A device for performing a multiplication operation in the optical domain

Abstract

A device for performing a multiplication operation in the optical domain includes a multiplication circuit 210, an input circuit 220 and an output circuit. The multiplication circuit 210 has multiple cells comprising at least one primary cell and at least one reference cell. The input circuit 220 provides at least one input signal, each input signal comprising an input optical signal at a data wavelength and an input reference optical signal at a reference wavelength. Upon sending the at least one input signal to the multiplication circuit, a first pair and a second pair of output adjusted signals are obtained for each input signal. The output circuit 230 detects and process the first and second pairs of output adjusted signals to obtain a result of a multiplication operation of the input vector formed by the input signals, with the coefficient matrix formed by transmission factors of the cell.

Description

Figure 1 is a diagram of an optical device 100 that includes a waveguide 110 coupled to an amplitude adjuster 120 formed on a substrate 130. The amplitude adjuster 120 may be an optical modulator or an optical amplifier or a combination of both. A controller (not shown), such as an electronic controller or an optical controller is provided to control the operation of the amplitude adjuster. The amplitude adjuster 120 is coupled to the waveguide 110, so that a light signal carried by the waveguide 110 interacts with the adjuster 120. The optical adjuster 120 may be implemented in different fashion and can be made of any material that is switchable between different states corresponding to different optical properties of the adjuster. An optical amplifier may be implemented as a semiconductor optical amplifiers SOAs. An optical attenuator may be Mach Zehnder modulators (MZMs) also referred to as Mach Zehnder interferometers (MZls), or electroabsorption modulators (EAMs), electro optic modulator (EOM), or microring resonators (MRR), or a phase-change material (PCM) modulators. An attenuator can be used to cancel or extinct an optical signal that should not be transferred to an output port. In this scenario the amplifier is turned off and the attenuator is turned on. The amplifier / attenuator combination may be implemented using a same component or as two separate components. An adjuster component, such as for instance an SOA, may be designed to perform signal amplification when a positive voltage is applied to it, and to perform signal attenuation when a negative voltage is applied to it. The device 100 may be used to perform a multiplication operation. The modulation of an optical signal can be used to perform a multiplication operation of an input optical signal by a predetermined coefficient. The adjuster 120 is operated to change an optical property of the modulator. Different optical properties correspond to different states of the adjuster. The state of the adjuster can be used to encode information. For instance data may be encoded in the amount of light transmitted through the waveguide 110. Depending on the choice of modulator, the optical property of the adjuster may be an absorption, a gain, a transmission, or a reflection property. For instance in the case of an EOM modulator, an electric signal may be provided to the EOM modulator and change its transmission factor, such that when an input signal travels through the optical waveguide, the modulator transmits a percentage of the input optical signal according to the transmission factor. In the case of an optical amplifier, the amplitude amplifier may have a transmission factor greater than 1, that account for the gain of the amplifier. Three mathematical values v, a and r are defined: v is the value encoded in the input power Pin of the input optical signal; a is the value encoded in the state of the adjuster / modulator 120; and r is the value encoded in the out power Pout of the output optical signal as a result of the multiplication v * a = r. To perform this operation, the values of “a” and “v” need to be mapped to modulator transmission states and the input power states as follows: v 6 [0. .1] maps to input power Pin E [Pmin.. Pmax]; a 6 [0..1] maps to modulator transmission t 6 [tmin.. tmax]. This includes 0 ,1 and values between 0 and 1. It will be appreciated that in another example v 6 [-1..1] and a 6 [-1..1]. There is a translation between mathematical value and DAC value [which adjusts the adjuster / modulator voltage) on the electronic side. A look up table may be provided for the translation. However, the minimum values Pmin and tmin are typically > 0. The minimum transmission value tmin is greater than zero because the modulator 120 does not fully attenuate the input signal even when set to zero transmission, [maximum absorption). For example, performing the mathematical operation 1*0 = 0, may be expressed as Pmax * tmin. If Pmax = 1 mW and tmin = 0.5, then Pmax * tmin = 0.5 mW. This value is greater than zero, and therefore inaccurate. At the same time performing the calculation 0.1*0.1=0.01 would photonically mean (Pmin+0.1*DeltaP)*(tmin+0.1*Deltat) with DeltaP being the difference between Pmax and Pmin und Deltat being the difference between tmax and tmin. Assuming Pmin=0.5 and tmax=1.0 (therefore DeltaP=0.5 and Deltat=0.5), this would lead to Pout=0.3025. So even though the mathematical result 0.01 is larger than 0, the photonic output is not. Because the modulator still transmits light even in its “closed” state, an offset needs to be subtracted from the measured optical output power of the multiplication. This offset is not constant, but input value (vector and matrix) dependent. In fact, a full matrix vector multiplication (MVM) needs to be performed to obtain the offset values for each matrix multiplication. As both the vectors and the matrix elements are programmed with optical modulators, they both contribute to the offset problem. Figure 2 is a diagram of a device for performing a multiplication operation