Method and apparatus for transmitting data from a transmitter device to a plurality of receiver devices

Abstract

Apparatus for communicating data between a transmitter device 16 and a first 51 and a second 52 receiver device, the receiver devices being connected, in use, to the transmitter device via a first 21 and a second 22 pair of wires respectively. Each receiver device is 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 respective receiver device and the transmitter device, and the transmitter device is operable to transmit signals onto the wires at the transmitter ends thereof in order to transmit signals via a direct differential mode to each respective receiver via its respective pair of wires. The transmitter device is additionally operable to transmit signals to both receivers via a single common indirect channel and comprises: a channel estimator 1670, 1680, 1690 for estimating the extent of coupling between the common indirect channel and each of the receiver devices based on readings received by the transmitter device from the receiver devices; and a processor 1690 for determining a plurality of weighting values in dependence upon the estimated extents of the couplings; the transmitter 16 being operable to transmit a first signal via the direct differential mode over the first pair 21, to transmit a second signal via the direct differential mode over the second pair 22 and to transmit a combined signal onto the indirect channel, wherein the combined signal comprises a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values; and wherein the transmitter further comprises a precoder 1640 for precoding the first, second and combined signals to pre-compensate them for the expected effects of cross-talk from the other ones of these signals, wherein the pre-coding of each signal, including the first and the second signals, is performed in dependence upon the determined weighting values.

Claims

1. A method of transmitting data from a transmitter device to a first, a second and a third receiver device, the receiver devices being connected to the transmitter device via a first, a second and a third pair of wires respectively, 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 and the transmitter devices, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via the direct differential mode to each respective receiver, and is additionally operable to transmit signals to both receivers via a single common indirect channel, the method comprising: measuring the extent of coupling between the common indirect channel and each of the receiver devices, determining a plurality of weighting values in dependence upon the measured extent of the couplings, transmitting a first signal via the direct differential mode over the first pair and a second signal via the direct differential mode over the second pair, and transmitting a combined signal onto the indirect channel, the combined signal comprising a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values, and wherein each of the signals is precoded prior to being transmitted in order to pre-compensate for the expected effects of cross-talk from the other signals, and wherein the pre-coding of each signal, including the first and the second signal, is performed in dependence upon the determined weighting values, wherein a first phantom mode channel is formed using a differential signal between signals of the first and second receiver devices, a second phantom mode channel is formed using a differential signal between signals of the first and third receiver devices, and a third phantom mode channel is formed using a differential signal between signals of the second and third receiver devices, and wherein the common indirect channel is a single ended phantom mode channel selected from a set of possible phantom mode channels formed by the first, second and third phantom mode channels.

2. A method according to claim 1 wherein the weighting values are determined additionally in dependence upon the instantaneous level of demand for data to be transmitted to a respective receiver.

3. A method according to claim 2 wherein the transmitter device and the receiver devices are operating in accordance with a physical layer retransmission scheme whereby a receiver requests retransmission of received data which is irreparably damaged because of errors in the received signals or in the detected or recovered data upon receipt.

4. A method according to claim 3 wherein the demand used in determining the weighting values reflects the demand for physical layer re-transmission of data caused by errors in received data.

5. A method of transmitting data from a transmitter device to a first and a second receiver device, the receiver devices being connected to the transmitter device via a first and a second pair of wires respectively, 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 and the transmitter devices, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via the direct differential mode to each respective receiver, and is additionally operable to transmit signals to both receivers via a single common indirect channel, the method comprising: measuring the extent of coupling between the common indirect channel and each of the receiver devices, determining a plurality of weighting values in dependence upon the measured extent of the couplings, transmitting a first signal via the direct differential mode over the first pair and a second signal via the direct differential mode over the second pair, and transmitting a combined signal onto the indirect channel, the combined signal comprising a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values, and wherein each of the signals is precoded prior to being transmitted in order to pre-compensate for the expected effects of cross-talk from the other signals, and wherein the pre-coding of each signal, including the first and the second signal, is performed in dependence upon the determined weighting values, wherein the method further comprises monitoring one or more metrics associated with the operation of the system and performing a redetermination of at least some of the weighting values and associated precoding coefficients in the event that, as a result of the monitoring, one or more monitored metric is observed to have changed by more than a predetermined threshold amount since last determining or re-determining the weighting values.

6. A method according to claim 5 wherein the monitored metric comprises one or more of channel transfer function estimations and levels of demand for data to be transmitted.

