Each function from TXI has a +90° or −90° phase difference when compared to any function from group TXQ, which is called “quadrature.” Further, two functions within a group may have a 180° phase difference, which is called “polarity inversion.” This means that change of mutual capacitances driven by waveforms from group TXI exhibit a phasor deviation which is perpendicular to phasor deviations otherwise caused by changes of mutual capacitances driven by the other waveforms from group TXQ. Memory-less nonlinear operation on stem(t) functions in general may not affect the properties of quadrature. Therefore, stein function can be shifted. This means the waveforms actually used to drive transmit electrodes can be sinusoidal, square, or impulse, without limitation.

Regarding CDMA codes, it is possible to drive TX electrodes according to one combined CDMA code or two independent CDMA codes.

FIG. 1 shows quadrature TX superposition of signals, using a phase shift of 90 degrees. The sinusoidal waveform transmit signal driving tx₁electrode is at 90° phase rotation (quadrature) relative to the sinusoidal waveform transmit signal driving tx₂electrode. The sinusoidal waveform transmit signal driving tx₃electrode is at 90° phase rotation (quadrature) relative to the sinusoidal waveform transmit signal driving tx₄electrode. The transmit signals are transmitted for two time periods (chip1 and chip2). The amplitude and phase of the phasors are measured by receive electrodes (rx₁, rx₂, rx₃, and rx₄) during both chip1 and chip2. The phasor measured by rx₃during chip1 indicates an interfering object (e.g., finger) is proximate the tx₂/rx₃mutual capacitance node at that time. The transmit signal transmitted by tx₂, which is in phase (I), and received by rx₃is reduced in magnitude during chip1 by a proximate interfering object, so that the amplitude of the phasor is reduced and the phase of the phasor is changed from a 45 degree position to a position of about 50 degrees, wherein 0 degrees is the horizontal axis extending to the right, 90 degrees is the vertical axis extending up, 180 degrees is the horizontal axis extending to the left, and 270 degrees is the vertical axis extending down.

FIGS. 2A through 2D show quadrature TX superposition.

FIG. 2A shows a sinusoidal transmit signal driving transmit electrodes tx₁and tx₂with a phase shift of 90 degrees between the sinusoidal transmit signals so the signals are in quadrature. There are no interferences at the mutual capacitance nodes where the transmit electrodes tx₁and tx₂intersect with the receive electrode rx₁. The component signal of the phasor received from tx₁has amplitude equal to one (1) and phase of ninety (90) degrees, and the component signal of the phasor received from tx₂has amplitude equal to one (1) and phase of zero (0) degrees. Thus, the phasor of the signal received by rx₁has amplitude equal to 1.4142 (square root of 2) and phase of forty-five (45) degrees.

FIG. 2B shows a sinusoidal transmit signal driving transmit electrodes tx₁and tx₂with a phase shift of 90 degrees between the sinusoidal transmit signals so the signals are in quadrature. There is an interference at the mutual capacitance node where the transmit electrode tx₁intersects with the receive electrode rx₁. The component signal of the phasor received from tx₁has amplitude equal to seven tenths (0.7) and phase of ninety (90) degrees, and the component signal of the phasor received from tx₂has amplitude equal to one (1) and phase of zero (0) degrees. Thus, the phasor of the signal received by rx₁has amplitude equal to 1.22 (square root of 1.49) and phase of thirty-five (35) degrees. For comparison, the phasor with amplitude equal to 1.4142 and phase of forty-five (45) degrees is shown as a grey arrow.

FIG. 2C shows a sinusoidal transmit signal driving transmit electrodes tx₁and tx₂with a phase shift of 90 degrees between the sinusoidal transmit signals so the signals are in quadrature. There is an interference at the mutual capacitance node where the transmit electrode tx₂intersects with the receive electrode rx₁. The component signal of the phasor received from tx₁has amplitude equal to one (1) and phase of ninety (90) degrees, and the component signal of the phasor received from tx₂has amplitude equal to seven tenths (0.7) and phase of zero (0) degrees. Thus, the phasor of the signal received by rx₁has amplitude equal to 1.22 (square root of 1.49) and phase of fifty-five (55) degrees. For comparison, the phasor with amplitude equal to 1.4142 and phase of forty-five (45) degrees is shown as a grey arrow.