in the optical domain. The optical system or device 200 includes a matrix multiplication unit 210 coupled to an input unit 220 and an output unit 230. The input unit 220 and the output unit 230 may be referred to as input and output circuits, respectively. A controller 205 is provided to control the operation of the various amplitude adjusters provided in the circuit 200. An amplitude adjuster may be an optical modulator or an optical amplifier or a combination of both. For instance the controller may adjust the transmission factor or transmission coefficients of the adjusters. When the adjuster is an amplifier the transmission factor may be greater than 1. The matrix multiplication unit 210 also referred to as multiplication circuit, has a plurality of cells comprising at least one primary cell also referred to as data cell, and at least one reference cell. The primary cell has a primary adjuster (M) having a primary transmission factor (A). The primary adjuster may be referred to as data adjuster and the primary transmission factor as data transmission factor. Each reference cell has a reference adjuster (Mca and Mcb) having a reference transmission factor (Aref). So each cell may be associated with a transmission factor of the cell. The matrix multiplication unit 210 has two input waveguides 212a and 212b (rows) coupled to the light source unit 220 and three output waveguides 213a, 213b, 213c (columns) coupled to the output unit 230. It will be appreciated that the number of input and output waveguides may vary and can be generalised to any numbers Nin input waveguides and Mout output waveguides. The input and output waveguides 212, 213 are arranged to form a grid of multiplication unit cells 211. For each unit cell, the input and output waveguides 212, 213 cross one another at a crossing point C. A coupler 214 is interposed between the input waveguide 212 and the associated output waveguide 213. The coupler 214 is provided with an amplitude adjuster M. The amplitude adjusters may be implemented as described above with respect to figure 1. The input waveguide 212 and the coupler 214 act as two directional couplers in the unit cell, with fixed transmission. The input waveguide 212 splits light from the input row so that part of the light is transmitted along 212 to the next cell and part of the light is sent to the adjuster M to adjust the amplitude of the light hence increase or attenuate the light intensity. The coupler 214 then adds the modulated light to the output waveguide 213 so that each unit cell contributes equally to the output. In figure 2, six unit cells are shown. Four primary cells labelled 211aa, 211ab, 211ba, 211bb are provided with adjusters Maa, Mab, Mba, Mbb. Two reference cells labelled 211ca, 211cb are provided with adjusters Mca, Mcb, respectively. Each adjuster has a corresponding transmission factor or transmission coefficient labelled A. For instance adjuster / modulator Maa has transmission factor An. The input unit 220 is configured to generate one or more input signals. Each input signal includes two signals: an input optical signal at a data wavelength [Ad] and an input reference optical signal at a reference wavelength [Aref]. The input unit 220 has a light source 221 coupled to a plurality of combiners or wavelength multiplexers 222a and 222b. The light source 221 is configured to provide optical signals with different wavelengths. In this example two wavelengths are used: Adi, and Aref. The output of multiplexer 232a is coupled to the input waveguide 212a, and the output of multiplexer 232b is coupled to the input waveguide 212b. The light source 221 is coupled to each multiplexer via two waveguides; a first waveguide fitted with a first modulator / adjuster Ml or M2 for providing a first input optical signal, and a second waveguide fitted with a reference modulator / adjuster Mlref or M2ref for providing an input reference optical signal. In figure 2, the multiplexer 222a receives the input optical signal VI, and the input reference optical signal Vref,l. Similarly, the multiplexer 222b receives the input optical signal V2, and the input reference optical signal Vref,2. The output unit 230 includes three splitters or wavelength demultiplexers labelled 232a, 232b and 232c, coupled to the output of the output waveguides 213a, 213b and 213c respectively. Each splitter / wavelength demultiplexer is adapted to split the output signal in a plurality of wavelength dependent sub signals. In this example the wavelength demultiplexers split the output signals in two sub signals at the data wavelength and the reference wavelength respectively. A pair of photodetectors is coupled to each demultiplexer via waveguides. The demultiplexer 232a is coupled to photodetectors DI and D2 for measuring photo current intensities from optical powers Oi,iand Oi,2, respectively. The demultiplexer 232b is coupled to photodetectors D3 and D4 for measuring photo current intensities from ¢)2,1 and ¢)2,2- The demultiplexer 232c is coupled to photodetectors D5 and D6, for measuring photo current intensities from Or,i and Or,2. The output of each photodetector is coupled to a subtraction circuit 235 for generating the result signals RI and R2. An input vector may have a plurality Nin of input signals. In figure 2 Nin=2, but the matrix multiplication unit 210 may be extended to receive any number Nin of inputs. It will also be appreciated that the input unit 220 may be extended to generate multiple input vectors. For example for two input vectors the light source 221 would be coupled to each multiplexer via three waveguides, and would provide signals at Adi for the first vector, Ad2 for the second vector, and Aref. In this case each demultiplexer would be connected to a third detector for detecting the second data wavelength Ad2. More generally for a number N of input vectors N different data wavelengths are provided: Adi- AdN, and the same reference wavelength Aref is used for all the input reference optical signals. Then each demultiplexer is coupled to N + l detectors. The