7. A method of transmitting data from a transmitter device to a first and a second receiver device, the receiver devices being connected to the transmitter device via a first and a second pair of wires respectively, 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 and the transmitter devices, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via the direct differential mode to each respective receiver, and is additionally operable to transmit signals to both receivers via a single common indirect channel, the method comprising: measuring the extent of coupling between the common indirect channel and each of the receiver devices, determining a plurality of weighting values in dependence upon the measured extent of the couplings, transmitting a first signal via the direct differential mode over the first pair and a second signal via the direct differential mode over the second pair, and transmitting a combined signal onto the indirect channel, the combined signal comprising a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values, and wherein each of the signals is precoded prior to being transmitted in order to pre-compensate for the expected effects of cross-talk from the other signals, wherein the pre-coding of each signal, including the first and the second signal, is performed in dependence upon the determined weighting values, and wherein the manner in which the weighting values are used to affect the first and second signals and the manner in which the combined signal is generated for transmission over the common indirect channel is performed in such a way that by assigning zero to all of the weighting values for a particular tone, the method reverts to a vectoring technique, for any such tone, in which the first and second signals are transmitted only onto their respective direct differential mode channels, and those signals are pre-coded to pre-compensate for the expected cross-talk effects of the signal being transmitted onto the other direct differential mode channel associated with the respective other pair of wires.

8. A method according to claim 1 wherein an indirect channel which is formed from a direct differential mode of transmission over a pair of wires connected between the transmitter device and the third receiver device is used to transmit a combined signal comprising a weighted sum of the first and second signals at a tone which is not used for transmissions between the transmitter and the third receiver device but is used for transmissions between the transmitter and the first and second receiver devices.

9. A method according to claim 1 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 and the first receiver device 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 device; and at least some of the weighting values.

10. A method according to claim 1 wherein at least some of the weighting values take values intermediate between zero and one.

11. A transmitter device for transmitting data from the transmitter device to a first and a second receiver device, the receiver devices being connected, in use, to the transmitter device via a first and a second pair of wires respectively, 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 respective receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via a direct differential mode to each respective receiver device via its respective pair of wires, and is additionally operable to transmit signals to both receiver devices via a single common indirect channel, the transmitter comprising: a channel estimator for estimating the extent of coupling between the common indirect channel and each of the receiver devices based on readings received by the transmitter device from the receiver devices; and a processor for determining a plurality of weighting values in dependence upon the estimated extents of the couplings; the transmitter being operable to transmit a first signal via the direct differential mode over the first pair, to transmit a second signal via the direct differential mode over the second pair and to transmit a combined signal onto the indirect channel, wherein the combined signal comprises a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values; wherein the transmitter further comprises a precoder for precoding the first, second and combined signals to pre-compensate them for the expected effects of cross-talk from the other ones of these signals, wherein the pre-coding of each signal, including the first and the second signals, is performed in dependence upon the determined weighting values, wherein a first phantom mode channel is formed using a differential signal between signals of the first and second receiver devices, a second phantom mode channel is formed using a differential signal between signals of the first and third receiver devices, and a third phantom mode channel is formed using a differential signal between signals of the second and third receiver devices, and wherein the common indirect channel is a single ended phantom mode channel selected from a set of possible phantom mode channels formed by the first, second and third phantom mode channels.

12. A non-transitory carrier medium carrying computer processor implementable instructions, which upon execution by the computer processor, execute the method of claim 1.

13. A transmitter device for transmitting data from the transmitter device to a first and a second receiver device, the receiver devices being connected, in use, to the transmitter device via a first and a second pair of wires respectively, 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 respective receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via a direct differential mode to each respective receiver device via its respective pair of wires, and is additionally operable to transmit signals to both receiver devices via a single common indirect channel, the transmitter comprising: a channel estimator for estimating the extent of coupling between the common indirect channel and each of the receiver devices based on readings received by the transmitter device from the receiver devices; and a processor for determining a plurality of weighting values in dependence upon the estimated extents of the couplings; the transmitter being operable to transmit a first signal via the direct differential mode over the first pair, to transmit a second signal via the direct differential mode over the second pair and to transmit a combined signal onto the indirect channel, wherein the combined signal comprises a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values, wherein the transmitter further comprises a precoder for precoding the first, second and combined signals to pre-compensate them for the expected effects of cross-talk from the other ones of these signals, wherein the pre-coding of each signal, including the first and the second signals, is performed in dependence upon the determined weighting values, and wherein the transmitter device is further being operable to monitor one or more metrics associated with the operation of the system and performing a redetermination of at least some of the weighting values and associated precoding coefficients in the event that, as a result of the monitoring, one or more monitored metric is observed to have changed by more than a predetermined threshold amount since last determining or re-determining the weighting values.

