Method and apparatus for transmitting data in differential and phantom mode in vectoring DSL

Abstract

A transmitter device 16 for transmitting data to a plurality of receiver devices 51, 52, 53, each of which is connected to the transmitter device via at least one respective pair of wires 21, 22, 23, each receiver device being operable to receive signals detected as a change over time in the potential difference across the local ends of each respective pair of wires extending between the receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the plurality of receiver devices in a plurality of different modes, over a plurality of different channels, the different modes including phantom and differential modes and the different channels including a first set of phantom channels, the transmitter comprising a phantom channel selector 1690 for selecting a second set of one or more phantom channels from the first set, the second set being a proper subset of the first set comprising one or more of the phantom channels of the first set, the selection being made in dependence upon the cross-talk coupling between the phantom channels of the first set and the reception of signals at each of the receivers detected as a change over time in the potential difference across the local ends of the respective pair of wires extending between the respective receiver device and the transmitter device; and a connector 1670 for connecting the selected phantom channels to the transmitter such that the transmitter is able to transmit signals from the transmitter onto the phantom channel or channels of the second set of phantom channels.

Claims

1. A method of transmitting data from a transmitter device to a plurality of receiver devices, each of which is connected to the transmitter device via at least one respective pair of wires, each receiver device being operable to receive signals detected as a change over time in the potential difference across the local ends of each respective pair of wires extending between the receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the plurality of receiver devices in a plurality of different modes, over a plurality of different channels, the different modes including phantom and differential modes and the different channels including a first set of phantom channels, the method comprising: selecting a second set of phantom channels from the first set, the second set being a proper subset of the first set comprising one or some of the phantom channels of the first set, the selection being made in dependence upon the cross-talk coupling between the phantom channels of the first set and the reception of signals at each of the receiver devices detected as a change over time in the potential difference across the local ends of the, or each, respective pair of wires extending between the respective receiver device and the transmitter device, and connecting the selected phantom channels to the transmitter device and transmitting signals from the transmitter device onto the phantom channels of the second set of phantom channels.

2. A method according to claim 1 wherein: the selected phantom channels include at least a first single ended phantom mode channel; the signals transmitted by the transmitter device include at least: a first signal transmitted via a first direct differential mode channel to a first receiver device connected to the transmitter device by a first twisted metallic pair over which the first signal is carried; a second signal transmitted via a second direct differential mode channel to a second receiver device connected to the transmitter device by a second twisted metallic pair over which the second signal is carried; and a phantom signal transmitted via the first single ended phantom mode channel and received by both the first and the second receiver devices in the differential mode; and the phantom signal comprises a weighted summation of the first and second signals, the weighting being made in accordance with a set of weighting values calculated in dependence upon measurements or estimations of the extent of mode conversion coupling between the single ended phantom channel and the first and second direct differential mode channels as detected by the first and second receiver devices respectively.

3. A method according to claim 2 wherein the first signal is generated in dependence upon: user data to be transmitted to the first receiver device; channel estimations of the first direct differential mode channel; channel estimations of the indirect channel between the transmitter device and the first receiver via the second direct differential mode channel; channel estimations of the extent of mode conversion coupling between the single ended phantom channel and the first direct differential mode channel as detected by the first receiver; and at least some of the weighting values.

4. A method according to claim 2 wherein at least some of the weighting values take values intermediate between zero and one.

5. A method according to claim 1 wherein the transmitter device transmits a single common signal over plural channels between the transmitter device and the receiver devices, the plural channels including the second set of phantom channels, and wherein a multiple access technique is used to provide overlaid virtual channels by which different data is directed to different ones of the receiver devices.

6. Processor implementable instructions for causing a processor to carry out the method of claim 1 during execution of the instructions.

7. A non-transitory computer readable medium storing processor implementable instructions which upon execution by a computer perform the method of claim 1.

8. A transmitter device for transmitting data to a plurality of receiver devices, each of which is connected to the transmitter device via at least one respective pair of wires, each receiver device being operable to receive signals detected as a change over time in the potential difference across the local ends of each respective pair of wires extending between the receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transceiver device and the plurality of receiver devices in a plurality of different modes, over a plurality of different channels, the different modes including phantom and differential modes and the different channels including a first set of phantom channels, the transmitter device comprising: a phantom channel selector for selecting a second set of phantom channels from the first set, the second set being a proper subset of the first set comprising one or some of the phantom channels of the first set, the selection being made in dependence upon the cross-talk coupling between the phantom channels of the first set and the reception of signals at each of the receiver devices detected as a change over time in the potential difference across the local ends of the respective pair of wires extending between the respective receiver device and the transmitter device; and a connector for connecting the selected phantom channels to the transmitter device such that the transmitter device is able to transmit signals from the transmitter device onto the phantom channels of the second set of phantom channels.

9. A transmitter device according to claim 8, wherein: the selected phantom channels include at least a first single ended phantom mode channel; the transmitter device is operable to transmit at least the following signals: a first signal transmitted via a first direct differential mode channel to a first receiver device connected to the transmitter device by a first twisted metallic pair over which the first signal is carried; a second signal transmitted via a second direct differential mode channel to a second receiver device connected to the transmitter device by a second twisted metallic pair over which the second signal is carried; and a phantom signal transmitted via the first single ended phantom mode channel and received by both the first and the second receiver devices in the differential mode; and the transmitter device is further operable to generate the phantom signal as a weighted summation of the first and second signals, the weighting being made in accordance with a set of weighting values calculated in dependence upon measurements or estimations of the extent of mode conversion coupling between the single ended phantom channel and the first and second direct differential mode channels as detected by the first and second receiver devices respectively.

10. A phantom channel connector for connecting a transmitter device to a selected set of phantom channels carried over a plurality of pairs of wires extending between the transmitter device and a plurality of receiver devices, the phantom channel connector comprising: a phantom channel selection signal receiver for receiving a phantom channel selection signal specifying a set of one or more phantom channels, the set of selected phantom channels comprising a subset of the total number of possible phantom channels to which the connector is operable to connect to the transmitter device, a set of one or more pairs of input terminals, each pair of input terminals being operable to receive a transmission signal for transmission over an associated selected phantom channel; a switch arrangement; and a plurality of phantom mode driving couplers for electrically coupling a voltage signal output from the switching arrangement to a plurality of pairs of wires in a manner suitable for driving a phantom mode signal over the pairs of wires; wherein the switching arrangement is operable to selectively couple the or each of one or more of the input terminals to any one of at least a plurality of the output terminals in dependence upon the received phantom channel selection signal such that, in use, a transmission signal applied to a pair of input terminals is capable of being transmitted over a selected phantom channel in dependence upon the received phantom channel selection signal.