input circuit 220 may also be adapted to generate a plurality of input reference optical signals, at different reference wavelengths. For instance the input circuit may provide a different reference wavelength per data wavelength. It will be appreciated that the light source may be implemented in different ways. It could be a single light source, for instance a tuneable light source or multiple light sources. This could include laser sources, integrated semiconductor laser sources, solid state light source such one or more light-emitting diodes LED, among others. The light source may also be a temporally incoherent light source. In operation the input optical signal at a first data wavelength (Adi) and the input reference optical signal at the reference wavelength (Aref) travel together but independently in the matrix 210. For each input signal two pairs of output modulated signals are obtained: a first pair of output modulated signals modulated by a primary modulator / adjuster, and a second pair of output modulated signals modulated by a reference modulator / adjuster. The output adjusted / modulated signals obtained at the output of waveguides 213a, 213b and 213c are then separated (demultiplexed based on their wavelength) before being detected by the photodetectors D1-D6. The one or more input signals form an input vector, and the transmission factors of the modulators / adjusters present in the multiplication circuit form a coefficient matrix. The subtraction circuit 235 is then used to process the first and second pairs of output modulated signals to obtain a result R (RI, R2) of a multiplication operation of the input vector with the coefficient matrix. By multiplying the input vector with reference matrix states (extra column 22 lea, 221cb) and multiplying the matrix states with a reference vector, one can obtain the input-dependent offset values to be subtracted to find the correct mathematical result of the matrix vector multiplication (MVM). In this way the reference values are obtained in parallel at the same time together with the data outputs. Using a balanced detection scheme between the input and reference vector outputs and a subsequent analogue electronic subtraction to remove the offset using the reference column, reveals the mathematical result in real time. In an alternative implementation the individual optical outputs of the matrix columns are converted to the electronic domain using a photodetector, and digitized using an ADC individually. The reference subtraction is subsequently carried out in the digital domain. The reference column removes the offset introduced by the matrix modulators. The reference vector removes the offset introduced by the input modulators. The analogue reference subtraction scheme allows to do the full MVM in real time. It will be appreciated that the adjusters (for instance modulators) of the input circuit 220 may be different from the adjusters present in the multiplication circuit 220. These means that the adjusters may have different minimum and maximum transmission coefficients. Figure 3 is a simplified diagram of the optical system of figure 2 for performing a single multiplication. The optical system 300 has an input stage 320 coupled to an input waveguide 312a and two output waveguides 313a and 313b forming cells 311aa and 311ba. The input stage 320 is provided with multiplexer 322a that received inputs from two waveguides fitted with modulators Ml and Mref, respectively. The cells 311aa and 311ba provided with modulators Ma and Mref respectively. Each modulator has an adjustable transmission coefficient t. The modulators Ml and Ma have transmission factors (also referred to as transmission coefficients) tv and ta, respectively. In this example the reference modulators Mref are identical and have transmissions coefficients tr. It will be appreciated that different reference modulator types with different tmin may be chosen which can have advantages in terms of signal to noise ratio depending on application. However, for the purpose of this example the reference modulators are treated as identical. The optical system 300 is used to perform the multiplication v ■ a = r with v, a, r being scalar v, a, r G [—1. .1], The scalar values v and a map to tv,ta G [^min- ■ ^max] according to: t = t . +                  t \ Lv Lmin '   2 \Lmax ^minJ and tn =     + (n+1)' (tmax — tmin), in which tmir, and tmnx are the minimum and (X       IILLIL         2       v H LLLA,       111111 / 7                       IILLIL             IILLLA maximum transmission factor / coefficients of the photonic modulators. The reference modulators are set to tr = (tmin + tmax) / 2- By setting the reference modulators to the middle value, multiplication of negative numbers can be achieved. It will be appreciated that the transmission coefficient of the reference modulators may be changed depending on numbers and ranges involved. The result r of the multiplication operation is expressed as: r = £12-212-21111212. in which 0^, O12, Orl, Or2 are the intensities Onorm measured by the photodetectors DI, D2, D3, D4, respectively. The value Onorm is the normalised intensity expressed as: 0     — P ' t — P f' t — P ■ t f + P f ■ t f '-'norm Lmax Lmax 1 ref Lmax Lmax Lref 1 ref Lref p • + P With Prpf =         in which PmnY and Pmirt are the minimum and maximum I CJ                         '                      H LLLA,            IILLIL power of the input signal. Pmin=P0*tmin and Pmax=P0*tmax, with P0 being some arbitrary constant laser power. In figure 2, the principle of scalar multiplication shown in figure 3 is extended to matrix vector multiplication (MVM). The optical system 200 is used to perform the multiplication A-V = R In which Aii’ is the mathematical value encoded in the adjuster / modulator of the corresponding primary cell; 7 / is the value encoded in the input power Pin l of the first input optical signal; V2' is the value encoded in the input power Pin_2 of the second input optical signal; R^is the value encoded in the out power Pout l of the