EP4677798A1

EP4677798A1 - Transmitting and receiving a symbol with a pseudorandom modification

Info

Publication number: EP4677798A1
Application number: EP23926563.0A
Authority: EP
Inventors: Guido Carlo FERRANTE; Hugo Tullberg
Original assignee: Telefonaktiebolaget LM Ericsson AB
Current assignee: Telefonaktiebolaget LM Ericsson AB
Priority date: 2023-03-09
Filing date: 2023-03-09
Publication date: 2026-01-14
Also published as: EP4677798A4; WO2024186244A1; CN120858553A

Abstract

Methods and apparatus are provided. In some examples, a method performed by a transmitting device of transmitting a symbol is provided. The method comprises determining, based on data to be transmitted, a symbol in a signal constellation, applying a pseudorandom modification to the symbol to obtain a modified symbol, and transmitting the modified symbol.

Description

TRANSMITTING AND RECEIVING A SYMBOL WITH A PSEUDORANDOM MODIFICATION

TECHNICAL FIELD

Examples of this disclosure relate to transmitting and receiving a symbol, for example a symbol to which a pseudorandom modification has been applied.

BACKGROUND

Wireless communication and mobile broadband provide flexibility and freedom and is increasingly present in our society. More and more people, businesses and societal functions use wireless communication to improve overall quality of life. However, the wireless medium is inherently not secure since the propagation channel is not exclusive to the intended transmitter and receiver, and an eavesdropper can listen to wireless transmissions. Additionally, an interferer or jammer can add signals or noise to the wireless medium. The difference between an interferer and a jammer is that the jammer has a malicious intent to degrade the communication.

Modern wireless communication systems such as 3GPP cellular communication systems use adaptive Modulation and Coding Schemes (MCS) to maximize throughput. 3GPP (the 3rd Generation Partnership Project) specifies, for each MCS, a QAM constellation and code rate, in 3GPP TS 36.211 , “Physical channels and modulation.” The MCS is selected based on the instantaneous SNR: the higher the SNR, the denser the signal constellation (and the higher the code rate) is selected.

3GPP uses axes-aligned Quadrature Amplitude Modulation (QAM), where the constellation points in a signal constellation are arranged in a square grid with equal vertical and horizontal spacing and aligned with the I and Q axes. The number of points in the constellation is typically a power of 4, e.g., 4-QAM, 16-QAM and 64-QAM. The use of a power of 4 allows for proper Gray code labeling, i.e. , that the label of neighboring constellation points only differs in one binary position. The axes-alignment allows the 2- dimensional QAM constellation to be decomposed into two independent, 1 -dimensional Amplitude Shift Keying (ASK) signals that can be treated independently, thus simplifying the demodulator at the receiver.

In general, a QAM constellation is any modulation that uses both phase and amplitude. Variations include rotated QAM, cross-QAM and hexagonal QAM. In rotated QAM, used in e.g., Digital Video Broadcast - Terrestrial (DVD-T2), the QAM constellation is rotated slightly. This introduces a controlled correlation between the I and Q dimensions which, combined with interleaving of the Q component, increases the diversity and resilience to fading.

The cross QAM constellation makes the constellation more circular by removing corner points and other points far from the origin. This lowers the maximum required power (or the Squared Euclidean Distance (SED) between remaining points can be increased for the same output power) and reduces the peak-to-average power ratio (PAPR). Cross constellations often have an odd number of bits in their labels, e.g., 32-CROSS and 128-CROSS having 5 and 7 bits for label of each constellation point, respectively. A drawback of a cross constellation is that they do not allow for a proper Gray labeling.

A hexagonal QAM constellation is a constellation constructed as a subset of a hexagonal lattice, which is the optimal 2-dimensional packing, A hexagonal QAM constellation maintains the same minimum distance as the quadratic QAM constellation but packs the constellation points close, which allows for a power saving of approximately 0.6 dB gain compared to the quadratic QAM constellation.

In recent years, Machine Learning (ML) has been applied to communication systems and constellation design. ML-designed constellations do not have any given structure as the previous constellations and their constellation diagram depends on the channel model and the optimization criterion/cost function used in the training. However, under an average power normalization constraint, the resulting constellations can be circular, well centered around the origin and resemble a lattice-based constellation, as in for example T. O’Shea and J. Hoydis, “An Introduction to Deep Learning for the Physical Layer,” IEEE Transactions on Cognitive Communications and Networking, vol. 3, no. 4, pp. 563-575, Dec. 2017, doi: 10.1109/TCCN.2017.2758370. Optimal shapes have been known for Additive White Gaussian Noise (AWGN) channels since the 1970s. ML-based optimizations can give numerically optimal shapes in the presence of interference, and potentially jamming, where analytical development is challenging.