FIG. 2D shows a sinusoidal transmit signal driving transmit electrodes tx₁and tx₂with a phase shift of 90 degrees so the signals are in quadrature. There is an interference at the mutual capacitance node where the transmit electrode tx₁intersects with the receive electrode rx₁and an interference at the mutual capacitance node where the transmit electrode tx₂intersects with the receive electrode rx₁. The component signal of the phasor received from tx₁has amplitude equal to seven tenths (0.7) and phase of ninety (90) degrees, and the component signal of the phasor received from tx₂has amplitude equal to seven tenths (0.7) and phase of zero (0) degrees. Thus, the phasor of the signal received by rx₁has amplitude equal to one (1) (square root of 1.0) and phase of forty-five (45) degrees. For comparison, the phasor with amplitude equal to 1.4142 and phase of forty-five (45) degrees is shown as a grey arrow. As can be seen, the phasor of the signal received by rx₁has a reduced amplitude as compared with the phasor of FIG. 2A.

The quadrature TX superposition may provide unambiguous interfering object positions. The quadrature TX superposition may allow to double the number of TX signals, i.e. electrodes, to be transmitted and measured simultaneously, while the SNR remains unchanged, compared to CDMA.

According to aspects, orthogonality of signals at the receiver electrode provides independence between different, superposed transmit signals, where it would otherwise be difficult to dissect the sum received signal into its components. While for signals orthogonal in time or code space, a guard interval can prevent such inter-channel interference, this may not work for transmit signals in quadrature, i.e., orthogonal in complex space, when experiencing different signal propagation delays.

Differences in signal propagation delay may be resolved by: (1) at the transmitter, adjusting the transmit signal phases or delays such that the two transmit signals at hand arrive at the receiver in quadrature (which may be considered a software solution: e.g., by transmit phase control); (2) on the channels, by ensuring that the propagation delay of two transmit signals in quadrature is approximately equal (which may be considered a hardware solution: e.g., by sensor layout, e.g., by adjusting feeding line lengths), or (3) algorithmically, by assigning quadrature space-time mapping vectors to a pair of transmit electrodes with approximately the same propagation delay to a receiver. Regarding this third propagation delay resolution method, dedicated space-time-map-to-Tx assignments provide independence between any transmit signals, and is achievable for a variety of sensor setups.

Multiplexing is a method of transmitting and receiving independent signals over a common channel, i.e., a common signal path for multiple transmit signals to a receiver. Signal independence can be yielded, for example, using time-division, frequency division, code division, or signal quadrature. To yield a desired receive signal phase (and, optionally, also signal amplitude), the received signal can be corrected in phase (and amplitude) in a so-called equalization step. Because all transmit signals share one single channel, one phase (and one amplitude) correction value may be considered.

With multiple-access systems, the different transmit signals can have individual channels to a receiver. Therefore, channel phase and attenuation should be corrected for each transmit signal with individual correction values (to adjust the Rx phase). Inter-symbol interference (ISI) due to mismatch of expected and actual receive sequence (symbol) boundaries (start/end) at the receiver, e.g., due to different signal propagation delays, can be explicitly suppressed with a so-called guard interval, or implicitly—for example—by using a low-pass filter function suppressing the first and/or last samples of a receive signal sequence. To avoid inter-channel (inter-Tx) interference, signal orthogonality may be imposed at the receiver.

For time-division and code-division signals, i.e., transmit signal orthogonal in time and/or in the code space, orthogonality can be achieved despite differences between signal propagation delays for the different transmit signals also by using a sufficiently long guard interval.

A transmit electrode TX matrix stack may allow manipulations, including: rows reordered, any row multiplied by a constant, real-valued factor, columns reordered, any column multiplied by a complex number. Matrices can be manipulated before being stacked in a theta matrix θ, and the theta matrix θ can be further manipulated, where

j
=

-
1

Θ
=

[

H
n

jH
n

]

where H_nis an orthogonal matrix of order n; for example, a Hadamard matrix, and

theta
⁢

matrix
⁢

Θ

=

[

H
n

jP
n

]

where H_nand P_nare two orthogonal matrices of order n but are not necessarily identical or equivalent. For example, a Hadamard matrix and a Paley type I matrix. Equivalent in this context means P_ncan be obtained from H_nby linear combinations of its rows.

When a column of the Tx matrix stack is manipulated, the inverse operation should be performed on the receiver side before further processing of the respective chip, like, e.g., CDMA decoding.

FIG. 3 shows how two different forms of orthogonality may be combined (QM+CDMA=QCDMA). The transmit signals of tx₁-tx₄are phase shifted by 90 degrees relative to the transmit signals of tx₅-tx₈. An orthogonal code may be used for CDMA extra-chip modulation, where quadrature modulation may happen within a chip (intra) or at the transition between chips (extra). A superposed TX signal, owing to orthogonality, may be brought by quadrature intra-chip modulation, where modulation may happen within a chip (intra) or at the transition between chips (extra). CDMA may be decoded as measured I/Q vectors instead of scalars. In the example shown in FIG. 3, the phasors received at the receive electrodes during a first chip are decoded by CDMA to determine the mutual capacitance node tx₂/rx₃is being interfered,

FIG. 4A shows a general case of QCDMA decoding, where the matrix of received chips, R, contains complex numbers. In the signal matrix 400 shown adjacent transmit electrodes tx1-tx8, the columns are chip time intervals, and the rows transmit electrodes, A numerical matrix 402 corresponds to the signal matrix 400. The decoding uses the complex conjugate of theta matrix θ, so that the correlation of an imaginary number with itself yields a positive result. An alternative is to use the complex conjugate of R instead. There is redundancy when computing θ·R: half θ rows are copies of other rows, oriented along the imaginary (j) axis. For example, the row for tx₈and the row for tx₄are related. Therefore, it is possible to compute M_c, wherein M_cis a map of real and imaginary components of their respective positions that may be used to recreate an expected 8×2 matrix (M) for mutual capacitance. The transmit signal matrix θ is multiplied by the receive signal matrix R to produce the mutual capacitance node matrix 404. The mutual capacitance node matrix 404 corresponds to the mutual capacitance nodes 406 comprising transmit electrodes tx₁-tx₈and receive electrodes rx₁-rx₂, wherein all of the mutual capacitance nodes have a measured signal value of 4, except for the mutual capacitance node corresponding to tx₂/rx₂, which has a measured signal value of 3.6 indicating an interference.

FIG. 4B shows an alternative case of QM decoding. When a single “combined CDMA code” is used, one receiver computes one phasor per chip, wherein a phasor may be a scalar complex number. The sequence of received chips is decoded by computing vectorial dot products. Because two rows of theta matrix 408 differ by a factor j, the vector dot product of the second rows may not be computed as is done in the “generalized decoding” described with reference to FIG. 4A. When two independent codes 410A and 410B are used, the receivers compute two sets of chip phasors 412A and 412B. Each set is decoded independently as complex scalars. Phasor changes (3.9+4j) in the major direction (due to the QPSK code set) are used, and phasor deviation (4+4j) in the perpendicular directions (due to the other CDMA code set) are ignored. Signals 410A and 410B from transmit signal matrix Θ are multiplied by the major direction receive signal matrix R to produce phasors 412A and 412B. As noted, the real component of phasor 412A used to produce the mutual capacitance node matrix 404, corresponds to the mutual capacitance nodes 406 comprising transmit electrodes tx₁-tx₈and receive electrodes rx₁-rx₂, wherein all of the mutual capacitance nodes have a measured signal value of 4, except for the mutual capacitance node corresponding to tx₂/rx₂, which has a measured signal value of 3.6 indicating an interference. See FIG. 4A. Whether the system operates as a single combined code or as two independent codes, if chip lengths are uneven then an additional processing is desired: either the template coefficients or the resulting phasor before CMDA decoding is normalized by the gain tied to the chip length.

FIG. 5 shows code variations, wherein transmit signals of tx-tx: of the code matrix are swapped with transmit signals of tx₅-tx₈during chip 2 and chip 4. In other examples, rows of the code matrix can be reordered, rows of the code matrix can be omitted, rows of the code matrix can be multiplied by −1 (but typically not by j, because it then would look like another row of the matrix and therefore not be orthogonal), columns of the code matrix can be multiplied by a unity vector of arbitrary phase, two columns of the code matrix can be swapped, and code matrices can be changed between two measurement frames.

As shown in FIG. 5 the chip boundaries are the same for all used transmit electrodes, and the receivers compute one phasor at a time. An orthogonal matrix Hn is built and constitutes the CDMA code. Rows of the matrix correspond to the sequency of chips applied to the transmit electrodes (for example+1 for 0° phase, −1 for 180′ phase). A taller matrix theta θ (not shown) may be created by vertically concatenating two, possibly different, orthogonal matrices Hn0 and j*Hn1 to produce a matrix theta (Transmit Θ). The resulting second matrix sits on the imaginary axis, since j=sgrt(−1). Matrix theta (Transmit Θ) can be further transformed with row permutations, column permutations, or multiplication of rows by −1 or multiplication of columns by j or −j. The content of the theta matrix (Transmit Θ) is then mapped to selection of transmission waveforms picked from their respective transmission groups and respective polarity.

TX waveforms may have the following properties.

I=(t)=cos(f(t))

Q(t) sin(f(t)), where f(t) is a function which provides the instantaneous phase. For example f(t)=2*pi*fc*t for a linear phase increase I(t) and Q(t) can then be further modified by adding a constant, inserting a threshold, or multiplying with an envelope function to control spectral leakage.

For two transmitters transmitting signals in quadrature over channels with different signal propagation delays to a receiver, orthogonality may be achieved in the superimposed received signal by assigning pairs of space-time maps which are in quadrature to electrodes with same or similar propagation delays.

FIG. 6 shows a plot of a touch level estimate matrix obtained using the space-time mapping matrix shown in FIG. 7A, with each Tx a row and each time slot a column. FIG. 7A shows a quadrature transmit electrode pair, which is a set of two transmit electrodes to which the same binary code word is assigned but with a 90 degree phase shift between the two. As illustrated in FIG. 7A, Tx1 and Tx9 are assigned the same binary code word (−1, 1, −1, 1, −1, 1, −1, 1), but Tx9 is shifted 90 degrees from Tx1 (S_Tx9=j×S_Tx1). Rows #8-#11 are 90-degree shifted versions of rows #0-#3, respectively. For example, the space-time maps for Tx #2 and Tx #10 are in quadrature, at the transmitters. However, because transmit electrodes Tx #2 and Tx #10 are relatively distant from each other on the touch sensor, i.e., the lengths of their feeding lines are relatively distant (not shown in FIG. 7A), different channel delays (signal propagation delays) result in loss of quadrature at the receiver, and thus inter-channel interference. This inter-channel interference may be overcome by assigning pairs of space-time maps which are in quadrature to electrodes with same or similar channel or propagation delays. Typically, neighboring transmit electrodes may have similar signal propagation delays and may be paired based on them having similar signal propagation delays. Signal propagation delays may remain substantially constant over time, or signal propagation delays may change over time.

FIG. 7B shows code word assignments for transmit electrodes of a capacitive touch sensing system comprising transmit electrodes and receive electrodes positioned to have mutual capacitances between the transmit electrodes and the receive electrodes at mutual capacitance nodes, wherein the mutual capacitance at a mutual capacitance node deviates when an interfering object is proximate. There are four Tx electrode pairs with code words in quadrature. The two electrodes of each of these pairs are located next to each other, to reduce the expected signal propagation delay. Further, Tx0, Tx1, Tx2 and Tx3 are not part of a Tx electrode pair, because their length is distinctively different from the length of Tx4-Tx11, which is why different signal propagation delays may be expected for them too. Transmit signals in quadrature may have approximately the same signal propagation delay to the receiver by: (1) mapping via a software configuration the pairing of transmit electrodes with the same channel or phase delay, or (2) hardware modifying a sensor layout so that transmit electrodes pairs have the same channel or propagation delay. FIG. 7B shows Tx4 and Tx5 are assigned the same binary code word (1, 1, 1, 1, 1, 1, 1, 1), but Tx5 is shifted 90 degrees from Tx4 (S_Tx5=j×S_Tx4). Tx6 and Tx7 are assigned the same binary code word (−1, 1, −1, 1, −1, 1, −1, 1), but Tx7 is shifted 90 degrees from Tx6 (S_Tx7=j×S_Tx6). Tx8 and Tx9 are assigned the same binary code word (1, −1, −1, 1, 1, −1, −1, 1), but Tx9 is shifted 90 degrees from Tx8 (S_Tx9=j×S_Tx8). Tx10 and Tx11 are assigned the same binary code word (−1, −1, 1, 1, −1, −1, 1, 1), but Tx11 is shifted 90 degrees from Tx10 (S_Tx11=j×S_Tx10).

FIG. 7C shows the code word assignments shown in FIG. 7B, and further shows that transmit signal phase may be used to compensate for the two channels' propagation delay difference, by means of ‘tuning’ phases φ₅, φ₇, φ₉, φ₁₁.

In an alternative example not illustrated, configurable phases are used to implement the 90, 180, 270 degree phase shifts of QCDMA. QM by itself, i.e., without CDM/CDMA, may make 0-degree or 90-degree phase shifts and not others.

FIGS. 8A and 8C show capacitive touch sensing systems, comprising transmit electrodes and receive electrodes, and FIGS. 8B and 8D are graphs showing received signals where an interfering object is proximate the same mutual capacitance node in both systems. The received signal graph shown in FIG. 8B corresponds to the system of FIG. 8A, and the received signal graph shown in FIG. 8C corresponds to the system of FIG. 8D. In FIG. 8A, the quadrature transmit electrode pairs are not adjacent to each other, and therefore have different propagation delays for the signals from the transmitters to the receivers. The graph of FIG. 8B shows a mutual dependency or a false touch is visible or present in the received signal. In FIG. 8C, the quadrature transmit electrode pairs are adjacent to each other, and therefore have similar propagation delays for the signals from the transmitters to the receivers. The graph of FIG. 8D shows no mutual dependency or false touch is visible or present in the received signal. When the electrodes of quadrature transmit pairs are not adjacent to each other, a mutual dependency may be introduced in the receive signal. When the electrodes of quadrature transmit pair are adjacent or neighboring, a mutual dependency may be avoided and thus not introduced in the receive signal.

FIG. 9 shows, for each mutual capacitance node, the signal deviation when a reference interfering object is proximate. The phasor angles differ, which is, amongst other reasons, caused by different lengths of electrode connection lines, so-called ‘feeding lines’. Two Tx signals in phase-quadrature may be assigned to two Tx electrodes with approximately the same phasor angle for each receive electrode. The phasor angles for Tx Electrode #5 differ distinctively from those for Tx Electrode #0. Therefore, Tx electrodes #5 and #0 are not ideally suitable for assigning a pair of phase-quadrature Tx signals. However, the phasor angles for Tx electrode #1 are very similar to those of #0, for which reason Tx electrodes #0 and #1 are a more suitable pair for quadrature-phase Tx signals. Row 0 and Row 8 of the space-time-mapping matrix may be assigned as space-time mapping vectors to Tx electrodes #0 and #1, respectively.