first output optical signal; and R'2is. the value encoded in the out power Pout_2 of the second output optical signal. The values R^ and R2' of vector R can be expressed as: R^ = A1±'■    + A12'■ V2' and R2' = A21' -V^ + A^' -V2'. The photodetectors D1-D6 detect the optical powers 0^, O12, O22, Or l, Or2 in parallel simultaneously. Each detected optical power is converted to a current (photo current) that is proportional to the optical power. The photodetector DI detects O11= Alt ■ Pin_l + ,d12 ■ Pin_2 at Adi. The photodetector D2 detects 2=    ■ Pin_refl + ,d12 ■ Pin_ref2 at Aref. The photodetector D3 detects O2;1= i421 ■ Pin_l + A22 ■ Pin_2 at Adi. The photodetector D4 detects O2;2= i421 ■ Pin_refl + A22 ■ Pin_ref2 at Aref. The photodetector D5 detects Orl= Aref ■ Pin_l + Aref ■ Pin_2 at Adi. The photodetector D6 detects Or2= Aref ■ Pin_refl + Aref ■ Pin_ref2 at Aref. In which Aii are transmission factors of the adjusters / modulators; Pin l is optical power of the input optical signal VI; Pin_2 is optical power of the input optical signal V2; Pin refl is optical power of the input reference optical signal Vrefl; Pin_ref2 is optical power of the input reference optical signal Vref2. The values of can be obtained from the detected values as follows: _ Ol,l~Ol,2~Or,l + °r,2                                  r   O2,l~°2,2~°r,l^ °r,2 ^norm                                            ^norm Figure 4 is a diagram of a balanced detection circuit. The circuit 400 includes two photodiodes coupled in series, a transimpedance amplifier and a voltage source. The pair of photodiodes is connected in parallel with the voltage source. The transimpedance amplifier has an input connected to node A between the photodiodes, and an output for providing an output voltage. In operation each photodiode generates a photocurrent. The difference in photocurrents is sent to the transimpedance amplifier, which in turn produces an output voltage proportional to that difference. Figure 5 shows a diagram of a circuit for obtaining the values RI and R2 of vector R. Three balanced detections circuits 510, 520, 530, are connected to a subtraction circuit 540. The balanced detection circuit 510 provides a voltage V(O1;1 — O12] proportional to the difference between the photocurrents of O1± and O12. Similarly the balanced detection circuit 520 provides a voltage V(O21 —O22], and the balanced detection circuit 530 provides a voltage and V(Or l — Or2). The circuit 540 receives each voltage output to generate the values RI and R2. It will be appreciated that the subtraction circuit 540 may be implemented either in an analogue form or as a digital circuit. Figure 6 is a flow chart of a method for performing a multiplication operation in the optical domain. The method includes steps 610-650. The proposed method provides accurate multiplication operations in the optical domain. By setting the reference states to the middle of the modulator ranges, multiplication with negative numbers (for both vector and matrix) can be achieved. By setting the reference modulators to different states, the ranges of values can be adjusted (continuously from purely positive to purely negative). The splitting ratios of the couplers used in multiplication circuits of figure 2 are set to achieve equal splitting of light to all outputs. However, different splitting ratios, may be selected. Figure 7A is a diagram illustrating the splitting ratios set to achieve equal splitting of light to all outputs. The numbers (ratios) indicate what fraction of light is split to the cross port. The adjusters / modulators are programmed to the matrix state. If the matrix values are fixed, there is no need for the programmable adjusters / modulators. Figure 7B is a diagram illustrating a multiplication matrix without any adjuster / modulator. In this case the desired optical attenuation of the optical signal is provided by the splitting ratios. Induced losses are controlled by selecting the splitting ratios appropriately for various couplers of the cell. For instance in the top left cell of figure 7B, instead of coupling 1 / 3 of the light down as in the standard implementation (see Figure 7 A), an attenuation coefficient (Al) is applied to the splitting ratio (1 / 3*A1). The light coupled to the column waveguide now is the same as if there was a modulator in state Al. One can also use the second splitting ratio in a cell. Looking at the top left cell in figure 7B if the first splitter is set to 1 / 3 as usual, the second one (currently 1 / 1) can be adjusted to include the transmission factor of the modulator. For a fully closed modulator, the splitting ratio is set to 0 / 1. In this case the light is scattered out of the circuit and not transferred to the column. Figure 7C is a diagram illustrating a multiplication matrix without any adjuster / modulator, and with some cells having no couplers. To achieve maximum dynamic range (previously between open and closed modulator state) one can even remove at least some splitters to encode a logic low (0). This is analogous to a modulator that attenuates the light completely. The splitting ratios illustrated in figures 7B and 7C are provided for example only and would need to be adjusted based on the required data patterns to be searched. When using a fixed matrix with no adjusters / modulators as shown in figure 7B or 7C, one may still add an additional reference column with matrix reference adjusters / modulators. The various waveguides / channels described above with reference to figures 1 to 7 may be integrated or fibre based. The device as described with reference to figures 2 to 7 may be implemented using an integrated optical circuit such as a photonic integrated circuit (PIC). A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the disclosure. Accordingly, the above description of the specific embodiments is made by way of example only and not for the purposes of limitation. It will be clear to 5 the skilled person that minor modifications may be made without significant changes to the operation described.