11. A phantom channel connector according to claim 10 wherein the driving couplers comprise centre tap connections to an inductor or transformer connected to one of the plurality of pairs of wires at the transmitter device end of the wires.

12. A phantom channel selector device which is operable to select, from a first set of possible phantom channels, a second set of selected phantom channels, the second set being a proper subset of the first set of phantom channels, the second set comprising one or more phantom channels carried over a plurality of pairs of wires, each of which extends between a transmitter device and one of a plurality of receiver devices, on to each of which selected phantom channel to transmit a transmission signal or signals, the phantom channel selector device comprising: a coupling data receiver for receiving receiver signal reception data and/or cross channel coupling data; a selection interface for communicating a phantom channel selection signal or message to a phantom channel connector, and a processor arranged to generate a phantom channel selection for communication to the phantom channel connector within the phantom channel selection signal or message in dependence upon the received signal reception data and/or cross channel coupling data, the phantom channel selection being made in dependence upon the cross-talk coupling between the phantom channels of the first set and the reception of signals at each of the receiver devices detected as a change over time in the potential difference across the local ends of the, or each, respective pair of wires extending between the respective receiver device and the transmitter device, wherein the phantom channel selection corresponds to the second set of phantom channels.

13. A transmitter device for transmitting data to a plurality of receiver devices, each of which is connected to the transmitter device via at least one respective pair of wires, each receiver device being operable to receive signals detected as a change over time in the potential difference across the local ends of each respective pair of wires extending between the receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transceiver device and the plurality of receiver devices in a plurality of different modes, over a plurality of different channels, the different modes including phantom and differential modes and the different channels including a first set of phantom channels, the transmitter device comprising: a processing system including a non-transitory computer readable medium storing instructions and at least one computer processor executing the instructions so that the processing system is configured to at least perform: a phantom channel selection which selects a second set of phantom channels from the first set, the second set being a proper subset of the first set comprising one or some of the phantom channels of the first set, the selection being made in dependence upon the cross-talk coupling between the phantom channels of the first set and the reception of signals at each of the receiver devices detected as a change over time in the potential difference across the local ends of the respective pair of wires extending between the respective receiver device and the transmitter device; and a connection which connects the selected phantom channels to the transmitter device such that the transmitter device is able to transmit signals from the transmitter device onto the phantom channels of the second set of phantom channels.

14. A transmitter device according to claim 13 wherein: the selected phantom channels include at least a first single ended phantom mode channel; the transmitter device is operable to transmit at least the following signals: a first signal transmitted via a first direct differential mode channel to a first receiver device connected to the transmitter device by a first twisted metallic pair over which the first signal is carried; a second signal transmitted via a second direct differential mode channel to a second receiver device connected to the transmitter device by a second twisted metallic pair over which the second signal is carried; and a phantom signal transmitted via the first single ended phantom mode channel and received by both the first and the second receiver devices in the differential mode; and the transmitter device is further operable to generate the phantom signal as a weighted summation of the first and second signals, the weighting being made in accordance with a set of weighting values calculated in dependence upon measurements or estimations of the extent of mode conversion coupling between the single ended phantom channel and the first and second direct differential mode channels as detected by the first and second receiver devices respectively.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In order that the present invention may be better understood, embodiments thereof will now be described with reference to the accompanying drawings in which:

(2) FIG. 1 is a schematic illustration of an example broadband connection deployment showing a Distribution Point Unit (DPU) and two customer premises having associated Customer Premises Equipment (CPE) modems connected to the DPU via respective Twisted Metallic Pair (TMP) connections;

(3) FIG. 2 is a schematic block diagram illustrating the principal components in a modem to modem connection operating in accordance with a first embodiment of the present invention;

(4) FIG. 3 is a schematic block diagram of the Multiple Phantom Access Device (MPAD) of FIG. 2, illustrating the device in greater detail;

(5) FIG. 4 is a schematic block diagram similar to FIG. 3, illustrating an alternative Multiple Phantom Access Device (MPAD) which is suitable for use with four rather than three wire pairs; and

(6) FIG. 5 is a graph illustrating an example pareto front for a simple case concerning selecting optimal phantom channels for use in assisting two different wire pairs/receivers.

SPECIFIC DESCRIPTION OF EMBODIMENTS

(7) FIG. 1 illustrates in overview an example broadband deployment in which embodiments of the present invention could be employed. As shown in FIG. 1, the example deployment comprises a Distribution Point Unit (DPU) 10 which is connected to three user premises 31, 32, 33 (which in this example are flats within a single house 30) via respective Twisted Metallic Pair (TMP) connections 21, 22, 23 which connect between an Access Node (AN) 16 (e.g. a Digital Subscriber Line Access Multiplexor (DSLAM)) within the DPU 10 and respective Customer Premises Equipment (CPE) modems 51, 52 via respective network termination points 41, 42 within the respective customer premises 31, 32. The DPU 10 additionally includes an Optical Network Termination (ONT) device 14 which provides a backhaul connection from the DPU 10 to a local exchange building via an optical fibre connection such as a Passive Optic-fibre Network (PON) and a controller 12 which coordinates communications between the AN 16 and the ONT 14 and which may perform some management functions such as communicating with a remote Persistent Management Agent (PMA).

(8) As will be apparent to a person skilled in the art, the illustrated deployment involving an optical fibre backhaul connection from a distribution point and a twisted metallic pair connection from the distribution point to the customers premises is exactly the sort of deployment for which the G.FAST standard is intended to be applicable. In such a situation, the TMP connections may be as short as a few hundred meters or less, for example possibly a few tens of meters only and because of this it is possible to use very high frequency signals (e.g. up to a few hundred Megahertz) to communicate over the short TMP's because the attenuation of high frequency signals is insufficient to prevent them from carrying useful information because of the shortness of the lines. However, at such high frequencies cross-talk becomes a significant issue. This is clearly especially going to be the case where the cross-talking lines travel alongside each other for part of their extent (as in the situation is illustrated in FIG. 1); however, cross-talk is still an issue at high frequencies (e.g. over 80 MHz) even where the lines only lie close to one another for a very small portion of their total extent (e.g. just when exiting the DPU 10). G.FAST currently proposes simply using vectoring techniques at all frequencies where there are cross-talking lines in order to mitigate against the cross-talk effects.