In the light of the latter examples, the 3GPP constellations may be unnecessarily restrictive, and signal constellations for future generations such as 6G should be designed to meet new requirements without requirements on decomposability or proper Gray labeling. A jammer may try to either create a denial-of-service situation or reduce the instantaneous SNR to reduce the users’ Quality of Service/Experience. The simplest form of jamming is barrage jamming where noise or a generic signal is transmitted to reduce the communication receiver’s SNR. Drawbacks of barrage jamming are that it requires substantial power from the jammer, it does not target a particular system or user, and is comparably easy to detect.

A smart jammer listens to the system it intends to jam and adapts its jamming signal to the system. Cellular systems are vulnerable in the setup phase since the initial synchronization signals and system information is sent in the clear. After the UE has been authenticated, signals are encrypted. Thus, a jammer can establish synchronization with the system but cannot read ACK/NACK or similar signals to determine whether a jamming attack is successful or not (from the jammers perspective).

To overcome this, a smart jammer can perform modulation classification. Modulation classification is a family of algorithms that automatically determines the modulation type of a received signal, either to guarantee that the signal is correctly demodulated (and that the transmitted message can be accurately recovered), or to identify an unknown signal. Modulation classification has found significant roles in military, civil, intelligence, and security applications, for example as suggested in Zhechen Zhu and Soke K. Nandi, “Automatic Modulation Classification - Principles, Algorithms and Applications,” Wiley, 2015.

Modulation classification is applicable both to analogue modulation (e.g., AM and FM) and digital modulation (e.g., PSK and QAM). A smart jammer can target a specific system and/or user, it will be harder to detect than a non-smart jammer, and it will use its power in a more efficient manner.

A smart jammer can listen to the broadcast and establish synchronization from the signals sent in the clear. Based on the publicly available knowledge of transmission formats (e.g. 3GPP standards that are openly available), the jammer would know where in the frame to transmit to reduce SNR or otherwise disrupt a transmission. The jammer can then use modulation classification to detect when the communication system switches to a lower- order modulation. The jammer can thus assess whether or not its transmissions are effective (causing performance degradation in the communication system) and adapt its transmissions.

One way to perform the modulation classification is that the jammer can generate a histogram or amplitude spectrum of the 3GPP constellation used in a signal transmitted by a transmitter it intends to jam. By observing the l/Q samples in some parts of the Physical Downlink Shared Channel (PDSCH) or Physical Downlink Shared Channel (PLISCH), for example, it can estimate the modulation order, and from there conclude whether it has been successful in forcing a reduction in the modulation order from an earlier transmission to a later transmission.

SUMMARY

Objects of embodiments of this disclosure may include providing a modulation scheme that limits information leakage about the modulation used. Objects of embodiments of this disclosure may also include one or more of eliminating or reducing the ability for an eavesdropper and/or smart jammer to determine the modulation order currently used by the communication system, and increasing the communication system’s robustness against jammers.

One aspect of the present disclosure provides a method performed by a transmitting device of transmitting a symbol. The method comprises determining, based on data to be transmitted, a symbol in a signal constellation, applying a pseudorandom modification to the symbol to obtain a modified symbol, and transmitting the modified symbol.

Another aspect of the present disclosure provides method in a receiving device of receiving a symbol. The method comprises receiving a symbol, applying a pseudorandom modification to the symbol to obtain a modified symbol, and determining received data based on the modified symbol.

A further aspect of the present disclosure provides apparatus for transmitting a symbol. The apparatus comprises a processor and a memory. The memory contains instructions executable by the processor such that the apparatus is operable to determine, based on data to be transmitted, a symbol in a signal constellation, apply a pseudorandom modification to the symbol to obtain a modified symbol, and transmit the modified symbol.

A still further aspect of the present disclosure provides apparatus for receiving a symbol. The apparatus comprises a processor and a memory. The memory contains instructions executable by the processor such that the apparatus is operable to receive a symbol, apply a pseudorandom modification to the symbol to obtain a modified symbol, and determine received data based on the symbol. An additional aspect of the present disclosure provides apparatus for transmitting a symbol. The apparatus is configured to determine, based on data to be transmitted, a symbol in a signal constellation, apply a pseudorandom modification to the symbol to obtain a modified symbol, and transmit the modified symbol.

