transmit power levels for the signals provided to the input terminals of the transmission lines L₁ to L_M during the second cycle of the method I. At the output terminals of the transmission lines L₁ to L_M the signal-to-noise ratios Sn(2)₁ to Sn(2)_M or the logarithmic signal-to-noise ratios Sndb(2)₁ to Sndb(2)_M are measured. Transmitting signals over the transmission lines L₁ to L_M and measuring their signal-to-noise ratios Sn(k)₁ to Sn(k)_M or their logarithmic signal-to-noise ratios Sndb(k)₁ to Sndb(k)_M is then iteratively repeated.

The iterations are repeated until the measured signal-to-noise ratios Sn(k)₁ to Sn(k)_M or the measured logarithmic signal-to-noise ratios Sndb(k)₁ to Sndb(k)_M reach sufficient convergence (k=k_max). At each of the iteration cycles k=2 to k=k_max−1 the signal-to-noise ratios Sn(k)₁ to Sn(k)_M or the logarithmic signal-to-noise ratios Sndb(k)₁ to Sndb(k)_M of the signals received at the output terminals of the transmission lines L₁ to L_M are measured and used for setting the transmit power levels p(k+1) of the signals provided to the input terminals of the transmission lines L₁ to L_M during the next iteration cycle k+1:

$\begin{array}{cc}{p\left(k+1\right)}_i=\frac{1}{{\mathrm{Sn}\left(k\right)}_i}·{p\left(k\right)}_i& \left(11\right)\end{array}$

Before the determined transmit power levels are used for providing signals to the transmission lines L₁ to L_M, the vector p(k+1) may be scaled:

$\begin{array}{cc}\hat{p}\left(k+1\right)=p\left(k+1\right)·\frac{p_{\max }}{\max \left(p\left(k+1\right)\right)}& \left(12\right)\end{array}$

In equation (12) max(p(k+1)) denotes the maximum component of the vector p(k+1). The scaled vector {circumflex over (p)}(k+1) is used for providing signals to the transmission lines L₁ to L_M at the iteration cycle k+1.

The following example shows the behavior of the method I. The simulated network comprises 20 transmission lines L₁ to L₂₀. The lengths of the transmission lines L₁ to L₂₀ are evenly distributed between 100 m and 500 m. Both FEXT disturbances and alien disturbances are considered.

FIG. 4 illustrates the convergence of the applied iterative method. In FIG. 4 a difference d(k) is plotted versus the iteration index k. The difference d(k) is the difference between the maximum logarithmic signal-to-noise ratio and the minimum logarithmic signal-to-noise ratio measured at each iteration cycle k:

d(k)=max(Sndb(k))−min(Sndb(k))   (13)

The upper diagram of FIG. 4 shows the difference d(k) on a linear scale, whereas the lower diagram of FIG. 4 shows the difference d(k) on a logarithmic scale. It can be seen from FIG. 4 that the difference d(k) between the maximum logarithmic signal-to-noise ratio and the minimum logarithmic signal-to-noise ratio becomes smaller than 0.1 dB after 3 iteration cycles, which means that the logarithmic signal-to-noise ratios measured at the output terminals of the transmission lines L₁ to L₂₀ have sufficiently converged at this point in time.

FIG. 5 shows a plot of the transmit power level p versus the length l of the transmission lines and a plot of the resulting logarithmic signal-to-noise ratios Sndb versus the length l in the presence of FEXT and alien noise. Data illustrated by circles were recorded when the maximum power level p_max was used for providing signals to the transmission lines L₁ to L₅₀. Data illustrated by asterisks were recorded after the iterative method described above had reached convergence (k=k_max). It is evident from FIG. 5 that performing the iterative method I results in a convergence of the signal-to-noise ratios of all transmission lines.