(9) In addition, in this scenario, by accessing at the DPU 10 (in particular at the Access Node (AN) 16) phantom channels, it is possible to exploit signals transmitted onto phantom channels which will crosstalk onto the conventional differential mode channels associated with each of the end user receivers (the termination point and CPE modem combinations 41/51, 42/52, 43/53) and change the signals received (compared to a conventional case where the phantom channels are not exploited in this way). Since there are three TMP connections 21-23, there are 3 possible (first order, pure) phantom channels which could be exploited in this way, formed by using the differential voltage signal between: the average voltage of TMP 21 and that of TMP 22; the average voltage of TMP 21 and that of TMP 23; and the average of TMP 22 and that of TMP 23. However, since there is no possible set of two of these possible (first order, pure) phantom channels which does not include at least one common TMP, only one of these can be used at the same time without having non-orthogonal (and hence complexly interfering) phantom channels being used simultaneously. Thus the present embodiment includes a Phantom ChannelMultiple Optimisation Problem device (PC-MOP) which, as is explained in greater detail below, acts to choose a single one out of the three possible phantom channels to usethe selection being performed such as to try to achieve a particular set of two (or more) objectives (e.g. to try to obtain the maximum benefit for two of the three receivers).

(10) Referring now to FIG. 2, there is shown a schematic illustration of the principal components within the AN 16 and CPE modems 51, 52, 53 allowing the indirect phantom channels to be utilised according to a first simple embodiment chosen to illustrate the basic principles of the approach.

(11) As shown, the AN 16 according to the embodiment illustrated in FIG. 2 comprises first, second and third Data Source, Data Encoder and Serial to Parallel converter (DSDESP) modules 1611, 1612 and 1613. These are essentially conventional functions within a DSL modem and will not be further described here except to point out that each one's output is a set of data values d.sub.1-d.sub.M each of which can be mapped to both a set of one or more bits and to a point within a modulation signal constellation associated with a respective tone on which the data value is to be transmitted. For example if a tone t.sub.1 is determined to be able to carry 3 bits of data a corresponding data value will be set to one of 2.sup.3=8 different values (e.g. to a decimal number between 0 and 7) each of which corresponds to a different constellation point within an associated signal constellation having 8 different constellation points. The data values for a single symbol can be thought of as forming a vector of data values (one for each data-carrying tone) and together carry the user data to be transmitted to the end user associated with a respective end user modem 51, 52, 53 together with any overhead data (e.g. Forward Error Correction data etc.).

(12) (N.B. It is worth noting that the assessment of the number of bits which any particular tone for any particular receiver may carry (per symbol) should be done with the benefit of the usage of any assisting phantom mode channels (as discussed below) and the benefit of vectoring taken into account. Thus it should be borne in mind that the present discussion relates to Showtime operation of the system once all training procedures have been completed. In overview the training involves firstly determining which phantom channel (or channels in embodiments in which more than one phantom channel can be exploited at the same timee.g. for embodiments in which more than 3 lines are connected to a common AN and are sufficiently closely cross-talk coupled to make exploitation of the phantoms worthwhile) to use and then setting parameters for its usage. Having determined how to best exploit the phantom channels, then the training continues by performing vectoring training to determine the vectoring parameters to use and then determining the number of bits which can be used with both assistance from the phantom channel(s) and from vectoring.)

(13) The data values leaving each DSDESP module 1611, 1612, 1613 are then passed (in an appropriate order) to respective Multiple bit level Quadrature Amplitude Modulation (M-QAM) modulators 1621, 1622, 1623 which convert each input data value to a respective complex number x.sub.1.sup.1 to x.sub.M.sup.1, x.sub.1.sup.2 to x.sub.M.sup.2 and x.sub.1.sup.3 to x.sub.M.sup.3 each of which represents a complex point within a complex number constellation diagram. For example a data value d.sub.1.sup.1=7 (=111 in binary) might be mapped by the M-QAM modulator 1621 to the complex number 1i for tone 1 where tone 1 has been determined (by say modem 51) to be able to carry 3 bits of data each.

(14) Each of these complex numbers x.sub.1.sup.1 to x.sub.M.sup.1, x.sub.1.sup.2 to x.sub.M.sup.2 and x.sub.1.sup.3 to x.sub.M.sup.3 is then entered into a vectoring precoder module 1630 (which in the present embodiment is a single common vectoring precoder module 1630) which performs a largely conventional vectoring operation in order to precode the transmissions to be sent using a combination of predetermined vectoring coefficients and information about the signals to be transmitted onto the other lines within the relevant vector group in a manner, which is well known to those skilled in the art, to compensate for the expected effects of cross-talk from the other lines in the vector group. The vectoring precoder module differs from a conventional vectoring precoder module in that it is operable to additionally precode the transmissions in such a way as to cause them to be pre-compensated for the expected crosstalk effects produced not only by the neighbouring lines operating in a direct differential mode (as per standard vectoring), but also for the effects of crosstalk coming from any signals being transmitted onto one or more phantom channels (or other channels which are not direct differential mode channels). In order to do this (as will become apparent form the detailed description below) it is necessary for the vectoring precoder module 1630 to receive information about channel estimations of the respective phantom channel(s) (or other channels which are not direct differential mode channels) and also information about any weighting values used to combine signals to be transmitted over the phantom channel(s) (or other channels which are not direct differential mode channels). The output from the vectoring precoder module 1630 is thus a set of further modified complex numbers {circumflex over (x)}.sub.1.sup.1 to {circumflex over (x)}.sub.M.sup.1, {circumflex over (x)}.sub.1.sup.2 to {circumflex over (x)}.sub.M.sup.2 and {circumflex over (x)}.sub.1.sup.3 to {circumflex over (x)}.sub.M.sup.3.

(15) The ability of the vectoring precoder module 1630 to receive the weighting values and channel estimation values which it needs to perform its precoding functions is illustrated in FIG. 2 by the line between the PC-MOP & MICOP & MRC & Management entity module 1690 (which performs general management functions in addition to its specific functions described in greater detail below and for brevity may hereinafter be referred to either as the management entity or the PC-MOP module) and the vectoring precoder module 1630. In the present embodiment, the PC-MOP module calculates appropriate values for the channel estimations and the weighting values required by the vectoring precoder module and the MICOP & MRC precoder module 1640. In order to do this, it needs data reported back to it from the end user modems. The processes and procedures for achieving this are largely conventional and well known to persons skilled in the art and so they are not discussed in great detail herein except to note that it relies on a backward path from the receivers 51, 52, 53 to the transmitter 16. This is achieved in practice, of course, in that the receivers 51, 52, 53 are in practice transceivers capable of receiving and transmitting signals over the TMP's 51, 52, 53 as is the transmitter 16the receiver parts of the transmitter 16 and the transmitter parts of the receivers 51, 52, 53 have simply been omitted from the drawings to avoid unnecessary complication of the figures because these parts are entirely conventional and not directly pertinent to the present invention. Moreover, each of the receivers additionally contains a management entity responsible for performing various processing and communication functions. Any of a number of suitable techniques can be employed for obtaining data useful in generating channel estimations. For example, known training signals can be transmitted onto selected channels by the transmitter 16 during a special training procedure and the results of detecting these by the receivers 51, 52, 53 can be sent back to the transmitter in a conventional manner. Additionally, special synchronisation symbols can be transmitted, interspersed with symbols carrying user data, at predetermined locations within a frame comprising multiple symbols (e.g. at the beginning of each new frame) and the results of attempting to detect these synchronisation symbols can also be sent back to the transmitter to generate channel estimation values. As is known to persons skilled in the art, different synchronisation signals/symbols can be sent over different channels simultaneously and/or at different times etc. so that different channel estimations (including importantly indirect channels and indirect channels can be targeted and evaluated, etc.