14. The transmitter device according to claim 13 wherein the monitored metric comprises one or more of channel transfer function estimations and levels of demand for data to be transmitted.

15. A transmitter device for transmitting data from the transmitter device to a first and a second receiver device, the receiver devices being connected, in use, to the transmitter device via a first and a second pair of wires respectively, 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 respective receiver device and the transmitter device, the transmitter device being operable to transmit signals onto the wires extending between the transmitter device and the receiver devices in order to transmit signals via a direct differential mode to each respective receiver device via its respective pair of wires, and is additionally operable to transmit signals to both receiver devices via a single common indirect channel, the transmitter comprising: a channel estimator for estimating the extent of coupling between the common indirect channel and each of the receiver devices based on readings received by the transmitter device from the receiver devices; and a processor for determining a plurality of weighting values in dependence upon the estimated extents of the couplings; the transmitter being operable to transmit a first signal via the direct differential mode over the first pair, to transmit a second signal via the direct differential mode over the second pair and to transmit a combined signal onto the indirect channel, wherein the combined signal comprises a weighted sum of the first and second signals, the weighting being done in accordance with the determined weighting values, wherein the transmitter further comprises a precoder for precoding the first, second and combined signals to pre-compensate them for the expected effects of cross-talk from the other ones of these signals, wherein the pre-coding of each signal, including the first and the second signals, is performed in dependence upon the determined weighting values, and wherein the manner in which the weighting values are used to affect the first and second signals and the manner in which the combined signal is generated for transmission over the common indirect channel is performed in such a way that by assigning zero to all of the weighting values for a particular tone, the method reverts to a vectoring technique, for any such tone, in which the first and second signals are transmitted only onto their respective direct differential mode channels, and those signals are pre-coded to pre-compensate for the expected cross-talk effects of the signal being transmitted onto the other direct differential mode channel associated with the respective other pair of wires.

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 metres or less, for example possibly a few tens of metres 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 crosstalk 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 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 1-i 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 i: {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 {umlaut over (x)}.sub.m.sup.i 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, MICOPMRC 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. {tp.sub.i, tp.sub.j}.sub.ij

(28) 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,

(29) i & jK when d is 2. Hence the extended channel becomes:

(30) $\left[H|H_{}\right]=H_T=\left(\begin{array}{ccccccc}{h}_{1,1}& h_{1,2}& \mathrm{.Math.}& h_{1,K}& h_{1,{}_1}& \mathrm{.Math.}& h_{1,{}_M}\\ h_{2,1}& h_{2,2}& \mathrm{.Math.}& h_{2,K}& h_{2,{}_1}& \mathrm{.Math.}& h_{2,{}_M}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{K,1}& h_{K,2}& \mathrm{.Math.}& h_{K,K}& h_{K,{}_1}& \mathrm{.Math.}& h_{K,{}_M}\\ h_{{}_1,1}& h_{{}_1,2}& \mathrm{.Math.}& h_{{}_1,K}& h_{{}_1,{}_1}& \mathrm{.Math.}& h_{{}_1,{}_M}\\ \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}\\ h_{{}_M,1}& h_{{}_M,2}& \mathrm{.Math.}& h_{{}_M,K}& h_{{}_M,{}_1}& \mathrm{.Math.}& h_{{}_M,{}_M}\end{array}\right)$
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:
max H.sub.,(1)
subject to:
.sub.m(2)

(31) 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

(32) $.Math.\frac{5}{2}.Math.=2$
and the maximum number of combinations is

(33) $\left(\begin{array}{c}5\\ 2\end{array}\right)=\frac{54321}{21\left(321\right)}=10.$
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.

(34) 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.

(35) 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.

(36) 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

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

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

(39) $\begin{array}{cc}\underset{k,n}{\overset{}{.Math.}}{p}_{k,t,n}{P}_m,tT& \left(4a\right)\\ \underset{t,n}{\overset{}{.Math.}}{}_{k,t,n}{\log }_2\left(1+p_{k,t,n}{}_{k,n}\right)R_k,kK& \left(4b\right)\\ \underset{k,t}{\overset{}{.Math.}}{}_{k,t,n}T,\left\{0,1\right\},nN,& \left(4c\right)\end{array}$
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.