FIG. 10 shows a block diagram of a system comprising a plurality of transmitters (1004-0-1004-N) to simultaneously transmit a plurality of transmit signals, one transmit signal per transmitter respectively; assign control logic 1002 to assign a first transmit signal to a first transmitter and a second transmit signal to a second transmitter, and so forth; and a receiver 1006 to receive a superimposed receive signal comprising a plurality of receive signal components which originate from the plurality of transmit signals, respectively, wherein a first receive signal component of the superimposed receive signal to originate from the first transmitter and a second receive signal component of the superimposed signal to originate from the second transmitter are to be in quadrature. A propagation delay control logic 1014 may measure the signal propagation delay for individual transmit signals (1008-0 through 1008-N) and provide the measured propagation delays to the assign control logic 1002. The propagation delay control logic 1014 may measure a first signal propagation delay and a second signal propagation delay without mutual capacitances at mutual capacitance nodes being deviated by a proximate interfering object. The propagation delay control logic 1014 may measure a first signal propagation delay and a second signal propagation delay with a mutual capacitance at a mutual capacitance node being deviated by a proximate interfering object. Further, as an example, first and second transmitters may have associated first and second signal propagation delays, respectively. Assign control logic 1002 assigns transmit signals to transmitters based on measured signal propagation delays provided by the propagation delay control logic 1014. For example, a first transmitter and a second transmitter may be paired by assignment of transmit signals based on the first signal propagation delay and the second signal propagation delay. The first transmitter and the second transmitter may be paired based on the first signal propagation delay and the second signal propagation delay being more similar to each other than either compared to another signal propagation delay.

One aspect provides sequentially ordering transmitters in a list according to the propagation delays of signals transmitted from the transmitters to a receiver. For example, the transmitters shown in FIG. 7C may be ordered Tx0 through Tx11 because Tx0 has the shortest propagation delay and Tx11 has the longest propagation delay. The transmitters may be paired by sequentially pairing consecutive transmitters in the list: Tx4 and Tx5; Tx6 and Tx7; Tx8 and Tx9; Tx10 and Tx11, wherein each pair is assigned two Tx signals in quadrature.

As shown in FIG. 10, a system may comprise: a plurality of transmitters (1004-0 through 1004-N) to simultaneously transmit a plurality of transmit signals (1008-0 through 1008-N), one transmit signal per transmitter respectively; assign control logic 1002 to assign a first transmit signal 1008-0 to a first transmitter 1004-0 and a second transmit signal 1008-1 to a second transmitter 1004-1; and a receiver 1006 to receive a superimposed receive signal 1010 comprising a plurality of receive signal components to originate from the plurality of transmit signals (1008-0 through 1008-N), respectively, wherein a first receive signal component of the superimposed receive signal 1010 to originate from the first transmitter 1004-0 and a second receive signal component of the superimposed receive signal 1010 to originate from the second transmitter 1004-1 are to be in quadrature, wherein the plurality of receive signal components are to be delayed relative to a plurality of signal propagation delays, respectively, wherein the plurality of transmitters (1004-0 through 1004-N) are ordered according to respective propagation delays (1008-0 is the fastest and 1008-N is the slowest); and wherein respective twos (1004-0 and 1004-1; 1004-2 and 1004-3; . . . ) of the plurality of transmitters are paired sequentially in order of signal propagation delay.

FIG. 11 shows a block diagram of a system comprising a plurality of transmitters (1104-0-1104-N) to simultaneously transmit a plurality of transmit signals, one transmit signal per transmitter respectively; phase shift control logic 1102 to shift a first transmit signal 1108-0 and a second transmit signal 1108-1; and a receiver 1106 to receive a superimposed receive signal comprising a plurality of receive signal components to originate from the plurality of transmit signals (1108-0 through 1108-N), respectively, wherein the phase shift control logic 1202 shifts individual transmit signals (1108-0 through 1108-N) in view of respective signal propagation delay so that paired transmit signals arrive at the receiver 1106 in quadrature. For example, transmit signal 1108-1 may have a longer propagation delay than transmit signal 1108-3, but transmitters 1104-1 and 1104-3 may be a quadrature pair because the phase shift control logic 1102 shifts one or both of the transmit signals