(16) As will be appreciated by those skilled in the art, the output of the vectoring precoder module 1630 is a set of modified (or predistorted) complex numbers {hacek over (x)}.sub.1.sup.1 to {hacek over (x)}.sub.M.sup.1, {hacek over (x)}.sub.1.sup.2 to {hacek over (x)}.sub.M.sup.2 and {hacek over (x)}.sub.1.sup.3 to {hacek over (x)}.sub.M.sup.3 as mentioned above. These complex numbers are then passed to a Mixed-Integer Convex Optimisation Problem and Maximal Ratio Combiner (MICOP and MRC) precoder module 1640 (hereinafter referred to as the MICOP and MRC precoder module 1640) which, in the present embodiment, uses weighting values together with channel estimation values provided to it by the PC-MOP module 1690 to calculate, from the modified complex numbers received from the vectoring pre-coder module 1640 (and the weighting values and channel estimation values from the PC-MOP module 1690), further modified (or further pre-distorted) values for the complex numbers to be passed to the IFFTs 1651-1652. Note that in addition to further modifying the received numbers {hacek over (x)}.sub.1.sup.1 to {hacek over (x)}.sub.M.sup.1, {hacek over (x)}.sub.1.sup.2 to {hacek over (x)}.sub.M.sup.2 and {hacek over (x)}.sub.1.sup.3 to {hacek over (x)}.sub.M.sup.3 to generate corresponding further modified complex numbers {umlaut over (x)}.sub.1.sup.1 to {umlaut over (x)}.sub.M.sup.1, {umlaut over (x)}.sub.1.sup.2 to {umlaut over (x)}.sub.M.sup.2 and {umlaut over (x)}.sub.1.sup.3 to {umlaut over (x)}.sub.M.sup.3 which are to form (ultimately) the signals to be used in driving the respective TMPs 21, 22, 23 in direct differential mode, the MICOP and MRC precoder module 1640 additionally generates a new set of complex numbers {umlaut over (x)}.sub.1.sup.4 to {umlaut over (x)}.sub.M.sup.4 which are to form (ultimately) the signals to be used to drive a (single ended) phantom mode channel to be accessed via the MPAD module described below. The precise way in which this is done is described below with reference to appropriate equations. Once these values have been calculated by the MICOP and MRC precoder 1640 they are passed to the respective IFFT modules 1651-1654 (super-script 1 values going to IFFT 1651, superscript 2 values going to IFFT 1652, etc.) and the next two steps of the processing are conventional and not relevant to the present invention. Thus each set of generated values (e.g. {umlaut over (x)}.sub.1.sup.1 to {umlaut over (x)}.sub.M.sup.1 is formed by the respective IFFT module into a quadrature time domain signal in the normal manner in Orthogonal Frequency Division Multiplexing (OFDM)/DMT systems). Then the time domain signals are processed by a suitable Analogue Front End (AFE) module 1661 to 1664 again in any suitable such manner including any normal conventional manner. After processing by the AFE module 1650, the resulting analogue signals are passed to the MPAD module 1670 (note MPAD stands for Multiple Phantom Access device).

(17) The MPAD module is described in greater detail below, but in overview it provides switchable access to centre taps of any of the TMPs such that any of the possible phantom channels associated with the connected lines can be driven by the incoming signal arriving from AFE 1664 as well as directly passing on the signals from AFE's 1661-1663 directly to TMPs 21-23 for driving in the normal direct differential mode.

(18) During transmission over the TMP connections 21, 22, 23 the signals will be modified in the normal way according to the channel response of the channel and due to external noise impinging onto the connections. In particular there will be cross-talking (and most particularly far-end cross-talking) between the three direct channels (the direct channels being one from the transmitter 16 to the modems 41-43 via the TMPs 21-23 and the phantom channel. However, the effect of the precoding is to largely precompensate for the effects of the cross talk. Additionally, the targeted receivers additionally benefit from increased SNR of the received signal destined for them arriving via cross talk from the phantom channel.

(19) After passing over the TMP connections 21, 22, 23 the signals are received by the modems 41-43 at a respective Analogue Front End (AFE) module 5150, 5250, 5350 which performs the usual analogue front end processing. The thus processed signals are then each passed to a respective Fast Fourier Transform (FFT) module 5140, 5240, 5340 which performs the usual conversion of the received signal from the time domain to the frequency domain. The signals leaving the FFT modules 5140, 5240, 5340, y.sub.1.sup.1 to y.sub.M.sup.1, y.sub.1.sup.2 to y.sub.M.sup.2 and y.sub.1.sup.3 to y.sub.M.sup.3 are then each passed, in the present embodiment, to a respective Frequency domain EQualiser (FEQ) module 5130, 5230, 5330. The operation of such frequency domain equaliser modules is well-known in the art and will not therefore be further described herein. It should be noted however, that any type of equalisation could be performed here, such as using a simple time-domain linear equalizer, a decision feedback equaliser, etc. For further information on equalisation in OFDM systems, the reader is referred to: Zero-Forcing Frequency-Domain Equalization for Generalized DMT Transceivers with Insufficient Guard Interval, by Tanja Karp, Steffen Trautmann, Norbert J. Fliege, EURASIP Journal on Applied Signal Processing 2004:10, 1446-1459.