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

(41) 0$\begin{array}{cc}\max C_{{}_m}=\underset{k,t,n}{\overset{}{.Math.}}{}_{k,t,n}{\log }_2\left(1+\frac{s_{k,t,n}{}_{k,t,n}}{{}_{k,t,n}}\right),& \left(5\right)\end{array}$ subject to:

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

(43) 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:

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

(45) To solve 7 and prove its optimality, Karush Kuhn Tucker (KKT) conditions must be satisfied. The conditions are: 1. Feasibility of the primal constraints as well as the multipliers, i.e. ( & ). 2. The gradient of 7 must become zero with respect to 6a and 4c.

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

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

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

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

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

(51) 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:

(52) ${}_{k,n}=\{\begin{array}{cc}1& \mathrm{if}\mathrm{the}{n}^{\mathrm{th}}\mathrm{tone}\mathrm{is}\mathrm{assigned}\mathrm{to}\mathrm{the}{k}^{\mathrm{th}}\mathrm{user},\\ 0& \mathrm{elsewhere}\end{array}.$

(53) In a similar fashion to 8, we differentiate 7 with respect .sub.k,n, rearrange and substitute 8 to obtain the following:

(54) $\begin{array}{cc}{}_{t,n}={\log }_2\left[{}_t\left(1-{}_k\right){}_{k,t,n}\right]-\frac{1}{\ln 2}\left[1-\frac{1}{{}_t\left(1-{}_k\right){}_{k,t,n}}\right],nN& \left(9\right)\end{array}$

(55) 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

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

(57) 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:

(58) 0$\begin{array}{cc}{C}_{\mathrm{binder}}=\underset{ph}{\overset{}{.Math.}}{C}_{{}_m}+\underset{\mathrm{dif}}{\overset{}{.Math.}}{C}_{\mathrm{dif}},& \left(11\right)\end{array}$

(59) 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:

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

(61) $\begin{array}{cc}\underset{n}{\overset{}{.Math.}}{p}_{\hat{k},t,n}{P}_k,\hat{k}K,tT,& \left(14a\right)\\ =\underset{n}{\overset{}{.Math.}}{\log }_2\left(1+p_{\hat{k},t,n}{}_{\hat{k},t,n}\right)-{}_t\left(\underset{n}{\overset{}{.Math.}}{p}_{\hat{k},t,n}-P_k\right)& \left(15\right)\\ p_{\hat{k},t,n}={}_t-\frac{1}{{}_{\hat{k},t,n}},\mathrm{if}{n}_{\hat{k},\hat{k}}=n_{\hat{k},{}_m},p_{\hat{k},t,n}\mathrm{becomes}\text{:}& \left(16\right)\\ p_{\hat{k},t,n}={}_t-\frac{n_{\hat{k},\hat{k}}}{{.Math.h_{\hat{k},\hat{k}}.Math.}^2+\underset{m}{.Math.}{}_{\hat{k},t,n}{.Math.h_{\hat{k},{}_m}.Math.}^2{p}_{{}_m,t,n}}& \left(17\right)\end{array}$

(62) 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) $\begin{array}{cc}\underset{n}{\overset{}{.Math.}}{p}_n{P}_T,& \left(19a\right)\end{array}$

(67) Applying the Lagrangian:

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

(69) Take

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

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

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

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

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

(75) 0$\begin{array}{cc}\underset{k}{\overset{}{.Math.}}{p}_{k,n}{p}_n,& \left(23a\right)\end{array}$

(76) Applying the Lagrangian:

(77) $\begin{array}{cc}=\underset{k}{.Math.}{\log }_2\left(1+p_{k,n}{}_{k,n}\right)-{}_n\left(\underset{k}{.Math.}{p}_{k,n}-p_n\right)& \left(24\right)\end{array}$

(78) Similarly to previous steps, the optimal power equation is obtained:

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

EXAMPLE-01

(80) Assume two users to share a p.sub.n. The optimisation problem can be simplified to:
max[(1+p.sub.1,n1,n)(1+p.sub.2,n2,n)](26) subject to:
p.sub.1,n+p.sub.2,n=p.sub.n,(27)

(81) 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:

(82) $\begin{array}{cc}{p}_{1,n}=\frac{p_n\left(\underset{k=1}{\overset{2}{.Math.}}{}_{k,n}\right)+{}_{1,n}-{}_{2,n}}{2\underset{k=1}{\overset{2}{.Math.}}{}_{k,n}}& \left(28\right)\end{array}$

(83) Finally p.sub.2,n is equal to p.sub.n-p.sub.1,n.