Since the method I improves the signal-to-noise ratios of longer transmission lines especially if FEXT is the dominant source of interference, it is interesting to know a measure of the presence of FEXT compared to alien noise. Such a measure is given by a variable η:

$\begin{array}{cc}\eta =\frac{a}{b}& \left(14\right)\end{array}$

In equation (14) variables a and b are introduced. The variables a and b are defined as follows:

a=max(Sndb(1))−min(Sndb(k_max))   (15)

b=max(Sndb(1))−min(Sndb(1))   (16)

In equations (15) and (16) the terms max(Sndb(1)) and min(Sndb(1)) denote the maximum and minimum components of the vector Sndb at k=1, respectively, when signals are provided to the transmission lines at the maximum power level. The term min(Sndb(k_max)) denotes the maximum component of the vector Sndb when the iterative method I has reached sufficient convergence meaning min(Sndb(k_max))≈max(Sndb(k_max)). The definitions of the variables a and b are also illustrated in FIG. 6.

If FEXT does not occur, the variable η is one. The higher the presence of FEXT, the more the variable η decreases.

Description of a Method II:

In the following an iterative method II, according to one embodiment is described which improves the signal-to-noise ratios of the shorter transmission lines compared to the iterative method I described above. The improvement is achieved by successively increasing the transmit power levels of the signals provided to the transmission lines L₁ to L_M−1 until the logarithmic signal-to-noise ratio obtained from at least one transmission line, which is usually the longest transmission line L_M, falls below a predetermined threshold value Sndb_min. The transmit power level of the signals provided to the longest transmission line L_M is kept constant.

Before starting the iterative method II transmit power levels {tilde over (p)}(0)_i (i=1, . . . , M) must be known, which, when used for providing signals to the transmission lines L₁ to L_M, produce equal logarithmic signal-to-noise ratios at the output terminals of the transmission lines L₁ to L_M. For example, the transmit power levels {tilde over (p)}(0)_i are given by the transmit power levels p(k_max)_i, which are obtained in the final iteration cycle k_max of the iterative method I, which produced an equal logarithmic signal-to-noise ratio Sndb(k_max)_i for all transmission lines L₁ to L_M.

Starting from the transmit power levels {tilde over (p)}(0)_i, the transmit power levels are successively increased at each iteration cycle until the logarithmic signal-to-noise ratio measured at the output terminal of at least one transmission line L_i is reduced by more than a predetermined parameter Δdb compared to the logarithmic signal-to-noise ratio Sndb(k_max)_i.

According to one embodiment, before starting the iterative method II it is verified whether Δdb<b−a. If this inequality is false, the maximum power level p_max may be chosen for all of the transmission lines L₁ to L_M and the iterative method II is not performed any further. If the inequality is true, the iterative method II is started.

The iteration cycles of the method II are denoted with {tilde over (k)} (=1, 2, . . . ). At the beginning of each iteration cycle signals are provided to the input terminals of the transmission lines L₁ to L_M. The signals are received at the output terminals of the transmission lines L₁ to L_M and the logarithmic signal-to-noise ratios Sndb({tilde over (k)})_i are measured for each signal. The transmit power levels {tilde over (p)}({tilde over (k)}) for each iteration cycle {tilde over (k)} are given by the following equations:

$\begin{array}{cc}\tilde{p}\left(\tilde{k}\right)=\left[\begin{array}{c}{\tilde{p}\left(\tilde{k}\right)}_1\\ {\tilde{p}\left(\tilde{k}\right)}_2\\ ⋮\\ {\tilde{p}\left(\tilde{k}\right)}_M\end{array}\right]& \left(17\right)\end{array}$

{tilde over (p)}({tilde over (k)}+1)={tilde over (p)}({tilde over (k)})·|1−{tilde over (g)}·{tilde over (d)}({tilde over (k)})|  (18)

{tilde over (p)}(0)=p(k_max)   (19)

In equation (19) {tilde over (g)} is a predetermined constant, which influences the convergence of the method, and {tilde over (d)}({tilde over (k)}) is a vector of functions {tilde over (F)} of the transmit power levels {tilde over (p)}({tilde over (k)})_i, which will be discussed in more detail later:

$\begin{array}{cc}{\tilde{d}\left(\tilde{k}\right)}_i=\tilde{F}\left(\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}\right)& \left(20\right)\end{array}$

Before the transmit power levels {tilde over (p)}({tilde over (k)}+1)_i are used for providing signals to the transmission lines L₁ to L_M, the vector {tilde over (p)}({tilde over (k)}+1) may be scaled:

$\begin{array}{cc}\hat{\tilde{p}}\left(\tilde{k}+1\right)=\tilde{p}\left(\tilde{k}+1\right)·\frac{p_{\max }}{\max \left(\tilde{p}\left(\tilde{k}+1\right)\right)}& \left(21\right)\end{array}$

In equation (21) max({tilde over (p)}({tilde over (k)}+1)) denotes the maximum component of the vector {tilde over (p)}({tilde over (k)}+1). The scaled vector

$\hat{\tilde{p}}\left(\tilde{k}+1\right)$

is used for transmitting signals during the iteration cycle {tilde over (k)}+1 over the transmission lines L₁ to L_M. Scaling causes the transmit power level {tilde over ({circumflex over (p)}({tilde over (k)}+1)_M of the longest transmission line L_M to be constant.

According to a further embodiment, the vector {tilde over (p)}({tilde over (k)}+1) of equation (18) is shifted once more:

$\begin{array}{cc}\widetilde{\stackrel{~}{p}}\left(\tilde{k}+1\right)=\tilde{p}\left(\tilde{k}+1\right)-\widetilde{\stackrel{~}{g}}·\tilde{d}\left(\tilde{k}\right)·p_{\max }& \left(22\right)\end{array}$

In equation (22)

$\widetilde{\stackrel{~}{g}}$

is a predetermined constant. The vector

$\widetilde{\stackrel{~}{p}}\left(\tilde{k}+1\right)$

may be scaled:

$\begin{array}{cc}\widehat{\tilde{\stackrel{~}{p}}}\left(\tilde{k}+1\right)=\widetilde{\stackrel{~}{p}}\left(\tilde{k}+1\right)·\frac{p_{\max }}{\max \left(\widetilde{\stackrel{~}{p}}\left(\tilde{k}+1\right)\right)}& \left(23\right)\end{array}$

The termination condition of the iterative method II is:

min(Sndb({tilde over (k)}_max))<min(Sndb(k_max))−Δdb   (24)

According to equation (24) the iterative method II is terminated or at least interrupted if at least one of the measured logarithmic signal-to-noise ratios at a iteration cycle {tilde over (k)}_max falls below the difference min(Sndb(k_max))−Δdb. In this case the iterative method II is either terminated or it is started again with smaller constants {tilde over (g)} and {tilde over ({tilde over (g)}. For restarting the iterative method II transmit power levels {tilde over (p)}({tilde over (k)}<{tilde over (k)}_max) are used.

In the following a simulation is presented which illustrates an embodiment of the iterative method II. The simulated network is a VDSL network and comprises 25 transmission lines L₁ to L₂₅ in a cable C. The lengths of the transmission lines L₁ to L₂₅ are evenly distributed between 200 m and 700 m. The network is based on a model as shown in FIG. 3. The type of interference is self-FEXT and alien noise. The parameter Δdb is set to 3 dB. For the function {tilde over (F)} (cf. equation (20)) a linear function, an exponential function and a logarithmic function are chosen:

$\begin{array}{cc}\tilde{F}\left(\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}\right)=\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}& \left(25\right)\\ \tilde{F}\left(\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}\right)={100}^{\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}}& \left(26\right)\\ \tilde{F}\left(\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}\right)={\log }_{10}\left(\frac{{\tilde{p}\left(\tilde{k}\right)}_i}{p_{\max }}\right)& \left(27\right)\end{array}$

FIG. 7 shows a plot of the transmit power level p versus the length l of the transmission lines L₁ to L₂₅ and a plot of the resulting logarithmic signal-to-noise ratio Sndb versus the length l in the presence of FEXT and alien noise. The three functions {tilde over (F)} according to equations (25) to (27) were used for the simulation. It is evident from FIG. 7 that performing the iterative method II results in better logarithmic signal-to-noise ratios for shorter transmission lines, whereas the signal-to-noise ratios of the longer transmission lines are only slightly decreased.

So far, methods I and II for determining transmit power levels for a single frequency channel were discussed. In order to adjust the total power spectrum density of all modems, the described iterative methods I and II may be performed for all frequency channels. For that, signals of different frequency channels can be transmitted over the transmission lines concurrently.

Description of a Method III:

In the following, a method III serving as a further embodiment is presented, an aim of which is to increase the bit rates of the longer transmission lines at the cost of reducing the bit rates of the shorter transmission lines. In this embodiment, the maximum transmit power P_max of each of the transmission lines L₁ to L_M is pre-determined. The maximum transmit power P_max is evenly distributed over the frequency channels used for transmitting signals over the transmission line L_i (i=1, . . . , N). If the number of the frequency channels used for transmitting signals over the transmission line L_i is N_i, then the maximum power spectral density or the maximum transmit power level p_max,i for each frequency channel is:

$\begin{array}{cc}{p}_{\max ,i}=\frac{P_{\max }}{N_i}& \left(28\right)\end{array}$

Furthermore, the maximum transmit power level p_max,i may also be selected among the value of equation (28) and a pre-determined value PSD_max of the maximum power spectral density:

$\begin{array}{cc}{p}_{\max ,i}=\min \left\{\frac{P_{\max }}{N_i},{\mathrm{PSD}}_{\max }\right\}& \left(29\right)\end{array}$

The method III described in the following aims to determine the optimal number N_opt,1 to N_opt,N of frequency channels (or transmission channels) used for the transmission over the transmission lines L₁ to L_M, respectively. In a first step of the method III, the number N_opt,M of frequency channels used for the longest transmission line L_M is determined. For this purpose, the method I, which has been described above, is carried out in order to determine the transmit power levels p₁ to p_M for signals provided to the input terminals of the transmission lines L₁ to L_M so that the signals received at the output terminals of the transmission lines L₁ to L_M exhibit equal signal-to-noise ratios Sn₁ to Sn_M. The method I is carried out for several frequency channels n (n=1, . . . , N_max) and for each frequency channel n a common signal-to-noise ratio Sn_n is detected for the transmission lines L₁ to L_M. By using the following equation, the channel capacity R can be calculated, which is the sum of the channel capacities of the frequency channels n=1 to n=N_max, wherein the channel capacity of the frequency channel n is the number of bits (or the amount of discrete information) that can be transmitted per unit time (or per data symbol) over the frequency channel n:

$\begin{array}{cc}R=\sum _{n=1}^{N_{\max }}\left({\log }_2\left(1+\frac{{\mathrm{Sn}}_n}{{\mathrm{Sn}}_{\mathrm{ref}}}\right)\right)\mathrm{bit}& \left(30\right)\end{array}$

Sn_ref is a reference signal-to-noise ratio, which may be adjusted, for example, depending on the wanted bit error rate, the margins and the coding gain. For the calculation of equation (30) only those summands may be considered that exhibit at least one bit. The maximum number of bits of each of the summands may be pre-determined, for example 15 bit.