(20) Once the received signal has passed through the AFE, FFT and FEQ modules, the resulting signals, {umlaut over (x)}.sub.1.sup.1 to {umlaut over (x)}.sub.M.sup.1, {umlaut over (x)}.sub.1.sup.2 to {umlaut over (x)}.sub.M.sup.2 and {umlaut over (x)}.sub.1.sup.3 to {umlaut over (x)}.sub.M.sup.3 should be similar to the complex numbers x.sub.1.sup.1 to x.sub.M.sup.1, x.sub.1.sup.2 to x.sub.M.sup.2 and x.sub.1.sup.3 to x.sub.M.sup.3 originally output by the M-QAM modulators 1621-1623 except that there will be some degree of error resulting from imperfect equalisation of the channel and the effect of external noise impinging onto the lines during transmission of the signals between the AN and the modems 41-43. This error will in general differ from one receiving modem to the next. This can be expressed mathematically as {umlaut over (x)}.sub.m.sup.1=x.sub.m.sup.1+e.sub.m.sup.1 etc. Provided the error however is sufficiently small the signal should be recoverable in the normal way after processing by the M-QAM demodulator modules 5120-5320 where a corresponding constellation point is selected for each value {umlaut over (x)}.sub.m.sup.i in dependence on its value (e.g. by selecting the constellation point closest to the point represented by the value unless trellis coding is being used, etc.). The resulting data values {umlaut over (d)}.sub.1.sup.1 to {umlaut over (d)}.sub.M.sup.1, {umlaut over (d)}.sub.1.sup.2 to {umlaut over (d)}.sub.M.sup.2 and {umlaut over (d)}.sub.1.sup.3 to {umlaut over (d)}.sub.M.sup.3 should mostly (apart from some small number of incorrectly detected values resulting from errors) correspond to the data values, {umlaut over (d)}.sub.1.sup.1 to {umlaut over (d)}.sub.M.sup.1, {umlaut over (d)}.sub.1.sup.2 to {umlaut over (d)}.sub.M.sup.2 and {umlaut over (d)}.sub.1.sup.3 to {umlaut over (d)}.sub.M.sup.3 originally entered to the corresponding M QAM modules 1621, 1622, 1623 respectively within the AN/transmitter 16. These values are then entered into a respective decoder (and received data processing) module 5110, 5210 and 5230 which reassembles the detected data and performs any necessary forward error correction etc. and then presents the recovered user data to whichever service it is addressed to in the normal manner, thus completing the successful transmission of this data.

(21) As mentioned above, following now from the above overview of FIG. 2, a more detailed explanation is provided of the non-conventional elements within the embodiment illustrated in FIG. 2 and described briefly above. Thus, the MPAD 1670 is a component which provides access to different combinations of phantom channels. MPAD 1670 tries all the possible combinations without repetition, e.g. phantom of pair 1 and pair 2 is equivalent to the phantom of pair 2 and pair 1 and so will not be repeated). Herein, MPAD (1670) selects a specific phantom and it allows the transmitter 16 and each respective receiver 51, 52, 53 to train up with each other and obtain the phantom channel as well as the direct differential mode pairs' channel coefficients at any given specific time slot. At this stage the receivers 51, 52, 53 report either the overall combined channel or the phantoms only to the PC-MOP module 1690 depending on what signals are transmitted by the transmitter 16 which is done under the control of the PC-MOP module so that it knows what data is being reported back to it by the receivers. At the same time the Interface 1680 confirms the identification of the selected and currently operational phantom channel to PC-MOP module 1690 (which is also selected by the interface 1680 under instruction from the PC-MOP module) so that all channel gains and their identifications are capable of being ascertained by PC-MOP 1690 for subsequently passing to the vectoring precoder module 1630 and the MICOP & MRC precoder module 1640 for use in performing their precoding functions. The operation continues until all the phantom channels' combinations are tested. Once the phantom tree is completed, PC-MOP 1690 decides the optimal phantom channels to be exploited to benefit specific pairs, all the pairs or to maximise the rate equilibrium of the users. The decision is then forwarded to the MPAD module 1670 via the Interface 1680 to execute the decision and enable the access to the selected optimal phantom channel (or channels in alternative embodiments where the MPAD connects to more than 3 TMPs).

(22) Once the optimum phantom channel is constructed and ready to be accessed, MICOP-MRC module 1640 then decides the optimal strategy to steer the constructed phantoms. This is done by selecting appropriate weighting values as described in greater detail below. The steering objective can be modified to maximise a specific pair or the rate equilibrium or any other desired objective.

(23) There now follows a mathematical explanation of the functioning of the various elements. In some cases the equations deal only with two direct differential mode signals and one phantom mode signal; however, it will be apparent to a person skilled in the art how to expand this to cover multiple different direct differential signals and multiple phantom signals based on the following example expositions. Thus, considering a system with K twisted pairs, each pair denoted by tp.sub.i where i, iK is the pair's index, there are

(24) $M=.Math.\frac{K}{d}.Math.$
first order orthogonal phantoms, where d is the required number of pairs to construct a single phantom channel. Similar rule applies for second order phantoms and so on until the orthogonal phantom tree is fully obtained. The total number of the first order orthogonal phantom candidates can be calculated by

(25) $\left(\begin{array}{c}K\\ d\end{array}\right)=\frac{K!}{d!\left(K-d\right)!}$
and we will consider this as the feasible domain for the PC-MOP problem, denoted by . The standard conventional channel is given as:

(26) $H=\left(\begin{array}{cccc}{h}_{1,1}& h_{1,2}& \mathrm{.Math.}& h_{1,K}\\ h_{2,1}& h_{2,2}& \mathrm{.Math.}& h_{2,K}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{K,1}& h_{K,2}& \mathrm{.Math.}& h_{K,K}\end{array}\right)$
where h.sub.i,j indicates the channel transfer function for the transmission by the transmitter onto the j.sup.th TMP (or phantom channel when extended as described immediately below) to the i.sup.th receiver as received at the i.sup.th receiver over the i.sup.th TMP or tp (=twisted pair).

(27) A phantom channel (.sub.m, mM) is derived from a pair of tp, i.e. {t.sub.i, tp.sub.j}.sub.ij, i & jK when d is 2. Hence the extended channel becomes:

(28) $\left[H|H_{}\right]=H_T=\left(\begin{array}{ccccccc}{h}_{1,1}& h_{1,2}& \mathrm{.Math.}& h_{1,K}& h_{1,{}_1}& \mathrm{.Math.}& h_{1,{}_M}\\ h_{2,1}& h_{2,2}& \mathrm{.Math.}& h_{2,K}& h_{2,{}_1}& \mathrm{.Math.}& h_{2,{}_M}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{K,1}& h_{K,2}& \mathrm{.Math.}& h_{K,K}& h_{K,{}_1}& \mathrm{.Math.}& h_{K,{}_M}\\ h_{{}_1,1}& h_{{}_1,2}& \mathrm{.Math.}& h_{{}_1,K}& h_{{}_1,{}_1}& \mathrm{.Math.}& h_{{}_1,{}_M}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{{}_M,1}& h_{{}_M,2}& \mathrm{.Math.}& h_{{}_M,K}& h_{{}_M,{}_1}& \mathrm{.Math.}& h_{{}_M,{}_M}\end{array}\right)$
where H.sub. is the phantom channel, H is the unextended channel (excluding phantom channels) and H.sub.T is the mixed mode channel. Herein, the PC-MOP can be formulated as follows:
maxH.sub.,(1)
subject to:
.sub.m(2)