Another aspect of the present disclosure provides apparatus for receiving a symbol. The apparatus is configured to receive a symbol, apply a pseudorandom modification to the symbol to obtain a modified symbol, and determine received data based on the symbol.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of examples of the present disclosure, and to show more clearly how the examples may be carried into effect, reference will now be made, by way of example only, to the following drawings in which:

Figure 1 shows an example of signal constellations for 64-QAM, 16-QAM and 4- QAM;

Figure 2 shows an example of amplitude spectra of the noiseless 64-QAM, 16-QAM and 4-QAM constellations of Figure 1;

Figure 3 shows an example of the amplitude spectra of Figure 2 including noise;

Figure 4 shows an example of amplitude spectra for a signal modulated with 64- QAM;

Figure 5 is a flow chart of an example of a method performed by a transmitting device of transmitting a symbol;

Figures 6A and 6B illustrate an example of performing a pseudorandom modification to a symbol;

Figures 7A and 7B show examples of amplitudes of symbols in signal constellations;

Figures 8A and 8B illustrate another example of performing a pseudorandom modification to a symbol;

Figure 9 shows an example of an amplitude spectrum of transmitted modified symbols;

Figure 10 is a flow chart of an example of a method in a receiving device of receiving a symbol;

Figure 11 shows an example of a system including a transmitting device and a receiving device;

Figure 12 is a schematic of an example of an apparatus for transmitting a symbol; and Figure 13 is a schematic of an example of an apparatus for receiving a symbol.

DETAILED DESCRIPTION

The following sets forth specific details, such as particular embodiments or examples for purposes of explanation and not limitation. It will be appreciated by one skilled in the art that other examples may be employed apart from these specific details. In some instances, detailed descriptions of well-known methods, nodes, interfaces, circuits, and devices are omitted so as not obscure the description with unnecessary detail. Those skilled in the art will appreciate that the functions described may be implemented in one or more nodes using hardware circuitry (e.g. analog and/or discrete logic gates interconnected to perform a specialized function, Application Specific Integrated Circuits (ASICs), Programmable Logic Arrays (PLAs), etc.) and/or using software programs and data in conjunction with one or more digital microprocessors or general purpose computers. Nodes that communicate using the air interface also have suitable radio communications circuitry. Moreover, where appropriate the technology can additionally be considered to be embodied entirely within any form of computer-readable memory, such as solid-state memory, magnetic disk, or optical disk containing an appropriate set of computer instructions that would cause a processor to carry out the techniques described herein.

Hardware implementation may include or encompass, without limitation, digital signal processor (DSP) hardware, a reduced instruction set processor, hardware (e.g. digital or analogue) circuitry including but not limited to application specific integrated circuit(s) (ASIC) and/or field programmable gate array(s) (FPGA(s)), and (where appropriate) state machines capable of performing such functions.

As indicated above, a jammer may use modulation classification to detect when a transmitter or communication system switches to a lower-order modulation, and thus assess whether or not its jamming transmissions are effective. By inferring the modulation order, a jammer can infer its effectiveness in disrupting the communication service without even attempting to hack the network or focus on specific control or other channels.

Figure 1 shows an example of signal constellations, with Q on the horizontal axis and I on the vertical axis. Each point represents a point or symbol in a signal constellation and has a corresponding label in the signal constellation. Thus, for example, transmitting a symbol having an amplitude and phase of one of the constellation points corresponds to transmitting data corresponding to the label of that constellation points. In Figure 1 , the small dots correspond to symbols in a 64-QAM constellation, and the larger circles correspond to a 16- QAM constellation. The corner points are common to both 64-QAM and 16-QAM, where they have the same maximum amplitude, and these four points are also the only four points in 4-QAM, also known as Quadrature Phase Shift Keying (QPSK).

In this disclosure, the example constellations given are normalized such that the corner points have an absolute value equal to 1. Due to the desire to fully utilize the available power, all constellations (including those in Figure 1) have their corner points at 1, and hence all constellations coincide at these points.

Figure 2 shows the amplitude histograms or “amplitude spectra” of the noiseless 64-QAM, 16-QAM and 4-QAM constellations. All constellations have four points with amplitude 1 , but apart from these points, the spectra are clearly distinguishable. A device such as a jammer that listens to a signal can thus determine from the amplitude information the modulation scheme used in the signal.

Figure 3 shows an example of the amplitude spectra of Figure 2 including noise. It can be seen that even in the presence of noise the different constellations are clearly distinguishable.

In this disclosure, methods and apparatus that hide the modulation order used by the communication system by adding a pseudo-random modification or perturbation to transmitted symbols. The pseudo-random perturbation is invertible at the receiver, e.g., the pseudo-random perturbation is known to both transmitter and receiver.

In some examples, the pseudo-random perturbation does not change the average transmitted power and/or the transmitted signal remains zero mean. The perturbation may in some examples be such that the “spectrum” of the modulation, i.e. , the distribution of amplitudes, is equal to a desired spectrum irrespective of the modulation used. As a result, the signal does not leak information about the modulation used.