Equation (30) has a maximum depending on the number N_max of frequency channels n. The number N_max, at which the channel capacity R of equation (30) reaches its maximum, is determined and is denoted as N_opt,M. The number N_opt,M defines the number of frequency channels used for transmitting signals over the longest transmission line L_M. The maximum transmit power level p_opt,M for each of the frequency channels of the longest transmission line L_M is:

$\begin{array}{cc}{P}_{\mathrm{opt},M}=\frac{P_{\max }}{N_{\mathrm{opt},M}}& \left(31\right)\end{array}$

In FIG. 8 two frequency ranges FR₁ and FR₂ are shown, in which data transmission over the transmission lines L₁ to

L_M is allowed according to the used transmission service, for example VDSL. The frequency ranges FR₁ and FR₂ are divided into frequency channels n and each frequency channel n is associated with a carrier frequency. Exemplarily the number N_opt,M of frequency channels is shown where equation (30) has a peak when considering transmission lines L₁ to L_M.

After having determined the optimal number N_opt,M of frequency channels for the longest transmission line L_M, the method II, which has been described above, may be carried out. For that, an appropriate parameter Δdb and a function {tilde over (F)} are selected. As a result the N_opt,M frequency channels used for the longest transmission line L_M exhibit all together the maximum transmit power P_max, whereas the transmit powers of the other transmission lines L₁ to L_M−1 are smaller than the maximum transmit power P_max.

In a second step of method III, the number N_opt,M−1 of the frequency channels used for the second longest transmission line L_M−1 is determined. For this purpose, the method steps described above for the longest transmission line L_M may be carried out analogously for the second longest transmission line L_M−1. For that, the longest transmission line L_M is no longer considered. This means that method I is carried out in order to determine the transmit power levels p₁ to p_M−1 for signals provided to the input terminals of the transmission lines L₁ to L_M−1 so that the signals received at the output terminals of the transmission lines L₁ to L_M−1 exhibit equal signal-to-noise ratios Sn₁ to Sn_M−1. Further, the number N_max, at which the channel capacity R of equation (30) reaches its maximum, is determined by varying the number of frequency channels and is denoted as N_opt,M−1. The number N_opt,M−1 defines the number of frequency channels used for transmitting signals over the second longest transmission line L_M−1 as schematically illustrated in FIG. 8. The number N_opt,M−1 may be larger than the number N_opt,M. The maximum transmit power level p_opt,M−1 for each of the frequency channels of the second longest transmission line L_M−1 is:

$\begin{array}{cc}{p}_{\mathrm{opt},M-1}=\frac{P_{\max }}{N_{\mathrm{opt},M-1}}& \left(32\right)\end{array}$

After having determined the optimal number N_opt,M−1 of frequency channels for the second longest transmission line L_M−1, the method II may be carried out as described above. As a result the N_opt,M−1 frequency channels used for the second longest transmission line L_M−1 exhibit all together the maximum transmit power P_max, whereas the transmit powers of the remaining transmission lines L₁ to L_M−2 are smaller than the maximum transmit power P_max.

In a third and in subsequent steps of method III, the number N_opt,M−2 of the frequency channels used for the third longest transmission line L_M−2 and the number N_opt,M−3 to N_opt,1 of the frequency channels used for the other transmission lines L_M−3 to L₁ may be determined. For this purpose, the method steps described above may be carried out analogously for the transmission lines L_M−2 to L₁.

Each step of method III leads to a number N_opt,i of frequency channels used for transmitting signals over the longest transmission line L_i, which is considered in the corresponding method step. The method III may be continued in the described manner until either all of the transmission lines exhibit the maximum transmit power P_max or until all of the frequency channels n of the available frequency range FR₁ and FR₂ have been used. In the latter case, the remaining transmission lines do not exhibit the maximum transmit power P_max.

Instead of classifying the transmission lines L₁ to L_M according to their lengths, the transmission lines L₁ to L_M may be classified according to their logarithmic signal-to-noise ratios SndB. In this case the transmission line L_M shows the lowest logarithmic signal-to-noise ratio, the transmission line L_M−1 shows the second lowest logarithmic signal-to-noise ratio etc.