(29) To illustrate the selection strategy of Pareto, we provide the following example: Assume a 5 pair cable in which pairs 5 and 4 are performing poorly in comparison to pairs 1, 2 and 3. Therefore, the phantoms may be derived and steered to maximise the performance of pairs 4 and 5. Maximum number of the first order orthogonal phantoms is

(30) $.Math.\frac{5}{2}.Math.=2$

(31) TABLE-US-00001 TABLE 1 First order phantom mode candidates {tp.sub.i, tp.sub.j}.sub.ij h.sub.k,.sub.m {1, 2} {1, 3} {1, 4} {1, 5} {2, 3} {2, 4} {2, 5} {3, 4} {3, 5} {4, 5} h.sub.5,.sub.m 0.5 0.3 0.4 0.45 0.25 0.1 0.3 0.2 0.3 0.2 h.sub.4,.sub.m 0.3 0.3 0.2 0.4 0.52 0.6 0.3 0.3 0.4 0.5
and the maximum number of combinations is

(32) $\left(\begin{array}{c}5\\ 2\end{array}\right)=\frac{54321}{21\left(321\right)}=10.$
Table 1 shows all the orthogonal phantom candidates and their mode-conversion crosstalk coefficient with the targeted pairs. To obtain Pareto front, we must determine the non-dominant solution, i.e. Pareto front. To examine the dominance of a set, it must contain at least one element greater than an element in another set if the objective function is set to maximisation. In this particular example, {1, 2} dominates {1, 3}, {1, 4}, {2, 5} and {3, 4}. Similarly, candidates {1, 5}, {2, 3} and {2, 4} dominant {1, 3}, {1, 4}, {2, 5} and {3, 4}. Hence {1, 2}, {1, 5}, {2, 3} and {2, 4} are the non-dominant solution and known as the Pareto front, see the example Figure below.

(33) In a similar way, the objective function can include more pairs to benefit from the phantoms, also the phantom directivity can be altered to optimise the direct paths of the phantom mode if they are accessible at the receiving end, i.e. direct phantom channels. This remains the choice of the network operator. Since predicting the phantom coupling strength from first principles is an arduous task, in the present embodiment, PC-MOP 1690 proceeds by simply initialising all possible phantom channels randomly in a non-repetitive pattern. Alternatively, however, one could also model the phantoms and predict their performance in advance and select the optimal combination without the random training in alternative embodiments.

(34) Once the phantoms are defined, it is advantageous to try to determine the optimal strategy to steer and split the indirect channels to maximise the overall binder capacity whilst fairness constraints between the users are kept satisfied. To achieve this, the indirect (phantom/crosstalk) channel utilisation problem is formulated as a Mixed-Integer Convex OPtimisation (MICOP) model in order to enable the PC-MOP 1690 to then derive a solution.

(35) In order to simplify the problem, to illustrate the operation of the PC-MOP 1690, consider a single phantom to be shared among K users to transmit N tones for a period of time T. Power level per tone is denoted by p.sub.k,t,n and the channel condition is .sub.k,t,n which is the ratio of power coupling coefficient to the noise level

(36) ${\left(\frac{{.Math.h_{k,{}_m}.Math.}^2}{n_{k,{}_m}}\right)}_{t,n}.$
The tone allocation factor is .sub.k,t,n and finally the optimal capacity of the m.sup.th phantom is C.sub..sub.m.

(37) $\begin{array}{cc}\max C_{{}_m}=\underset{k,t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+p_{k,t,n}{}_{k,t,n}\right),& \left(3\right)\end{array}$ subject to:

(38) $\begin{array}{cc}\underset{k,n}{.Math.}{p}_{k,t,n}{P}_{{}_m},tT& \left(4a\right)\\ \underset{t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+p_{k,t,n}{}_{k,n}\right)R_k,kK& \left(4b\right)\\ \underset{k,t}{.Math.}{}_{k,t,n}T,\left\{0,1\right\},nN,& \left(4c\right)\end{array}$
Equation (3) is the objective function in which its limit is subject to the maximum transmitting power in 4a and the tone sharing criteria in 4c.

(39) The optimisation problem in its current form is non-linear with no known analytical solution. However, a simple modification has been applied to 3.

(40) 0$\begin{array}{cc}\max C_{{}_m}=\underset{k,t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+\frac{s_{k,t,n}{}_{k,t,n}}{{}_{k,t,n}}\right),& \left(5\right)\end{array}$ subject to:

(41) $\begin{array}{cc}\underset{k,n}{.Math.}{s}_{k,t,n}{P}_{{}_m},tT& \left(6a\right)\\ \underset{t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+\frac{s_{k,t,n}{}_{k,t,n}}{{}_{k,t,n}}\right)R_k,kK& \left(6b\right)\\ \underset{k}{.Math.}{}_{k,n}1,nM,tT& \left(6c\right)\end{array}$

(42) The modified problem in 5 is concave and hence it is solvable as a convex problem. This problem as it stands provide the optimal TDMA and FDMA access to the phantoms. The analytical solution proceeds with the Lagrangian as follows:

(43) $\begin{array}{cc}=\underset{k,t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+\frac{s_{k,t,n}{}_{k,t,n}}{{}_{k,t,n}}\right)-\underset{t}{.Math.}{}_t\left(\underset{k,n}{.Math.}{s}_{k,t,n}-P_{{}_m}\right)-\underset{t,n}{.Math.}{}_{t,n}\left(\underset{k}{.Math.}{}_{k,t,n}-1\right)-\underset{k}{.Math.}\left[\underset{t,n}{.Math.}{}_{k,t,n}{\log }_2\left(1+\frac{s_{k,t,n}{}_{k,t,n}}{{}_{k,t,n}}\right)-R_k\right],& \left(7\right)\end{array}$

(44) To solve 7 and prove its optimality, Karush Kuhn Tucker (KKT) conditions must be satisfied. The conditions are:

(45) 1. Feasibility of the primal constraints as well as the multipliers, i.e. ( & ).

(46) 2. The gradient of 7 must become zero with respect to 6a and 4c.

(47) Starting by differentiating 7 with respect to s.sub.k,n, i.e.