Claims

1. A device for performing a multiplication operation in the optical domain, the device comprisinga multiplication circuit comprising a plurality of cells, the said plurality of cells comprising at least one primary cell and at least one reference cell;an input circuit adapted to provide at least one input signal, wherein each input signal comprises an input optical signal at a data wavelength and an input reference optical signal at a reference wavelength;the device being configured such that upon sending the said at least one input signal to the multiplication circuit, a first pair of output adjusted signals adjusted by the primary cell, and a second pair of output adjusted signals adjusted by the reference cell, are obtained for each input signal;the device further comprising an output circuit adapted to detect the first and second pairs of output adjusted signals; wherein the said at least one input signal forms an input vector, and wherein transmissions factors of the cells form a coefficient matrix; and to process the first and second pairs of output adjusted signals to obtain a result of a multiplication operation of the input vector with the coefficient matrix.

2. The device as claimed in claim 1, wherein each reference cell has a matrix reference amplitude adjuster having a reference transmission factor.

3. The device as claimed in claim 1 or 2, wherein each primary cell has a primary amplitude adjuster having a primary transmission factor, or wherein at least one primary cell has a coupler andwherein the cell transmission factor is based on splitting ratios of the coupler.

4. The device as claimed in any of the claims 1 to 3, wherein the first pair of output adjusted signals is adjusted by the primary amplitude adjuster, and the second pair of output adjusted signals is adjusted by the reference amplitude adjuster.