One way to implement such a perturbation is for example to add a pseudo-random variable to modulated symbols and apply a modulo operation to keep the signal within amplitude boundaries, e.g., in a square of side A along both I and Q axes. Alternatively, examples are provided that result in the same probability density function (pdf) regardless of the modulation order used and without using a modulo operation, e.g. where the pseudo-random perturbation is specific to the modulation order used.

Advantages of examples of this disclosure may include one or more of the following:

• Creates a modulation scheme with an amplitude spectrum that limits information leakage about the modulation used.

• Eliminates or reduces the ability for an eavesdropper and/or smart jammer to determine the modulation order currently used by the communication system.

• Increases the system’s robustness against jammers.

• Allows use of already existing signal constellations and reuse of existing system blocks by adding just one block at the transmitter (Tx) and one block at the receiver (Rx) to add and invert the perturbation, respectively.

• For Gray labeled constellations such as those specified by 3GPP, if the channel noise wraps the perturbed point to the “other side” of a QAM constellation (once the modulo operation is performed at the receiver), it only causes one bit error per dimension in the symbol label, so it is not worse than current systems.

In the absence of noise (for example as shown in Figure 2), the distribution of the amplitudes is concentrated on a finite number of points. Such points are characteristic of the modulation and one can infer the modulation order from their positions. Figure 3 shows the amplitude spectrum of Figure 2 including the effects of noise, and the modulation order can still be inferred. Figure 4 shows an example of amplitude spectra for a signal modulated with 64- QAM, with an amplitude spectrum 400 in the absence of noise and an amplitude spectrum 402 including the effects of noise.

Figure 5 is a flow chart of an example of a method 500 performed by a transmitting device of transmitting a symbol. The method 500 comprises, in step 502, determining, based on data to be transmitted, a symbol in a signal constellation, such as for example a 4-QAM (or QPSK) constellation, 16-QAM constellation, 64-QAM constellation, 128-QAM constellation, 256-QAM constellation, 1024-QAM constellation or any other order of QAM constellation. Furthermore, the signal constellation may be square or rectangular, or may be any other shape.

The method 500 comprises, in step 504, applying a pseudorandom modification to the symbol to obtain a modified symbol. The pseudorandom modification may be applied for example to an amplitude and/or phase of the symbol. Alternatively, for example, the pseudorandom modification may be applied to a real and/or imaginary component of the symbol on a signal constellation. Step 506 of the method 500 comprises transmitting the modified symbol, for example to a receiver or receiving device.

Figures 6A and 6B illustrate an example of performing a pseudorandom modification to a symbol. Figures 6A and 6B show an example QAM-16 signal constellation 600 including a plurality of constellation points, with Q along the horizontal axis and I along the vertical axis. A transmitter may wish to transmit a symbol 602, shown in Figure 6A, that has a label corresponding to data that is to be transmitted. According to example methods disclosed herein, a transmitting device may perform a pseudorandom modification 604 to the symbol 602 to obtain a modified symbol 606, which is then transmitted instead of the symbol 602. The next transmitted modified symbol (corresponding to further data to be transmitted) may have a different pseudorandom modification, e.g. using the next value in a pseudorandom function. As the modification is pseudorandom, across multiple transmitted symbols, the amplitude spectrum of the transmitted symbols may be independent of the modulation order used.

The method 500 may also in some examples comprise applying a respective pseudorandom modification to a plurality of further symbols to obtain a plurality of modified further symbols, which may then be transmitted. As a result, the distribution of amplitude and/or phase of the modified symbol and the plurality of modified further symbols may be independent of the signal constellation. Thus, a device such as a jammer or otherwise receiving or monitoring multiple transmitted symbols of the signal would not be able to determine the modulation order used in the signal.

Once the pseudorandom modification has been applied, in some examples, the modified symbol may be outside of an area enclosing the points in the symbol constellation, and may even be outside of the maximum permitted amplitude. Therefore, in some examples, the method 500 may comprise, after applying the pseudorandom modification to the symbol, performing a modulo operation to obtain the modified symbol. The modulo operation may “wrap” the modified symbol to the “other side” of the signal constellation in the event that the modified symbol is outside of the area enclosing the points in the symbol constellation, for example. If this is not the case, then the modulo operation would have no effect on the modified symbol. Thus, for example, the modulo operation maintains the modified symbol within a predetermined region on the signal constellation, such as for example a region that incorporates all symbols in the signal constellation. In this disclosure, to “wrap” the modified symbol to the other side of the signal constellation may mean for example that where the modified symbol lies outside a boundary of the signal constellation, or outside of the area enclosing the points referred to above, an operation is performed on the modified symbol to move the symbol to within the boundary or area. This may involve, or have the effect of, for example, subtracting an integer multiple of the size of the area along a particular axis from the coordinate of the modified symbol along that axis so that the resultant coordinate lies within the boundary or area. This can also be performed on the other axis and the other coordinate of the modified symbol. The resultant modified symbol, further modified by the wrap or modulo operation, will then lie within the boundary or area.