(48) $\frac{}{s_{k,n}}=0,$
then rearrange to obtain the optimal power formula:

(49) $\begin{array}{cc}{p}_{k,t,n}={}_t\left(1-{}_k\right)-\frac{1}{{}_{k,t,n}},& \left(8\right)\end{array}$
where

(50) ${}_t=\frac{1}{\ln 2{}_t}.$
To guarantee feasible 8 and 4a,

(51) $\frac{1}{{}_{k,t,n}}{}_t\frac{P_{{}_m}+\underset{k,n}{.Math.}\frac{1}{{}_{k,t,n}}}{\underset{k,n}{.Math.}\left(1-{}_k\right)}.$

(52) The sharing factor can be used simply to guarantee that a single tone can only be assigned to a single user, e.g. tone 1 assigned to user 1 is represented by .sub.1,1=1 and elsewhere .sub.k1,1=0. Hence constraint 4c is relaxed to:

(53) ${}_{k,n}=\{\begin{array}{cc}1& \mathrm{if}\mathrm{the}{n}^{\mathrm{th}}\mathrm{tone}\mathrm{is}\mathrm{assigned}\mathrm{to}\mathrm{the}{k}^{\mathrm{th}}\mathrm{user},\\ 0& \mathrm{elsewhere}\end{array}.$
In a similar fashion to 8, we differentiate 7 with respect .sub.k,n, rearrange and substitute 8 to obtain the following:

(54) $\begin{array}{cc}{}_{t,n}={\log }_2\left[{}_t\left(1-{}_k\right){}_{k,t,n}\right]-\frac{1}{\ln 2}\left[1-\frac{1}{{}_t\left(1-{}_k\right){}_{k,t,n}}\right],nN& \left(9\right)\end{array}$
The user which maximises 9 for tone n represents the optimal user. Hence k is obtained by:
{circumflex over (k)}=arg max.sub.t,n, tT, nN(10)
and therefore, by assessing which k (i.e. which end CPE receiver) to select for each tone, n, a weighting value, of (in this embodiment) zero or one, is determined for each line, at each tone, in dependence upon the measured extent of the couplings between a phantom mode channel, .sub.m and each differential mode channel k as determined by a receiver receiving signals in the differential mode (recall that

(55) ${}_{k,t,n}={\left(\frac{{.Math.h_{k,{}_m}.Math.}^2}{n_{k,{}_m}}\right)}_{t,n}).$

(56) Similarly to section 1, the method can be applied to the differential lines except that the k domain is limited to each line itself. Hence, the binder capacity in total, becomes:

(57) 0$\begin{array}{cc}{\mathrm{��}}_{\mathrm{binder}}=\underset{\mathrm{ph}}{.Math.}{C}_{{}_m}+\underset{\mathrm{dif}}{.Math.}{C}_{\mathrm{dif}},& \left(11\right)\end{array}$

(58) once the phantom sharing and power allocation policies are obtained. The power allocation per line needs to be re-configured to ensure that the phantom gain results in (or at least does not exceed) the capacity gain. The optimisation problem is similar to 5 excluding 4c. Line's channel gain in the presence of phantom gain thus becomes:

(59) $\begin{array}{cc}{}_{\hat{k},t,n}=\left(\frac{{.Math.h_{\hat{k},\hat{k}}.Math.}^2}{n_{\hat{k},\hat{k}}}+\frac{\underset{m}{.Math.}{}_{\hat{k},t,n}{.Math.h_{\hat{k},{}_m}.Math.}^2{P}_{{}_m,t,n}}{n_{\hat{k},{}_m}}\right)& \left(12\right)\\ \max C_{\hat{k},t}=\underset{n}{.Math.}{\log }_2\left(1+p_{\hat{k},t,n}{}_{\hat{k},t,n}\right),tT& \left(13\right)\end{array}$ subject to:

(60) $\begin{array}{cc}\underset{n}{.Math.}{p}_{\hat{k},t,n}{p}_k,\hat{k}K,tT,& \left(14a\right)\\ =\underset{n}{.Math.}{\log }_2\left(1+p_{\hat{k},t,n}{}_{\hat{k},t,n}\right)-{}_t\left(\underset{n}{.Math.}{p}_{\hat{k},t,n}-P_k\right)& \left(15\right)\\ p_{\hat{k},t,n}={}_t-\frac{1}{{}_{\hat{k},t,n}},& \left(16\right)\end{array}$

(61) if n.sub.{circumflex over (k)},{circumflex over (k)}=n.sub.{umlaut over (k)}.sub.m, p.sub.{circumflex over (k)},t,n becomes:

(62) $\begin{array}{cc}{p}_{\hat{k},t,n}={}_t-\frac{n_{\hat{k},\hat{k}}}{{.Math.h_{\hat{k},\hat{k}}.Math.}^2+\underset{m}{.Math.}{}_{\hat{k},t,n}{.Math.h_{\hat{k},{}_m}.Math.}^2{p}_{{}_m,t,n}}& \left(17\right)\end{array}$
Note: Tone/subcarrier spacing is excluded from the optimisation problems because it is a constant and hence the units of the current capacity are bandwidth-normalised (known as bandwidth or spectrum efficiency) in

(63) $\frac{\mathrm{bps}}{\mathrm{Hz}}.$

(64) An alternative formulation to the above described embodiment allows the exploitation of indirect (phantom/crosstalk) channels over the same spectrum and simultaneously for all or plural existing line users at any one or more tones, n, subject to a power constraint for the entire spectrum. To illustrate how this is achieved, the problem is decomposed; firstly, the power allocation per tone/carrier is determined and then the distribution of tone power between the active users is optimized. To enable this, the problem becomes:

(65) $\begin{array}{cc}\max \underset{n}{.Math.}{\log }_2\left(1+p_n\underset{k}{.Math.}{}_{k,n}\right)& \left(18\right)\end{array}$ subject to:

(66) $\begin{array}{cc}\underset{n}{.Math.}{p}_n{p}_T,& \left(19a\right)\end{array}$
Applying the Lagrangian:

(67) $\begin{array}{cc}=\underset{n}{.Math.}{\log }_2\left(1+p_n\underset{k}{.Math.}{}_{k,n}\right)-\left(\underset{n}{.Math.}{p}_n-p_T\right)& \left(20\right)\end{array}$

(68) Take

(69) $\frac{}{p_n}$
and then rearrange to obtain:

(70) $\begin{array}{cc}{p}_n={}^{-1}-\frac{1}{\underset{k}{.Math.}{}_{k,n}},& \left(21\right)\end{array}$

(71) Equation (21) is substituted into (19a) to calculate the multiplier, , and then again into (21) to calculate the optimal spatial frequency power level.

(72) Now the distribution of p.sub.n between K users is optimised.