Description of a Method IV:

In the following, a method IV is presented for determining crosstalk transfer functions H_{ji, i≠j} caused by FEXT and interfering signals r caused by alien noise. The transfer functions H_ii may be determined by using a common method known to a person skilled in the art. The transfer functions H_ii and H_{ji, i≠j} as well as the interfering signals r may be used to determine the signal-to-noise ratios Sn_i and Sndb_i according to equations (2) and (3). In case there is no interference between different frequency channels, such as in DMT transmission systems, the transfer functions H_{ji, i≠j} and the interfering signals r may be determined separately for each frequency channel. In the following the method IV is therefore described for only one frequency channel, but may be applied to other frequency channels as well.

The interference channel model shown in FIG. 3 may be extended by adding equalizers EQ₁ to EQ_M and deciders D₁ to D_M as illustrated in FIG. 9. The equalizers EQ₁ to EQ_M multiply the received signals with the inverses 1/H′₁₁ to 1/H′_MM of the transfer functions H′₁₁ to H′_MM, respectively. The interference channel model of FIG. 9 may be rearranged by integrating the equalizers EQ₁ to EQ_M into the transfer functions H′_ii and H′_{ji, i≠j}, which results in an interference channel model as shown in FIG. 10. In this interference channel model all transfer functions H_ii are 1. Further, the power of the interfering signals r caused by alien noise needs to be weighted:

$\begin{array}{cc}r_i^2=\frac{1}{H_{\mathrm{ii}}}·r_i^{\mathrm{\prime 2}}& \left(33\right)\end{array}$

Moreover, equation (1) has to be adapted:

$\begin{array}{cc}{y}_i=u_i+\sum _{j=1,j\ne i}^Mu_j·H_{\mathrm{ji}}+r_i,& \left(34\right)\end{array}$

wherein the signals u₁ to u_M are the output signals of the deciders D₁ to D_M, respectively.

For the determination of the FEXT transfer functions H_{ji, i≠j} a linear system of equations can be established. For i=1 the following equation is obtained:

$\begin{array}{cc}\left[\begin{array}{c}{y}_1\left(1\right)-u_1\left(1\right)\\ y_1\left(2\right)-u_1\left(2\right)\\ ⋮\\ y_1\left(L\right)-u_1\left(L\right)\end{array}\right]=\left[\begin{array}{cccc}{u}_2\left(1\right)& u_3\left(1\right)& \cdots & u_M\left(1\right)\\ u_2\left(2\right)& u_3\left(2\right)& \cdots & u_M\left(2\right)\\ ⋮& ⋮& & ⋮\\ u_2\left(L\right)& u_3\left(L\right)& \cdots & u_M\left(L\right)\end{array}\right]·\left[\begin{array}{c}{H}_{21}\\ H_{31}\\ ⋮\\ H_{M1}\end{array}\right]& \left(35\right)\end{array}$

In equation (35) 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 (35) may be rewritten as:

Δy₁=U₁·H₁   (36)

This system of linear equations may be solved by using a least mean square algorithm:

H ₁=(U₁^*TU₁)⁻¹·(U₁^*T·Δy₁)=Q⁻¹·b   (37)

Q=(U₁^*T·U₁)   (38)

b=U ₁ ^*T ·y ₁   (39)

In equation (37) 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.

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

$\begin{array}{cc}{q}_{\mathrm{\nu \mu }}=\sum _{k=1}^LU_{\nu +1}^{*}\left(k\right)·U_{\mu +1}\left(k\right)& \left(40\right)\\ b_{\nu }=\sum _{k=1}^LU_{\nu +1}^{*}\left(k\right)·\Delta y_1\left(k\right)& \left(41\right)\end{array}$

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)   (42)

q _νμ(λ)=q_νμ(λ−1)+U_ν+1*(λ)·U_μ+1(λ)   (43)

for λ=2, 3, . . . , L and ν, μ=1, 2, . . . , M−1

b _ν(1)=U_ν+1*(1)·Δy₁(1)   (44)

b _ν(λ)=b_ν(λ−1)+U_ν+1*(λ)·Δy₁(λ)   (45)

for λ=2, 3, . . . , L and ν, μ=1, 2, . . . , M−1

During a first test interval, the M−1 elements of the first column of the transmission matrix Ĥ comprising the transfer functions H_ji can be calculated as described above. The other columns of the matrix Ĥ are calculated accordingly. FIG. 11 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.