As indicated herein, in some examples, a transmitter-receiver pair can choose to hide the modulation used in a signal by transmitting a perturbed signal including modified symbols whose distribution does not depend on the unperturbed distribution of the symbol(s) X. Instead of transmitting X, the transmitter will transmit a pseudo-random function of X, say V O, that is invertible.

In some examples, the transmitting device may choose different modulations, which correspond to different random variables, e.g. ^{x x}t, and so on. The objective of the perturbation is to map such random variables to other random variables 1, 2, etc. following the same amplitude spectrum distribution. For example, denoting fx the density of X and supposing that ^xi and ^x correspond to two QAM signals, e.g., 4-QAM and 16-QAM respectively, the two densities fx₂ and fx₂ are different, but the densities of the perturbed signals are not, namely f > = fy.

In other words, in some examples, the signal constellation comprises a currently used signal constellation in a plurality of signal constellations, where the currently used signal constellation is the constellation from which the (unmodified) symbol is taken. Thus, the pseudorandom modification may be based on the currently used signal constellation. That is, for example, a pseudorandom function used for modifying 16-QAM symbols may be different to a pseudorandom function used for modifying 4-QAM symbols, and so on.

Figures 7A and 7B show examples of amplitudes of symbols in signal constellations. Specifically, Figure 7A shows amplitudes 700 of symbols 702 in a 2-PAM (pulse amplitude modulation) signal constellation, and Figure 7B shows amplitudes 704 of symbols 706 in a 4- PAM signal constellation. For a particular 2-PAM symbol 708, in the example shown, a pseudorandom modification is performed on the symbol 708 such that the resulting modified symbol has an amplitude within a particular range 710. Similarly, for a particular 4-PAM symbol 712, in the example shown, a pseudorandom modification is performed on the symbol 712 such that the resulting modified symbol has an amplitude within a particular range 714. However, the range 714 is less than the range 710, such that the amplitude of multiple symbols may be distributed within an amplitude range -A to A as shown and hence be independent of the modulation order.

In the simplest case, the pseudorandom function V’W is linear, i.e. , we transmit X + Z where Z is a pseudo-random variable that perturbs X. In practice, Z is drawn from a pseudo-random number generator whose seed has been securely exchanged beforehand. Thus, in some examples, the method 500 may include before applying the pseudorandom modification to the symbol, exchanging a seed for the pseudorandom modification with a receiver of the modified symbol.

Notice that the linear case is general if Z is allowed to depend on X, such as for example shown in Figures 7A and 7B. However, for the sake of simplicity, the following discussion of examples of this disclosure refers to the case where Z is independent of X and the case where the resulting quantity, namely X + Z, is further transformed by a deterministic nonlinear function (a modulo operation).

It can be shown that, in the additive case, a large family of target distributions can be obtained for X + Z. In fact, if Z is independent of X, then denoting the density of X and Z by fx and /z, respectively, the density of X + Z is given by their convolution: fx+z — fx * fz

Therefore, by fixing a target density f, we solve our problem if we can find fz such that f = fx * fz. This can be easily done by resorting to the Fourier domain. Denote X the Fourier transform. The solution of the problem is as follows: provided that all Fourier transforms exist. This last observation is not trivial, in the sense that it is not always true that the Fourier transforms exist. For example, there is a relationship that holds among the support (i.e., the interval of frequencies corresponding to non-zero amplitudes) of f\ (fx and fz). However, since we are free to choose /, and fx is known, then we have considerable flexibility, and it is possible to find (/, fz) pairs that solve the problem. In another example, consider, for the sake of simplicity, the case of modulations on one axis only, such as PAM (the generalization to QAM is straightforward; see below). Suppose that the transmitter can use 2-PAM and 4-PAM. To hide the modulation used, the transmitter could add a zero-men uniform perturbation over an interval as large as the distance between the constellation points. The resulting signal is uniformly distributed irrespective of whether the transmitter chose 2-PAM or 4-PAM, as illustrated above with reference to Figures 7A and 7B. A zero-mean two-dimensional uniform distribution over a square with side equal to the distance between two QAM constellation points along one axis leads to a transmitted signal that is uniform over a square in the complex plane.

In general, the jammer will observe an f, which in this case is uniform, for different fx because we can choose accordingly different fz for different modulation orders. Notice that, to accomplish this goal, the power (variance) of X may be adjusted and may possibly lead to a communication performance loss. Using a nonlinear transformation, we can keep fx unchanged and still reach the goal of transmitting signals with a fixed distribution f irrespective of fx.

In examples where a nonlinear transformation is used, then more flexibility may be available. The following discusses an example of using a modulo operation as a nonlinear transformation since it solves the problem with full generality for a QAM constellation. Suppose that the nonlinear transformation that we are going to apply is the following:

X (X) := mod(X + Z, r)

This means that, given X, we first add a pseudo-random variable Z to it and then we apply the modulo operation with parameter r. If Z is uniform along both the I and Q axes with sufficiently high variance (such that the interval upon which each constellation point is displaced is at least as large as the distance between two points along the same axis) and r is taken such that the transmitted power is unchanged, then all QAM constellations can be transformed into signals that are uniform over a square in the complex plane.

Figures 8A and 8B illustrate another example of performing a pseudorandom modification to a symbol, where the pseudorandom modification includes a modulo operation. Figures 8A and 8B show an example QAM-16 signal constellation 800 including a plurality of constellation points, with Q along the horizontal axis and I along the vertical axis. A transmitter may wish to transmit a symbol 802, shown in Figure 8A, that has a label corresponding to data that is to be transmitted. According to example methods disclosed herein, a transmitting device may perform a pseudorandom modification 804 (e.g. adding a pseudorandom variable 2) to the symbol 802 to obtain a symbol 806. However, this symbol is outside of a region 808 (e.g. the predetermined region referred to above, or the area or boundary referred to above). Therefore, a modulo operation “wraps” the symbol 806 such that the resulting modified symbol 810 is within the region 808. Thus, modulo operation maintains the modified symbol 810 within the predetermined region 808 on the signal constellation 800. The modified symbol 810 may then be transmitted.

Figure 9 shows an example of an amplitude spectrum of transmitted modified symbols in examples using the modulo operation. This is an example of the amplitude distribution that is always observed by an observer (e.g. a jammer) in examples described above using a modulo operation irrespective of the initial modulation order.

Figure 10 is a flow chart of an example of a method 1000 in a receiving device of receiving a symbol. The method 1000 comprises, in step 1002, receiving a symbol. This may be for example the modified symbol transmitted by a transmitting device as described above. Step 1004 of the method 1000 comprises applying a pseudorandom modification to the symbol to obtain a modified symbol. This may be for example the inverse/reverse of the pseudorandom modification performed by the transmitting device, and hence the “modified symbol” in the receiving device may correspond to the original, unmodified symbol in the transmitting device. Step 1006 of the method 1000 comprises determining received data based on the modified symbol, e.g. determining the label of the modified symbol in the signal constellation. Thus, the receiving device may determine the data transmitted by the symbol (i.e. the modified symbol transmitted by the transmitting device and received at the receiving device).

Figure 11 shows an example of a system 1100 including a transmitting device 1102 and a receiving device 1104. In some examples, the transmitting device 1102 performs any example of the method 600 described above, and/or the receiving device performs any example of the method 1000 described above. The transmitting device 1102 includes an information source 1106 (e.g. source of data to be transmitted), encoder 1108 and demodulator 1110 which provides a symbol. The transmitting device 1102 also includes a symbol modifier 1112 which modifies the symbol from the modulator 1110 to provide a modified symbol, which is transmitted over channel 1114 to the receiving device. The modification is of the manner described herein, and hence the distribution of amplitudes of multiple transmitted modified symbols does not leak information regarding the order of the modulation used in modulator 1110.

The receiving device 1104 includes a symbol demodifier 1116 to demodify the modified symbol (i.e. perform the reverse of the operation performed by the symbol modifier 1112). The resulting symbol, referred to as the “modified symbol” in the context of the method 1000 performed by the receiving device, is provided to demodulator 1118, decoder 1120 and information sink 1122. In some examples, Some of the blocks and functions shown may be combined. For example, the (de)modulation and symbol (de)modification may be performed by a single block in the transmitting device 1102 and/or receiving device 1104.

Figure 12 is a schematic of an example of an apparatus 1200 for transmitting a symbol. The apparatus 1200 comprises processing circuitry 1202 (e.g. one or more processors) and a memory 1204 in communication with the processing circuitry 1202. The memory 1204 contains instructions, such as computer program code 610, executable by the processing circuitry 1202. The apparatus 1200 also comprises an interface 1206 in communication with the processing circuitry 1202. Although the interface 1206, processing circuitry 1202 and memory 1204 are shown connected in series, these may alternatively be interconnected in any other way, for example via a bus.