(73) 0$\begin{array}{cc}\max \underset{k}{.Math.}{\log }_2\left(1+p_{k,n}{}_{k,n}\right)& \left(22\right)\end{array}$ subject to:

(74) $\begin{array}{cc}\underset{k}{.Math.}{p}_{k,n}{p}_n,& \left(23a\right)\end{array}$
Applying the Lagrangian:

(75) $\begin{array}{cc}=\underset{k}{.Math.}{\log }_2\left(1+p_{k,n}{}_{k,n}\right)-{}_n\left(\underset{k}{.Math.}{p}_{k,n}-p_n\right)& \left(24\right)\end{array}$
Similarly to previous steps, the optimal power equation is obtained:

(76) $\begin{array}{cc}{p}_{k,n}={}_n^{-1}-\frac{1}{{}_{k,n}},& \left(25\right)\end{array}$

Example-01

(77) Assume two users to share a p.sub.n. The optimisation problem can be simplified to:
max[(1+p.sub.1,n.sub.1,n)(1+p.sub.2,n.sub.2,n)](26) subject to:
p.sub.1,n+p.sub.2,n=p.sub.n,(27)
The problem in (26) is easily solvable, two equations and two unknowns. One can prove the optimal power allocation from both problem (22) and (26) is:

(78) $\begin{array}{cc}{p}_{1,n}=\frac{p_n\left(\underset{k=1}{\overset{2}{.Math.}}{}_{k,n}\right)+{}_{1,n}-{}_{2,n}}{2\underset{k=1}{\overset{2}{.Math.}}{}_{k,n}}& \left(28\right)\end{array}$
Finally p.sub.2,n is equal to p.sub.np.sub.1,n.

Example-02

(79) In terms of signal precoding and real signal injection for a given MPAD (1670) settings, consider the following: The data, [d.sub.i d.sub.2], are first modulated, e.g. using M-QAM, at a given subcarrier (n) to produce the original data symbols:

(80) $X=\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$ The precoded data symbols (using MICOP-MRC) are calculated as follows:

(81) $\hat{X}=\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)=\left(\begin{array}{c}\frac{x_1{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}\\ \frac{x_2{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}+\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)$
where .sub.1+.sub.2=1. Note that

(82) $p_n={.Math.\frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}.Math.}^2+{.Math.\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}.Math.}^2\mathrm{where}{.Math.\frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}.Math.}^2=p_{1,n}\mathrm{and}$${.Math.\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}.Math.}^2=p_{2,n}.$
Hence,

(83) ${}_1=\frac{.Math.h_{1,3}.Math.\sqrt[2]{p_{1,n}}}{.Math.x_1{h}_{1,3}^{*}.Math.}\mathrm{and}{}_2=\frac{.Math.h_{2,3}.Math.\sqrt[2]{p_{2,n}}}{.Math.x_2{h}_{2,3}^{*}.Math.},$
see Example-01. Index n is dropped from the matrices for clarity. Non-vectored received signals:

(84) $\tilde{Y}=\left(\begin{array}{ccc}{h}_{1,1}& h_{1,2}& h_{1,3}\\ h_{2,1}& h_{2,2}& h_{2,3}\end{array}\right)\left(\begin{array}{c}\frac{x_1{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}\\ \frac{x_2{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}+\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)$ To remove the unwanted coupling after combining, the new channel coefficients must be calculated using the MRC coefficients since that the 1630 sees include the MICOP-MRC part of the channel:

(85) 0$\left(\begin{array}{ccc}{h}_{1,1}& h_{1,2}& h_{1,3}\\ h_{2,1}& h_{2,2}& h_{2,3}\end{array}\right)\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)=\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)$ The vectoring precoder in 1630 becomes:

(86) ${\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)$
Note that the right hand matrix above represents a normalisation to prevent the channel inverse (which is the left hand matrix) from excessively amplifying signal components before attempting to transmit them over the physical channels. A corresponding de-normalisation is then performed by each receiver. It should be noted that embodiments of the present invention are not limited to any particular type of vectoring or normalisation methodology adopted, but rather can be used together with any appropriate form of vectoring and/or normalisation. However, in the present embodiment, the full system thus becomes:

(87) $\left(\begin{array}{c}{y}_1\\ y_2\end{array}\right)=\left(\begin{array}{ccc}{h}_{1,1}& h_{1,2}& h_{1,3}\\ h_{2,1}& h_{2,2}& h_{2,3}\end{array}\right)\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right){\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right).$
And finally, the transmitted X is estimated at FEQs by:

(88) $\stackrel{\mathrm{.Math.}}{X}=\left(\begin{array}{c}{\stackrel{\mathrm{.Math.}}{x}}_1\\ {\stackrel{\mathrm{.Math.}}{x}}_2\end{array}\right)={\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{c}{y}_1\\ y_2\end{array}\right)$
Signal tracking in 16
1. After data source (1611):

(89) $D=\left(\begin{array}{c}{d}_1\\ d_2\end{array}\right)$
2. After M-QAM (1621):

(90) $X=\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$
3. After the vectoring unit (1630):

(91) $\stackrel{}{X}=\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)={\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$

(92) Expanded to:

(93) $\stackrel{}{X}=\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\frac{1}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}\left(\begin{array}{cc}.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.& -\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\\ -\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}& .Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\end{array}\right)\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$

(94) and hence,

(95) $\stackrel{}{X}=\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\frac{1}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}(\begin{array}{cc}\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math..Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)& \begin{array}{c}\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\\ \left(-\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\end{array}\\ \begin{array}{c}\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\\ \left(-\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\end{array}& \left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\end{array})\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$

(96) Finally:

(97) $\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\left(\begin{array}{c}\frac{\begin{array}{c}{x}_1\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)+\\ x_2\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(-\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\end{array}}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}\\ \frac{\begin{array}{c}{x}_1\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\left(-\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)+\\ x_2\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\end{array}}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}\end{array}\right)$
4. After MICOP-MRC (1640)

(98) 0$\hat{X}=\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\left(\begin{array}{ccc}& \frac{{\stackrel{}{x}}_1{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}& \\ & \frac{{\stackrel{}{x}}_2{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}& \\ \frac{{\stackrel{}{x}}_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& +& \frac{{\stackrel{}{x}}_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)$

(99) or equivalently:

(100) $\hat{X}=\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)\left(\begin{array}{c}\frac{\begin{array}{c}{x}_1\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)+\\ x_2\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(-\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\end{array}}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}\\ \frac{\begin{array}{c}{x}_1\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\left(-\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)+\\ x_2\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\end{array}}{\begin{array}{c}[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\\ \left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)]\end{array}}\end{array}\right)$
5. Finally the transmitted signal Y is modelled as:

(101) $Y=\left(\begin{array}{c}{y}_1\\ y_2\end{array}\right)=\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)\left(\begin{array}{c}{\hat{x}}_1\\ {\hat{x}}_2\end{array}\right)+\left(\begin{array}{c}{n}_1\\ n_2\end{array}\right)$