5. The device as claimed in any of the preceding claims, wherein the input stage comprises a light source coupled to at least one combiner via at least one data waveguide provided with an input amplitude adjuster, and a reference waveguide provided with an input reference amplitude adjuster.

6. The device as claimed in claim 5, wherein the light source is configured to provide optical signals at one or more data wavelengths and at the reference wavelength, respectively.

7. The device as claimed in claim 5 or 6, wherein the input circuit isconfigured to generate a plurality of input reference optical signals, at different reference wavelengths.

8. The device as claimed in claim 6 or 7, wherein each input reference amplitude adjuster, and each matrix reference adjuster is operable in a plurality of states that include a first state for minimum transmission, a second state for maximum transmission, and a plurality of reference states between the first state and the second state, and wherein each input reference amplitude adjuster and each matrix reference amplitude adjuster is set to a reference state.

9. The device as claimed in any of the preceding claims, wherein the output stage comprises a plurality of splitters, wherein each splitter is coupled to a pair of photodetectors; and a processing circuit configured to process the first and second pairs of output modulated signals to obtain the result of a multiplication operation of the input vector with the coefficient matrix.

10. The device as claimed in claim 9, wherein the processing circuit is configured to perform a normalisation operation.

11. The device as claimed in claim 9 or 10, wherein each pair of photodetector forms part of a balanced detection circuit.

12. The device as claimed in any of the preceding claims wherein the multiplication circuit comprisesa plurality of input channels;a plurality of output channels; anda plurality of coupling channels, each coupling channel being configured to couple an input channel to an output channel, wherein a plurality of coupling channels comprises an amplitude adjuster configured to adjust an amplitude of an optical signal.

13. The device as claimed in claim 12, wherein the amplitude adjuster comprises at least one of an optical attenuator and an optical amplifier.

14. The device as claimed in any of the claims 1 to 13, wherein the multiplication circuit is adapted to multiply a plurality of input vectors with the coefficient matrix sequentially, and / or wherein the multiplication circuit is adapted to multiply a plurality of input vectors with the coefficient matrix in parallel on differentwavelength channels, each input vector having its own data wavelength.

15. A method of performing a multiplication operation in the optical domain, the method comprisingproviding a multiplication circuit comprising a plurality of cells, the said plurality of cells comprising at least one primary cell and at least one reference cell;providing at least one input signal, wherein each input signal comprises an input optical signal at a data wavelength and an input reference optical signal at a reference wavelength;sending the said at least one input signal to the multiplication circuit to obtain for each input signal a first pair of output adjusted signals adjusted by the primary cell, and a second pair of output adjusted signals adjusted by the reference cell;detecting the first and second pairs of output adjusted signals;wherein the said at least one input signal forms one or more input vectors, and wherein transmissions factors of the cells form a coefficient matrix;processing the first and second pairs of output adjusted signals to obtain a result of a multiplication operation of the input vector with the coefficient matrix.

16. The method as claimed in claim 15, wherein the first pair of output adjusted signals comprises a first adjusted signal at the first wavelength and a reference adjusted signal at the second wavelength, and wherein the second pair of output adjusted signals comprises a second adjusted signal at the first wavelength and a second reference signal at the second wavelength; wherein the processing step comprisessubtracting the reference adjusted signal at the second wavelength from the first adjusted signal at the first wavelength to obtain a first difference;subtracting the second reference adjusted signal at the second wavelength from the second adjusted signal at the first wavelength to obtain a second difference; andsubtracting the second difference from the first difference.

17. The method as claimed in claim 15 or 16, comprisingadjusting the amplitude of a first optical signal at the first wavelength using an input adjuster to obtain the input optical signal; andadjusting the amplitude of a second optical signal at the second wavelength using an input reference adjuster to obtain the input reference optical signal.

18. The method as claimed in claim 17, wherein each primary cell has a primary amplitude adjuster, and wherein each reference cell has a matrix reference amplitude adjuster, each adjuster having a plurality of transmission states.

19. The method as claimed in claim 18, further comprising mapping vector values to the to the transmission states of the input adjusters and mapping matrix values to the transmission states of the primary amplitude adjusters.

20. The method as claimed in any of the claim 15 to 19, comprising setting the transmission factor of the reference adjusters to a predefined value.

21. The method as claimed in any of the claims 15 to 20, wherein the input vector comprises a data vector and a reference vector.

22. The method as claimed in any of the claims 15 to 21, wherein the 5            coefficient matrix comprises a data matrix and a reference matrix.

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