During a second test interval, the matrix Ĥ may be used to determine the noise power of the alien signals, which is schematically illustrated in FIG. 12. For this purpose, the signals u outputted by the decider D are weighted by the matrix Ĥ so that signals y′ are obtained. The vector Δr, which is the difference between the signals y and y′, is a measure of the alien noise. The mean square of the vector Δr gives the alien noise power pr_i. The signal-to-noise power Sn_i of the transmission line L_i may be calculated as follows:

$\begin{array}{cc}{\mathrm{Sn}}_i=\frac{p_i}{\sum _{j=1,j\ne i}^Mp_j·{H_{\mathrm{ji}}}^2+{\mathrm{pr}}_i}& \left(46\right)\end{array}$

Description of Simulation Results:

In the following a simulation is presented which illustrates the methods described above. The simulated network is a VDSL network and comprises 25 transmission lines L₁ to L₂₅ of the type AWG 24. The lengths of the transmission lines L₁ to L₂₅ are evenly distributed between 300 m and 800 m. FIG. 13 shows the line attenuation over frequency for the shortest transmission line L₁ and the longest transmission line L₂₅ and also the allowed frequency ranges FR₁ and FR₂ for upstream transmission.

The simulation is carried out for data transmission in the upstream direction (from the transceivers RT₁ to RT_M to the central office CO). The network is based on a model as shown in FIG. 3. FIG. 14 shows the minimum and maximum FEXT attenuation. Reflections at the terminations of the cables are considered as can be seen from the periodic parts of FIG. 14. All interference signals caused by alien noise have the same power level. The alien noise is superimposed by an additional white noise signal having a power spectral density of −140 dBm/Hz. The maximum transmit power P_max of each of the transmission lines L₁ to L₂₅ is 13.5 dBm. The power spectral density is not limited.

FIGS. 15 and 16 illustrate the results of the simulation. The transmit power for each of the transmission lines L₁ to L₂₅ are shown in FIG. 15. The bit rates of the transmission lines L₁ to L₂₅ are shown in FIG. 16. Data illustrated by asterisks were recorded using the method III, whereas data illustrated by circles were recorded using method II. Data illustrated by plus signs were recorded when signals were transmitted over all transmission lines L₁ to L₂₅ having the maximum transmit power. It can be seen from FIG. 15 that when performing the method III the transmission lines having a length above 530 m use the full maximum transmit power P_max of 13.5 dBm, whereas the shorter transmission lines have smaller transmit powers.

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.

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.

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 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.

Claims

1. A method, comprising: selecting a first number of transmission channels from a plurality of transmission channels for a first number of transmission links, wherein the selection depends on channel capacities of the first number of transmission channels; andselecting a second number of transmission channels from the plurality of transmission channels for a second number of transmission links, wherein the selection depends on channel capacities of the second number of transmission channels.

2. The method of claim 1, wherein: the first number of transmission channels is selected such that a sum of the channel capacities of the first number of transmission channels is maximized, orthe second number of transmission channels is selected such that a sum of the channel capacities of the second number of transmission channels is maximized.

3. The method of claim 1, wherein the second number of transmission channels is greater than the first number of transmission channels.

4. The method of claim 1, wherein the second number of transmission links is smaller than the first number of transmission links.

5. The method of claim 1, wherein the second number of transmission links comprises the first number of transmission links except one transmission link, the excluded link comprising the transmission link of the first number of transmission links having the lowest signal-to-noise ratio.

6. The method of claim 1, wherein the second number of transmission links comprises the first number of transmission links except one transmission link, the excluded link comprising the transmission link of the first number of transmission links having the longest length.

7. The method of claim 1, wherein the transmission links comprise hard-wired transmission lines.

8. The method of claim 1, wherein for each of the transmission links a maximum transmit power is pre-determined.

9. The method of claim 1, wherein the channel capacity of each of the transmission channels depends on signal-to-noise ratios of signals transmitted over the respective transmission channel.

10. The method of claim 1, wherein transmit power levels of signals transmitted over the transmission links are adjusted such that signals transmitted over the same transmission channel have the same signal-to-noise ratio after transmission.

11. The method of claim 1, wherein for each of the transmission channels a single signal-to-noise ratio is used to determine the channel capacity of the respective transmission channel.

12. A method, comprising: selecting a first number of transmission channels from a plurality of transmission channels, wherein the selection depends on signal-to-noise ratios of signals transmitted over a first number of transmission links; andselecting a second number of transmission channels from the plurality of transmission channels, wherein the selection depends on signal-to-noise ratios of signals transmitted over a second number of transmission links.

13. The method of claim 12, wherein: for each of the transmission channels a single signal-to-noise ratio is used to select the first number of transmission channels, orfor each of the transmission channels a single signal-to-noise ratio is used to select the second number of transmission channels.

14. The method of claim 12, wherein transmit power levels of signals transmitted over the transmission links are adjusted such that signals transmitted over the same transmission channel have the same signal-to-noise ratio after transmission.

15. A device, comprising: a first selection circuit configured to select a first number of transmission channels from a plurality of transmission channels for a first number of transmission links, wherein the selection depends on channel capacities of the first number of transmission channels; anda second selection circuit configured to select a second number of transmission channels from the plurality of transmission channels for a second number of transmission links, wherein the selection depends on channel capacities of the second number of transmission channels.

16. The device of claim 15, wherein: the first selection unit selects the first number of transmission channels such that a sum of the channel capacities of the first number of transmission channels is maximized, orthe second selection unit selects the second number of transmission channels such that a sum of the channel capacities of the second number of transmission channels is maximized.

17. The device of claim 15, wherein the second number of transmission links comprises the first number of transmission links except one transmission link, the excluded link comprising the transmission link of the first number of transmission links having the lowest signal-to-noise ratio.

18. The device of claim 15, wherein the second number of transmission links comprises the first number of transmission links except one transmission link, the excluded link comprising the transmission link of the first number of transmission links having the longest length.

19. The device of claim 15, wherein the channel capacity of each of the transmission channels depends on signal-to-noise ratios of signals transmitted over the respective transmission channel.

20. The device of claim 15, further comprising an adjustment circuit configured to adjust transmit power levels of signals transmitted over the transmission links such that signals transmitted over the same transmission channel have the same signal-to-noise ratio after transmission.

21. The device of claim 15, wherein for each of the transmission channels a single signal-to-noise ratio is used to determine the channel capacity of the respective transmission channel.

22. A device, comprising: a first selection circuit configured to select a first number of transmission channels from a plurality of transmission channels, wherein the selection depends on signal-to-noise ratios of signals transmitted over a first number of transmission links; anda second selection circuit configured to select a second number of transmission channels from the plurality of transmission channels, wherein the selection depends on signal-to-noise ratios of signals transmitted over a second number of transmission links.

23. The device of claim 22, wherein: for each of the transmission channels a single signal-to-noise ratio is used to select the first number of transmission channels, orfor each of the transmission channels a single signal-to-noise ratio is used to select the second number of transmission channels.

24. The device of claim 22, further comprising an adjustment circuit configured to adjust transmit power levels of signals transmitted over the transmission links such that signals transmitted over the same transmission channel have the same signal-to-noise ratio after transmission.