In one embodiment, the memory 1204 contains instructions executable by the processing circuitry 1202 such that the apparatus 1200 is operable/configured to determine, based on data to be transmitted, a symbol in a signal constellation, apply a pseudorandom modification to the symbol to obtain a modified symbol, and transmit the modified symbol. In some examples, the apparatus 1200 is operable/configured to carry out the method 600 described above with reference to Figure 6.

Figure 13 is a schematic of an example of an apparatus 1300 for receiving a symbol. The apparatus 1300 comprises processing circuitry 1302 (e.g. one or more processors) and a memory 1304 in communication with the processing circuitry 1302. The memory 1304 contains instructions, such as computer program code 610, executable by the processing circuitry 1302. The apparatus 1300 also comprises an interface 1306 in communication with the processing circuitry 1302. Although the interface 1306, processing circuitry 1302 and memory 1304 are shown connected in series, these may alternatively be interconnected in any other way, for example via a bus. In one embodiment, the memory 1304 contains instructions executable by the processing circuitry 1302 such that the apparatus 1300 is operable/configured to receive a symbol, apply a pseudorandom modification to the symbol to obtain a modified symbol, and determine received data based on the symbol. In some examples, the apparatus 1300 is operable/configured to carry out the method 1000 described above with reference to Figure 10.

It should be noted that the above-mentioned examples illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative examples without departing from the scope of the appended statements. The word “comprising” does not exclude the presence of elements or steps other than those listed in a claim, “a” or “an” does not exclude a plurality, and a single processor or other unit may fulfil the functions of several units recited in the statements below. Where the terms, “first”, “second” etc. are used they are to be understood merely as labels for the convenient identification of a particular feature. In particular, they are not to be interpreted as describing the first or the second feature of a plurality of such features (i.e. , the first or second of such features to occur in time or space) unless explicitly stated otherwise. Steps in the methods disclosed herein may be carried out in any order unless expressly otherwise stated. Any reference signs in the statements shall not be construed so as to limit their scope.

Claims

1. A method (500) performed by a transmitting device (1102) of transmitting a symbol, the method comprising: determining (502), based on data to be transmitted, a symbol (602, 802) in a signal constellation (600, 800); applying (504) a pseudorandom modification (604, 804) to the symbol to obtain a modified symbol (606, 810); and transmitting (506) the modified symbol.

2. The method of claim 1 , comprising applying a respective pseudorandom modification to a plurality of further symbols to obtain a plurality of modified further symbols.

3. The method of claim 2, comprising applying the pseudorandom modification such that a distribution of amplitude and/or phase of the modified symbol and the plurality of modified further symbols is independent of the signal constellation.

4. The method of claim 2 or 3, comprising transmitting the plurality of modified further symbols.

5. The method of any of claims 1 to 4, wherein applying (504) a pseudorandom modification (604, 804) to the symbol (602, 802) comprises applying a pseudorandom modification to an amplitude and/or phase of the symbol.

6. The method of any of claims 1 to 5, wherein applying (504) a pseudorandom modification (604, 804) to the symbol (602, 802) comprises applying a pseudorandom a Real and/or Imaginary modification to the symbol in the signal constellation.

7. The method of any of claims 1 to 6, comprising, after applying (504) the pseudorandom modification (604, 804) to the symbol (602, 802), performing a modulo operation to obtain the modified symbol (810).

8. The method of claim 7, wherein the modulo operation maintains the modified symbol (810) within a predetermined region (808) on the signal constellation (800).

9. The method of claim 8, wherein the predetermined region (808) incorporates all symbols in the signal constellation (800).

10. The method of any of claims 1 to 9, wherein the signal constellation (600, 800) comprises a currently used signal constellation in a plurality of signal constellations.

11. The method of claim 10, wherein the pseudorandom modification (604, 804) is based on the currently used signal constellation (600, 800).

12. The method of claim 10 or 11 , wherein the plurality of signal constellations each have a different modulation order.

13. The method of any of claims 1 to 12, comprising, before applying (504) the pseudorandom modification (604, 804) to the symbol (602, 802), exchanging a seed for the pseudorandom modification with a receiver (1104) of the modified symbol (606, 810).

14. The method of any of claims 1 to 13, wherein applying (504) the pseudorandom modification (604, 804) to the symbol (602, 802) comprises performing a predetermined pseudorandom function on the symbol.

15. The method of any of claims 1 to 14, wherein determining (502), based on the data to be transmitted, the symbol (602, 802) in the signal constellation (600, 800) comprises modulating the data.

16. The method of claim 15, wherein modulating the data comprises selecting the symbol (602, 802) in the signal constellation (600, 800) with a label that corresponds to the data.

17. A method (1000) in a receiving device (1104) of receiving a symbol, the method comprising: receiving (1002) a symbol (606, 810); applying (1004) a pseudorandom modification to the symbol to obtain a modified symbol (602, 802); and determining (1006) received data based on the modified symbol.

18. The method of claim 17, wherein the pseudorandom modification comprises an inverse of a pseudorandom modification (604, 804) performed by a transmitter (1104) of the symbol.

19. The method of claim 17 or 18, comprising: receiving a plurality of further symbols; and applying a respective pseudorandom modification to the plurality of further symbols to obtain a plurality of modified further symbols.

20. The method of claim 19, comprising, for each modified further symbol, determining respective received data based on the modified further symbol.

21. The method of claim 19 or 20, wherein a distribution of amplitude and/or phase of the symbol and the plurality of further symbols is independent of a signal constellation that includes the modified symbol and the plurality of further symbols.

22. The method of any of claims 17 to 21, wherein applying (1004) a pseudorandom modification to the symbol (606, 810) comprises applying a pseudorandom modification to an amplitude and/or phase of the symbol.

23. The method of any of claims 17 to 22, wherein applying (1004) a pseudorandom modification to the symbol (606, 810) comprises applying a pseudorandom a Real and/or Imaginary modification to the symbol in a signal constellation (600, 800) that includes the symbol.

24. The method of any of claims 17 to 23, comprising, after applying (1004) the pseudorandom modification to the symbol (810), performing a modulo operation to obtain the modified symbol (802).

25. The method of claim 24, wherein the modulo operation maintains the modified symbol (800) within a predetermined region (808) on the signal constellation (800).

26. The method of claim 25, wherein the predetermined region (808) incorporates all symbols in the signal constellation (800).

27. The method of any of claims 17 to 26, wherein the pseudorandom modification is based on a signal constellation (600, 800) that includes the symbol (602, 802).

28. The method of claim 27, wherein the signal constellation (600, 800) is one of a plurality of signal constellations that each have a different modulation order.

29. The method of any of claims 17 to 28, comprising, before applying (1004) the pseudorandom modification to the symbol (606, 810), exchanging a seed for the pseudorandom modification with a transmitter (1104) of the symbol.

30. The method of any of claims 17 to 29, wherein applying (1004) the pseudorandom modification to the symbol (606, 810) comprises performing a predetermined pseudorandom function on the symbol.

31. The method of any of claims 17 to 30, wherein determining (1006) the received data based on the modified symbol (602, 802) comprises demodulating the data.

32. The method of claim 31 , wherein demodulating the data comprises determining a label of a symbol in a signal constellation (600, 800) that corresponds to the modified symbol (602, 802).

33. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out a method (500, 1000) according to any of claims 1 to 32.

34. A carrier containing a computer program according to claim 33, wherein the carrier comprises one of an electronic signal, optical signal, radio signal or computer readable storage medium.

35. A computer program product comprising non transitory computer readable media having stored thereon a computer program according to claim 33.

36. Apparatus (1200) for transmitting a symbol (602, 802), the apparatus comprising a processor (1202) and a memory (1204), the memory containing instructions executable by the processor such that the apparatus is operable to: determine (502), based on data to be transmitted, a symbol (602, 802) in a signal constellation (600, 800); apply a pseudorandom modification (604, 804) to the symbol to obtain a modified symbol (606, 810); and transmit the modified symbol.

37. The apparatus of claim 36, wherein the memory (1204) contains instructions executable by the processor (1202) such that the apparatus (1200) is operable to perform the method (500) of any of claims 2 to 16.

38. Apparatus (1300) for receiving a symbol (606, 810), the apparatus comprising a processor (1302) and a memory (1304), the memory containing instructions executable by the processor such that the apparatus is operable to: receive (1002) a symbol (606, 810); apply (1004) a pseudorandom modification to the symbol to obtain a modified symbol (602, 802); and determine (1006) received data based on the symbol.

39. The apparatus of claim 38, wherein the memory (1304) contains instructions executable by the processor (1302) such that the apparatus (1300) is operable to perform the method (1000) of any of claims 18 to 32.

40. Apparatus for transmitting a symbol (606, 810), the apparatus configured to: determine (502), based on data to be transmitted, a symbol (602, 802) in a signal constellation (600, 800); apply (504) a pseudorandom modification (604, 804) to the symbol to obtain a modified symbol (606, 810); and transmit the modified symbol.

41. The apparatus of claim 40, wherein the apparatus is configured to perform the method (500) of any of claims 2 to 16.

42. Apparatus for receiving a symbol (606, 810), the apparatus configured to: receive (1002) a symbol (606, 810); apply (1004) a pseudorandom modification to the symbol to obtain a modified symbol (602, 802); and determine received data based on the symbol.

43. The apparatus of claim 42, wherein the apparatus is configured to perform the method (1000) of any of claims 18 to 32.