EXAMPLE-02

(84) In terms of signal precoding and real signal injection for a given MPAD (1670) settings, consider the following: The data, [d.sub.1 d.sub.2], are first modulated, e.g. using M-QAM, at a given subcarrier (n) to produce the original data symbols:

(85) $X=\left(\begin{array}{c}{X}_1\\ X_2\end{array}\right)$ The precoded data symbols (using MICOP-MRC) are calculated as follows:

(86) $\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)$$\mathrm{where}$${}_1+{}_2=1.$$\mathrm{Note}\mathrm{that}{p}_n={.Math.\frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}.Math.}^2+{.Math.\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}.Math.}^2$$\mathrm{where}$${.Math.\frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}.Math.}^2=p_{1,n}$$\mathrm{and}$${.Math.\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}.Math.}^2=p_{2,n}.\mathrm{Hence},{}_1=\frac{.Math.h_{1,3}.Math.\sqrt[2]{p_{1,n}}}{.Math.x_1{h}_{1,3}^{*}.Math.}$$\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:

(87) $\tilde{Y}=\left(\begin{array}{ccc}{h}_{1,1}& h_{1,2}& h_{1,3}\\ h_{2,1}& h_{2,2}& h_{2,3}\end{array}\right)\left(\begin{array}{c}\frac{x_1{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}\\ \frac{x_2{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{x_1{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}+\frac{x_2{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)$ 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:

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

(89) ${\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)$

(90) 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:

(91) $\left(\begin{array}{c}{y}_1\\ y_2\end{array}\right)=\left(\begin{array}{ccc}{h}_{1,1}& h_{1,2}& h_{1,3}\\ h_{2,1}& h_{2,2}& h_{2,3}\end{array}\right)\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right){\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& \frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\\ \frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right).$

(92) And finally, the transmitted X is estimated at FEQs by:

(93) 0$\stackrel{\mathrm{.Math.}}{X}=\left(\begin{array}{c}{\stackrel{\mathrm{.Math.}}{x}}_1\\ {\stackrel{\mathrm{.Math.}}{x}}_2\end{array}\right)={\left(\begin{array}{cc}.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.& 0\\ 0& .Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\end{array}\right)}^{-1}\left(\begin{array}{c}{y}_1\\ y_2\end{array}\right)$

(94) Signal Tracking in 16 1. After data source (1611):

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

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

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

(98) $\stackrel{}{X}=\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\frac{1}{\left[\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}\right]}\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)$$\mathrm{and}\mathrm{hence},\stackrel{}{X}=\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\frac{1}{\left[\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}\right]}\left(\begin{array}{cc}\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(.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)\\ \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(.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}\right)\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)$ Finally:

(99) $\left(\begin{array}{c}{\stackrel{}{x}}_1\\ {\stackrel{}{x}}_2\end{array}\right)=\left(\begin{array}{c}\frac{x_1\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)+x_2\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(-\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)}{\left[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)*\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\right]}\\ \frac{x_1\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)*\left(-\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)+x_2\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)*\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)}{\left[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)*\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\right]}\end{array}\right)$ 4. After MICOP-MRC (1640)

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

(101) $\hat{X}=\left(\begin{array}{cc}\frac{h_{1,1}^{*}}{.Math.h_{1,1}.Math.}& 0\\ 0& \frac{h_{2,2}^{*}}{.Math.h_{2,2}.Math.}\\ \frac{{}_1{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}& \frac{{}_2{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\end{array}\right)\left(\begin{array}{c}\frac{x_1\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)+x_2\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(-\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}-\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)}{\left[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)*\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\right]}\\ \frac{x_1\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)*\left(-\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}-\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)+x_2\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)*\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)}{\left[\left(.Math.h_{1,1}.Math.+{}_1.Math.h_{1,3}.Math.\right)*\left(.Math.h_{2,2}.Math.+{}_2.Math.h_{2,3}.Math.\right)-\left(\frac{h_{1,2}{h}_{2,2}^{*}}{.Math.h_{2,2}.Math.}+\frac{{}_2{h}_{1,3}{h}_{2,3}^{*}}{.Math.h_{2,3}.Math.}\right)*\left(\frac{h_{2,1}{h}_{1,1}^{*}}{.Math.h_{1,1}.Math.}+\frac{{}_1{h}_{2,3}{h}_{1,3}^{*}}{.Math.h_{1,3}.Math.}\right)\right]}\end{array}\right)$ 5. Finally the transmitted signal Y is modelled as: