Nonlinear distortion compensation in a receiver device

Abstract

There is provided techniques for compensating for nonlinear distortion. A method is performed by a receiver device. The method comprises receiving, at an input of the receiver device, a signal over a wireless channel from an output of a transmitter device. The signal comprises pilot symbols and data symbols. The method comprises estimating nonlinear distortion of the signal. The estimating is based on a signal model comprises characteristics of a complete time-domain version of the signal at the output of the transmitter device and characteristics of a time-domain version of the signal at the input of the receiver device. Each of characteristics is obtained using a non-linear transformation of the signal. The method comprises compensating the signal for the estimated nonlinear distortion.

Description

[0001]NONLINEAR DISTORTION COMPENSATION IN A RECEIVER DEVICE TECHNICAL FIELD Embodiments presented herein relate to a method, a receiver device, a computer program, and a computer program product for compensating for nonlinear distortion. BACKGROUND In general terms, increasing the data rate of a wireless access system can either be performed by increasing the bandwidth of the transmitted signal or by increasing the spectral efficiency of the physical layer, e.g., the modulation order of the symbols carried by the transmitted wireless signal. Since bandwidth is usually a scarce resource (e.g., since many communication systems are already installed and the frequency spectrum is often fully occupied), increasing spectral efficiency of the wireless signal is often the only possible solution. Hence, finding techniques for the wireless signal to carry more bits per consumed spectral bandwidth (in terms of bits / Hz) are of importance. Especially techniques that enable an increased rate in existing, already installed, wireless access system, even though these systems were not initially designed for high spectral efficiency. Examples of modulation orders used in the physical layer in current wireless access systems range from 4 QAM to 256 QAM (where QAM is short for quadrature amplitude modulation), i.e., from 2 bits / symbol up to 8 bits / symbol. To substantially increase the spectral efficiency, modulation orders should be increased to 4096 QAM or even higher (such as 16k QAM). Such an increase of modulation order gives 12 bits / symbol (or 14 bits / symbol), i.e., an increase of 50% or even up to 75% without increasing the bandwidth of the wireless signal. However, increasing the spectral efficiency increases the sensitivity of the wireless system, such as the sensitivity to noise, and distortion might increase. One degrading factor in wireless systems is the nonlinear distortion in analogue components, such as power amplifiers, mixers and low noise amplifiers. Nonlinear components contribute with nonlinear amplitude and phase distortion to the wireless signal, which will limit the possible spectral efficiency if not handled (i.e., if not compensated for). Distortion can, for example, be reduced by using better performing analogue components, but this leads to increased complexity and power consumption of the system. Sensitivity to nonlinear distortion can also be reduced by introducing signal processing which estimates and compensates for the distortion, where such signal processing can be situated in the receiver and / or transmitter. Signal processing for estimating distortion in wireless communication systems commonly rely on having a few known pilot symbols embedded in the transmitted symbols. It is of interest to keep the number of necessary pilots to a minimum in order not to limit the pilot overhead in the transmitted signal. It is also of interest to keep the complexity of the processing to a minimum, still having a well performing system. Reference is here made to Fig.1(a) which schematically illustrates a communication system 10 where a transmitter (Tx) device 100 and a receiver device (200) are configured to communicate with each other, as indicated by a bidirectional arow, over a channel ^^. Further detail of the operations performed by the transmitter device 100 and the receiver device 200 and how the channel impacts signals as transmitted by the transmitter device 100 to the receiver device 200 is illustrated in the block diagram of Fig.1(b). Before transmission, the sequence of payload symbols, containing data symbols and possibly also known pilot symbols at known frequencies, is transformed into time domain, e.g., by applying in inverse discrete Fourier transform (IDFT) to the sequence of payload symbols. To achieve perfect compensation of the (frequency selective) channel, a cyclic prefix is introduced in the transmitter, where the length of the cyclic prefix corresponds to the memory of the channel. Then the transformed sequence of payload symbols is serialized and upconverted to radio frequency using a high-frequency oscillator. This high-frequency oscillator might be affected by nonlinear distortion. The wireless signal is furthermore amplified in a power amplifier (PA) which might contribute with nonlinear distortion. Hence, the nonlinear distortion affects the modulated signal in time domain. Commonly, the QAM symbols of the time-domain signal are carried by ^^ orthogonal frequency-division multiplexing (OFDM) subcarriers. The nonlinear distortion causes inter-carrier cross talk. In other words, QAM symbols on different OFDM subcarriers will disturb each other. The transmission to the receiver is over a channel. The channel might be a frequency selective channel and be affected by additive white gaussian noise (AWGN). The received signal is in the receiver device amplified using a low noise amplifier (LNA) and down-converted from radio frequency using a local oscillator before being de-serialized. Both amplification and down conversion might contribute with nonlinear distortion. The cyclic prefix is then removed. The resulting signal is transformed to the frequency domain using a discrete Fourier transform (DFT). The nonlinear distortion, denoted ^^dist, can conveniently be modeled as nonlinear and additive, and thus be formulated as: where the nonlinear distortion is applied in the time domain, ^^−1^^, using a function ^^ parameterized with a vector ^^ together with a linear contribution ^^−10(i.e., a linear gain), where ^^ and ^^are ^^ × ^^ matricesrepresenting the DFT and the IDFT, respectively, and where the transmitted QAM symbols are represented by the vector ^^ of length ^^. The received observed signal ^^′, affected by the frequency selective channel, AWGN and nonlinear distortion in both the transmitter and receiver, can, using complex baseband notation, therefore be formulated as ^^′ = ^^0,Rx^^^^Tx + ^^^^Rx(^^−1^^^^Tx + ^^, ^^Rx) + ^^, (2)where ^^ is a complex and normal distributed vector of length ^^ that represents the AWGN, and where^^Tx = ^^0,Tx^^ + ^^^^Tx(^^−1^^, ^^Tx). (3)where the subscript Tx here has been introduced to denote parameters and functions having been affected by the transmitter. The received observed signal can therefore be formulated as where the subscript Rx here has been introduced to denote parameters and functions having been affected by the receiver. The system includes a cyclic prefix, and the cyclic filtering can be modeled by a diagonal matrix, ^^, containing the frequency domain channel gains for each OFDM subcarrier. The transmitter nonlinearity ismodeled with a nonlinear time domain function ^^Tx(^^, ^^Tx) operating in the time domain, parameterized by thevector variable ^^Txwith a linear contribution parametrized by ^^0,Tx, and the receiver nonlinearity is modeled witha nonlinear time domain function ^^Rx(^^, ^^Rx) parameterized by the vector variable ^^Rx with a linear contributionparameterized by ^^0,Rx. Either the receiver device 200 itself (as in the non-limiting illustrative example in Fig.1(b), or some external estimation block, might be configured to estimate the nonlinear distortion. In general terms, estimating the nonlinear distortion translates to estimating the vector variables ^^Tx, ^^Rx, ^^0,Txand ^^0,Rxusing the observed signal ^^′. Since the observed signal carries unknown payload symbols (but where the QAM-modulation might be known), the transmitter device and the receiver device normally rely on pilot symbols embedded in thetransmitted signal ^^, where the number of pilots is ^^pilot ≪ ^^. That is, pilot symbols are symbols with values andlocations in the transmitted signal that are assumed to be known by the receiver device. However, current techniques for estimating the nonlinear distortion are either of low computational complexity but far from acceptable in terms of performance accuracy or offers good performance accuracy (sometimes even close to optimal) but with significant computational complexity and / or delay which makes the techniques unfeasible for implementation. There is therefore a need for low-complexity, high-performance, techniques for estimating nonlinear distortion in a communication system where only a sparse number of pilot symbols are used in the transmitted signal. SUMMARY An object of embodiments herein is to address the above issues and provide efficient estimation of nonlinear distortion in a communication system with low computational complexity but high performance accuracy. A particular object is to provide efficient estimation of nonlinear distortion in a communication system where only a sparse number of pilot symbols are used in the transmitted signal. According to a first aspect there is presented a method for compensating for nonlinear distortion. The method is performed by a receiver device. The method comprises receiving, at an input of the receiver device, a signal over a wireless channel ^^ from an output of a transmitter device. The signal comprises pilot symbols and data symbols. The method comprises estimating nonlinear distortion of the signal. The estimating is based on a signal model comprises characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device. Each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^. The method comprises compensating the signal for the estimated nonlinear distortion. According to a second aspect there is presented a receiver device for compensating for nonlinear distortion. The receiver device comprises processing circuitry. The processing circuitry is configured to cause the receiver device to receive, at an input of the receiver device, a signal over a wireless channel ^^ from an output of a transmitter device. The signal comprises pilot symbols and data symbols. The processing circuitry is configured to cause the receiver device to estimate nonlinear distortion of the signal. The estimating is based on a signal model comprises characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device. Each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^. The processing circuitry is configured to cause the receiver device to compensate the signal for the estimated nonlinear distortion. According to a third aspect there is presented a receiver device for compensating for nonlinear distortion. The receiver device comprises a receive module configured to receive, at an input of the receiver device, a signal over a wireless channel ^^ from an output of a transmitter device. The signal comprises pilot symbols and data symbols. The receiver device comprises an estimate module configured to estimate nonlinear distortion of the signal. The estimating is based on a signal model comprises characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device. Each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^. The receiver device comprises a compensate module configured to compensate the signal for the estimated nonlinear distortion. According to a fourth aspect there is presented a computer program for compensating for nonlinear distortion. The computer program comprises computer code which, when run on processing circuitry of a receiver device, causes the receiver device 200 to perform actions. One action comprises the receiver device to receive, at an input of the receiver device, a signal over a wireless channel ^^ from an output of a transmitter device. The signal comprises pilot symbols and data symbols. One action comprises the receiver device to estimate nonlinear distortion of the signal. The estimating is based on a signal model comprises characteristics of a complete time- domain version of the signal, ^^−1^^, at the output of the transmitter device and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device. Each of characteristics is obtained using a non- linear transformation of the signal ^^−1^^^^. One action comprises the receiver device to compensate the signal for the estimated nonlinear distortion. According to a fifth aspect there is presented a computer program product comprising a computer program according to the fourth aspect and a computer readable storage medium on which the computer program is stored. The computer readable storage medium could be a non-transitory computer readable storage medium. Advantageously, these aspects provide efficient estimation of nonlinear distortion in a communication system with low computational complexity but high performance accuracy. Advantageously, these aspects provide efficient estimation of nonlinear distortion in a communication system where only a sparse number of pilot symbols are used in the transmitted signal. Advantageously, these aspects enable the nonlinear distortion to be estimated with high accuracy, for example in a minimum mean square error (MMSE) or least squares (LS) sense. Advantageously, these aspects enable accurate estimation of the nonlinear distortion since the nonlinear distortion can be minimized in an MMSE sense using pilot symbols. This is due to the fact that the model is reformulated compared to existing techniques and due to the fact that the estimation can consider all statistics. Advantageously, the model considers both nonlinear distortion in the transmitter device and in the receiver device and enables the nonlinear distortion to be jointly estimated using only pilot symbols. In this way, the cases of nonlinear distortion only in the transmitter device or only in the receiver device, are thereby also covered. Other objectives, features and advantages of the enclosed embodiments will be apparent from the following detailed disclosure, from the attached dependent claims as well as from the drawings. Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a / an / the element, apparatus, component, means, module, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, module, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. BRIEF DESCRIPTION OF THE DRAWINGS The inventive concept is now described, by way of example, with reference to the accompanying drawings, in which: Fig.1a is a schematic diagram illustrating communications systems according to embodiments; Fig.1b is a schematic diagram illustrating a transmitter device, a receiver device and how a signal transmitted therebetween is impacted according to embodiments; Figs.2 and 3 are flowcharts of methods according to embodiments; Fig.4 shows simulation results according to an embodiment; Fig.5 is a schematic diagram showing structural units of a receiver device according to an embodiment; Fig.6 is a schematic diagram showing functional modules of a receiver device according to an embodiment; and Fig.7 shows one example of a computer program product comprising computer readable storage medium according to an embodiment. DETAILED DESCRIPTION The inventive concept will now be described more fully hereinafter with reference to the accompanying drawings, in which certain embodiments of the inventive concept are shown. This inventive concept may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the inventive concept to those skilled in the art. Like numbers refer to like elements throughout the description. Any step or feature illustrated by dashed lines should be regarded as optional. The embodiments disclosed herein relate to techniques for compensating for nonlinear distortion. In order to obtain such techniques there is provided a receiver device 200, a method performed by the receiver device 200, a computer program product comprising code, for example in the form of a computer program, that when run on a receiver device 200, causes the receiver device 200 to perform the method. In some embodiments, the receiver device 200 can be any wired or wireless receiver capable of receiving OFDM modulated signals experiencing nonlinear distortion. In some embodiments, the receiver device 200 is, or is part of, a network equipment, an access node, or a user equipment. In some aspects, it is assumed that the transmitted signal is required to fulfil standards restricting spectral emission and that the signal to noise ratio (SNR) typically is high for systems intended for high spectral efficiency (where the variance of ^^ thus is low). The system model in Equation (4) can be modified as follows: 5 The nonlinear distortion is typically a function of the amplitude a transmitted signal and can be modeled in a multiple number of ways. The nonlinear distortion can, for example, be modeled as memory polynomials or using look-up tables. For simplifying expressions and to improve readability, but without loss of generality, the nonlinear 10 distortion will be modeled as a third order nonlinearity. That is, where ^^(^^, ^^) = ^^^^^^^^^^^^^^−1^^, (6) where the diagonal matrix ^^^^contains the time domain column vectors ^^−1^^. Hence, the element-wise, time- domain, multiplication is performed using diagonal matrices and a vector (i.e., ^^−1^^). Each time instant of the symbol in the transmitted signal is thereby assumed to be affected by the distortion ^^|^^^^|2^^^^. 15 Using Equation (5), the resulting third-order model becomes: There are two nonlinear contributions; one for the transmitted time-domain signal, based on ^^−1^^, and one for the received time-domain signal, based on ^^−1^^^^. Most part of the vector ^^ is unknown due to the unknown payload. This can be visualized by reformulating ^^ = ^^pilot + ^^payload, where the vector ^^pilot contains the pilot20 symbols in the pilot positions and zeros where the payload symbols are situated, and vice versa for ^^payload. That is, the vector ^^payloadcontains the payload (or data) symbols in the payload positions and zeros where the pilot symbols are situated. Hence, the pilot and payload vectors are orthogonal to each 0. Using this notation, Equation (7) can be formulated as:25 Here, all terms containing a payload contribution are collected as a noise (denoted ^^). Only the terms containing the pilot symbols are explicitly shown in Equation (8). The matrices and vectors ^^^^pilot / ^^^^^^pilot / ^^−1^^^^pilot / ^^−1^^pilotand ^^^^payload / ^^^^^^payload / ^^−1^^^^payload / ^^−1^^payloadrepresent two different (orthogonal) subspaces, namely the pilot subspace and the payload subspace, respectively. The sparse pilot subspace, represented by ^^^^pilot / ^^^^^^pilot, has a rank which is significantly lowerthan the size of the transmitted symbol, and the rank is ^^pilot ≪ ^^payload < ^^. The pilot subspace of thetransmitted and received time-domain signals will have cumulative distribution functions (CDFs) which differ significantly from the corresponding CDFs of Equation (7). This is a disadvantage since the model is nonlinear. In other words, the frequency domain pilot nonlinear contributions, will differ significantly from the original contrib^^ −1 ution ^^Rx^^^^^^^^^^^^^^ ^^^^ and ^^Tx^^^^^^^^^^^^^^^^−1^^. The time-domain payload distortion parts, and ^^Tx^^^^^^^^payload^^^^^^payload^^−1^^payload, are completely lacking from the modeling since and are treated as noise. This is a drawback since the model is nonlinear. The nonlinear distortion represented by the pilot subspace will not reflect the nonlinear distortion of the complete signal. Hence, the separation of the signal into the two subspaces will not capture the true nonlinear distortion of the transmitted and received time-domain signals. The CDF of the transmitted time-domain signal, ^^−1^^pilot, and the CDF of the received time-domain signal, ^^−1^^^^pilot, differ significantly from the true CDFs of ^^−1^^^^ and ^^−1^^. In fact, most of the distortion will be captured by the payload part of the signal ^^−1^^^^payloadand ^^−1^^payload. At least some of the herein disclosed embodiments are therefore based on finding a better model so that the pilot parts of the nonlinear model can be avoided, and / or replaced. At least some of the herein disclosed embodiments are therefore based on replacing the nonlinear distortion contributions with some appropriate models reflecting the CDF of the true time-domain nonlinear contributions ( ^^^^^^^^^^^^−1^^ and ^^^^^^^^^^^^^^^^−1^^^^). In general terms, this can be achieved by using approximations of the transmitted signal ^^−1^^, and the received signal, ^^−1^^^^. Using the model in Equation (7), an approximation of ^^−1^^ and ^^−1^^^^ is ^^−1^^−1^^ and ^^−1^^, respectively, assuming that the nonlinear distortion parameters on average are zero, and / or that the distortion is comparatively low (i.e., where the linear part (i.e., the undistorted part) is dominant compared to the distortion). Such an approximation will depend on the modeling, and using the example model in Equation (8), it is a suitable approximation for this specific case. With knowledge about the nonlinear distortion, an improved estimate of the time-domain signals can be achieved by inverting the known, e.g., most probable, distortion parametrization. Fig.2 is a flowchart illustrating an embodiment of a method for compensating for nonlinear distortion. The methods are performed by the receiver device 200. The methods are advantageously provided as computer programs 720. S102: The receiver device 200 receives a signal ^^′. The signal ^^′ is received at an input of the receiver device 200. The signal ^^′ is received over a channel ^^. The channel ^^ could be a wireless channel, an optical fiber channel, or other type of wired channel. The signal ^^′ is received from an output of a transmitter device 100. The signal comprises pilot symbols and data symbols. In general terms, the receiver device 200 is configured to estimate the nonlinear distortion based on a model that considers characteristics of the time-domain transmitted signal and characteristics of the time-domain received signal, both obtained from the received input time-domain signal, as in step S104. S104: The receiver device 200 estimates nonlinear distortion of the signal. The estimating is based on a signal model. The signal model comprises characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device 100. The signal model further comprises characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device 200. Each of characteristics is obtained using a non- linear transformation of the signal ^^−1^^^^. ^^−1^^ is thus the complete transmitted time-domain signal, and ^^−1^^^^ is thus the received input time-domain signal. In some embodiments, in the signal model, an approximation ^̂^ of the signal ^^−1^^ is used by the non-linear transformation to obtain the characteristics of the signal ^^−1^^. Likewise, in some embodiments, in the signal model, an approximation of the signal ^^−1^^^^ is used by the non-linear transformation to obtain the characteristics of the signal ^^−1^^^^. S106: The receiver device 200 compensates the signal for the estimated nonlinear distortion. Thereby, by reformulating the observed signal model in Equation (4), or in Equation (5), using an approximation of the transmitted time-domain signal, ^^−1^^, the nonlinear distortion of the transmitter can be accurately estimated using available low-complexity estimation methods, regardless of the positions of the pilot symbols in the received signal. Likewise, using and approximation of the received time-domain signal, ^^−1^^^^, the nonlinear distortion of the receiver can be accurately estimated using available low-complexity estimation methods, regardless of the positions of the pilot symbols in the received signal. Hence, the positions of the pilot signals in the transmitted signal ^^ becomes irrelevant. Correspondingly, in some embodiments, the signal model is transparent with respect to locations of the pilot symbols in the received signal. An approximation, or estimate, of the complete transmitted time-domain signal, ^^−1^^, is thus used in the modeling the transmitted signal nonlinear distortion. The transmitted signal contains mostly data in the form of payload symbols, which are unknown to the receiver device 200. Likewise, an approximation, or estimate, of the received input time-domain signal, ^^−1^^^^, is used in the modeling the received input signal nonlinear distortion. As for the transmitted signal, most parts of the received signal is unknown to the receiver device 200. There could be different ways to represent the characteristics of the signals. In some embodiments, in the signal model, the characteristics of the signal represent the CDF of the signal ^^−1^^, and / or the characteristics of the signal ^^−1^^^^ represent the CDF of the approximation of the signal ^^−1^^^^. In some aspects, knowledge of the nonlinear distortion of the system can be utilized for the approximations. In some non-limiting examples, the approximations can be some function of and ^^−1^^^^, respectively, i.e., afunction compensating or inverting some known part of the nonlinearity ^^(^^−1^^^^, ^^−1^^, ^^).The resulting approximation, or estimation, errors have statistics that can be derived from the actual system model. With the approximations, the transmitted and received time-domain signals characteristics (such as the CDFs) can be modeled with a known error, and estimation can be performed using only a sparse number of known pilots in the frequency domain. The resulting re-formulated model, including nonlinear parameters of the transmitter and receiver, can be used LS or MMSE estimators. The received signal can be modelled as a linear combination of the transmitted signal and the channel transfer function, a non-linear function of transmitted signal, and a nonlinear function of the transmitted signal and the channel transfer function. In general terms, since the transmitted signal only comprises a few pilot symbols, most transmitted symbols (i.e., the data symbols) are treated as unknown in the modelling. In some embodiments, in the signal model, the data symbols are treated as having unknown values. In some aspects, the unknown symbols are replaced with something that has limited nonlinear distortion, and where the statistics of the nonlinear distortion might be known. In some examples, the unknown symbols are replaced with estimates of the data symbols. That is, in some embodiments, in the signal model and as part of estimating the nonlinear distortion, the data symbols are replaced by an estimate of the data symbols based on the received signal. As systems can have nonlinear distortion both the transmitter and receiver, or only the transmitter, or only the receiver, the nonlinear functions can be replaced by the all-zero function, i.e., a constant which is zero. That is, a system with nonlinearity only in the receiver can be modelled as a linear combination of the transmitted signal and the channel transfer function and a nonlinear function of the transmitted signal and the channel transfer function. Most of the transmitted signal is commonly unknown to the receiver device 200, except for the known pilot symbols at known frequencies in the frequency domain. The nonlinear function of the transmitted signal can therefore be approximated using a nonlinear function of the received signal with an estimate of the channel transfer function. The nonlinear function of the transmitted signal and the channel transfer function is approximated using a nonlinear function of the received signal. The nonlinear functions can, for example, be polynomials of some order, e.g., of the third or fifth order. The nonlinear functions can also, for example, be memory polynomials, where the memory polynomial contains time- shifted polynomials of some order. The nonlinear functions can also, for example, be look-up tables addressed using the amplitude of the signal, and where each table entry contains the corresponding added distortion. As for polynomial modelling, the table-based modelling can contain memory, where the memory is modelled using several tables addressed with corresponding time delayed versions of the amplitude of the signal. The nonlinear distortion induced by the transmitter device 100 and the receiver device 200 can be estimated jointly (simultaneously) using only a sparse number of pilots. Hence, in some embodiments, in the signal model, the characteristics of the signal ^^−1^^ and the characteristics of the signal ^^−1^^^^ are jointly estimated. That is, in some embodiments, in the signal model, the characteristics of the signal ^^−1^^ is free from nonlinear distortion. The case with nonlinear distortion either only in the transmitter device 100 or only in the receiver device 200 can be addressed by setting either of the nonlinear distortions in Equation (4) to the identity. The case where only nonlinear distortion only in the receiver device 200 could represent an example where (digital) pre-distortion is implemented in the transmitter device 100 to handle the nonlinear distortion in the transmitter device 100. Using the estimates of the time-domain signals, denoted ^^−1^̂^ and ^^−1^^^̂^, Equation (7) can be formulated as follows by approximating ^^′ with ^^, where ^^ is expressed as ^^ = ^^ ^^ −10^^^^ + ^^Rx^^^^^̂^^^^^^̂^ ^^ ^^^̂^ + ^^Tx^^^^^^^̂^^^^^̂^^^^−1^̂^ +^^^^^ −1 ^^ −1 ^^ −1Rx^^^^^^^^^^^^ ^^ ^^^^ + ^^Tx^^^^^^^^^^^^ ^^ ^^ − ^^Rx^^^^^̂^^^^^^̂^ ^^ ^^^̂^ − ^^Tx^^^^^^^̂^^^^^̂^^^^−1^̂^approximation noise, ^^ + ^^ (9) by adding and subtracting the terms containing the estimates. Hence, Equation (9) does not introduce any further modeling approximations and the equality still holds. The resulting model can thus be formulated as: where the statistics of the approximation noise ^^ can be derived using, for example, Equation (9). As above, ^^ is a frequency domain representation of the wireless channel, ^^ is the signal as transmitted, ^^0is a gain parameter,^^Tx and ^^Rx are nonlinear distortion parameters, ^^^^^̂^ = diag{^^^^−1^̂^}, ^^^̂^ = diag{^^−1^̂^}, ^̂^ represents a frequency-domain approximation of the time-domain signal ^^−1^^, ^^ represents approximation noise, ^^ represents noise of the wireless channel, ^^ is a forward DFT, and ^^−1is an inverse DFT. The approximation of the transmitted time-domain signal, ^^−1^̂^, is nonlinearly mapped using ^^^^^̂^^^^^̂^^^^−1^̂^, and the received time-domain signal, is nonlinearly mapped using . The CDF of are similar to the CDF of the true signal vectors ^^−1^^^^ and The nonlinear distortion parameters, ^^Txand ^^Rx, and the gain, ^^0, can be estimated jointly using, for example, a linear MMSE estimator or an LS estimator. In other words, in the signal model, the received signal ^^′ can be modeled as a linear combination of the transmitted signal and the channel transfer function, a nonlinear function of the received signal, and a model of the channel transfer function. In some examples, the nonlinear function of the received signal is a third-order nonlinear function. In some examples, the nonlinear functions are described as memory polynomials, that is, several time-shifted polynomials of some orders. The positioning of the pilot symbols in the transmitted ^^ is irrelevant, and Equation (10) can be seen as a system of ^^ equations, all capturing the CDF of the true signal in the transmitter device 100 and the receiver device 200, respectively, where any number of equations can be used for estimating the nonlinear distortion. The used number of equations can, for example, be the number of pilots, ^^pilot.An ^^pilot × ^^ matrix, denoted ^^, can be used for extracting the pilot positions from Equation (10). Each row of ^^is all-zero except one element which is one. In other words, ^^^^pilotcorresponds to a vector of length ^^pilotcontaining only the pilot symbols. A model for ^^ (being an approximation of ^^′) and only considering pilot symbols can, using Equation (10), therefore be formulated as ^^^^ = ^^ ^^^^^^ + ^^ ^^^^ ^^ ^^ ^^^^̂^ ^^−1^^^̂^ + ^^ ^^^ ^ −10 Rx ^^^̂^ Tx ^^^^^^̂^^^^̂^ ^^ ^̂^ + ^^^^ + ^^^^, (11)An estimator (e.g., a linear MMSE estimator or an LS estimator) can be based on only the pilot frequencies of the received signal and the known transmitted pilot symbols. The method of approximating the transmitted signal can, as mentioned above, be applied to several different models. In another example, a matrix form is used to formulate a more general model of the nonlinear distortion. With respect to Equation (11), this more general model for ^^ (being an approximation of ^^′) becomes ^^^^ = ^^0^^^^^^ + ^^^^Rx^^Rx + ^^^^Tx^^Rx + ^^^^ + ^^^^, (12)As above, ^^ is a frequency domain representation of the wireless channel, ^^ is the signal as transmitted, ^^0is a gain parameter, ^^Txand ^^Rxare nonlinear distortion parameters (or vectors), ^^ represents approximation noise, ^^ represents noise of the wireless channel, ^̂^ represents a frequency-domain approximation of the time-domainsignal ^^−1^^, and ^^ is an ^^pilot × ^^ matrix where all elements of each row of ^^ is zero except one element,where ^^pilotis number of pilot symbols and ^^ is the number of total symbols in the received signal ^^. Further, ^^Rxis a matrix containing columns of different orders and time-shifts of ^^−1^^^̂^, and ^^Txis a matrix containing columns of different orders and time-shifts of ^^−1^̂^. A third-order column for the transmit distortion, ^^Tx, can, forexample, be represented as (^^−1^̂^) ⊙ ⊙ (^^−1^̂^), where ^^∗ is the element wise conjugate of ^^ and^^^^⊙^^^^is the element wise (Hadamard) product between ^^^^and ^^^^. A memory effect of the nonlinear distortion corresponds to shifting the elements of a column vector. A third-order distortion memory effectcorresponds to shifting the elements of the column (^^−1^̂^) ⊙ (^^−1^̂^)∗ ⊙ (^^−1^̂^) an appropriate number ofsteps. Using Equation (10) as a nonlinear model, the parameter space contains two vector parameters, namely ^^Rxand ^^Rx, and one scalar parameter, namely ^^0. A linear MMSE estimator or an LS estimator can be used to estimate them jointly. The nonlinear distortion can also be modeled in different ways. In some aspects, each of Equations (10), (11), and (12) can be seen as a system of ^^ equations that can be used for estimating the nonlinear distortion. The used number of equations can, for example, be the number of pilot symbols, ^^pilot. Therefore, in some embodiments, the signal comprises ^^pilotnumber of pilot signals, the signal model is representable by a system of equations, and the nonlinear distortion is estimated from ^^pilotnumber of the equations. Further aspects, embodiments, and examples of how to estimate the nonlinear distortion in step S104 will be disclosed next with reference to the flowchart of Fig.3. S104-2: The receiver device 200 estimates the transmitted signal ^^. This estimate is represented by the approximation ^̂^. S104-4: The receiver device 200 formulates statistics of the approximation error (i.e., of the error between ^^ and ^̂^. Hence, in some embodiments, in the signal model and as part of estimating the nonlinear distortion, the data symbols are iteratively estimated. Only statistics can be estimated, derived, or otherwise formulated since the transmitted signal ^^ comprises data symbols that per se are not known to the receiver device 200. S104-6: The receiver device 200 estimates the nonlinear distortion (with or without decisions). Here, the decision is on the payload symbols (i.e., on the data symbols of the received signal). As an example,Equation (10) or (11) can be reformulated such that the vector ^^ contains pilots, decisions, and payload; ^^ =^^pilot + ^^dec + ^^payload.Since the payload symbols are corrupted by noise, the decisions might be incorrect. To overcome this, the decision-based approach can, for example, be implemented using a sequential approach, where several (optional) possible decisions can be made for each data symbol. Hence, in some embodiments, a sequence of decisions is taken on at least some of the data symbols when the data symbols are iteratively estimated. The different decisions can be modeled as a tree, where the branches in the tree with the best performance criteria becomes the (final) decision. Hence, in some embodiments, the sequence of decisions is represented by branches in a tree structure, where each branch in the tree structure represents one of the decisions, and, in the signal model and as part of estimating the nonlinear distortion, the data symbols are represented by the branches, that according to a performance criterion, yield best performance. One such performance criterion for evaluating the different branches is the error signal created by the difference between the compensated input signal and the symbol decisions related to the compensated signal. Another such performance criterion is the error signal created by the difference between the compensated received signal and the pilot symbols, where the difference is evaluated only for the pilot symbols. Step S104-2 can then be entered again, where a new estimation of the transmitted signal ^^ is performed based on the nonlinear distortion as estimated. Alternatively, step S104-2 is only entered again after the compensation of the received signal has been performed in step S106 such that the new estimation of the transmitted signal ^^ can be performed based on the received signal as compensated. Hence, in some embodiments, in the signal model and as part of estimating the nonlinear distortion, the data symbols are iteratively estimated. Fig.4 shows simulations of a transmitted OFDM signal with 1024 subcarriers. The signal comprises a payload that is modulated using 64-QAM symbols and 10 distributed pilots modulated using 4-QAM symbols. The additive white gaussian noise (AWGN) in the receiver corresponds to a signal to noise ratio (SNR) of 50dB. The channel models a Rayleigh fading channel with an exponentially decaying impulse response. Fig.4(a) shows the received distorted signal, where the distortion is of the third-order in both the transmitter device and the receiver device. Fig.4(b) shows the corresponding compensated signal where the third-order compensation parameters have been estimated using an MMSE estimator. A comparison can here be made to Fig.4(c) which shows an AWGN- only reference simulation for comparison. Thus, as shown in Fig.4(b), even though the distortion is severe, the herein disclosed embodiments enable the received signal to be fully compensated using only 10 pilots for estimating the nonlinear distortion. Fig.5 schematically illustrates, in terms of a number of structural units, the components of a receiver device 200 according to an embodiment. Processing circuitry 210 is provided using any combination of one or more of a suitable central processing unit (CPU), multiprocessor, microcontroller, digital signal processor (DSP), etc., capable of executing software instructions stored in a computer program product 710 (as in Fig.7), e.g. in the form of a storage medium 230. The processing circuitry 210 may further be provided as at least one application specific integrated circuit (ASIC), or field programmable gate array (FPGA). Particularly, the processing circuitry 210 is configured to cause the receiver device 200 to perform a set of operations, or steps, as disclosed above. For example, the storage medium 230 may store the set of operations, and the processing circuitry 210 may be configured to retrieve the set of operations from the storage medium 230 to cause the receiver device 200 to perform the set of operations. The set of operations may be provided as a set of executable instructions. Thus the processing circuitry 210 is thereby arranged to execute methods as herein disclosed. The storage medium 230 may also comprise persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid state memory or even remotely mounted memory. The receiver device 200 may further comprise a communications (comm.) interface 220 at least configured for communications with other entities, functions, nodes, and devices, such as the transmitter device 100. As such the communications interface 220 may comprise one or more transmitters and receivers, comprising analogue and digital components. The processing circuitry 210 controls the general operation of the receiver device 200 e.g. by sending data and control signals to the communications interface 220 and the storage medium 230, by receiving data and reports from the communications interface 220, and by retrieving data and instructions from the storage medium 230. Other components, as well as the related functionality, of the receiver device 200 are omitted in order not to obscure the concepts presented herein. Fig.6 schematically illustrates, in terms of a number of functional modules, the components of a receiver device 200 according to an embodiment. The receiver device 200 of Fig.6 comprises a number of functional modules; a receive module 210a configured to perform step S102, an estimate module 210b configured to perform step S104, and a compensate (Comp.) module 210c configured to perform step S106. The receiver device 200 of Fig. 7 may further comprise a number of optional functional modules, as represented by functional module 210d, for example to implement the steps of the flowchart in Fig.3. In general terms, each functional module 210a:210d may in one embodiment be implemented only in hardware and in another embodiment with the help of software, i.e., the latter embodiment having computer program instructions stored on the storage medium 230 which when run on the processing circuitry makes the receiver device 200 perform the corresponding steps mentioned above in conjunction with Fig 6. It should also be mentioned that even though the modules correspond to parts of a computer program, they do not need to be separate modules therein, but the way in which they are implemented in software is dependent on the programming language used. Preferably, one or more or all functional modules 210a:210d may be implemented by the processing circuitry 210, possibly in cooperation with the communications interface 220 and / or the storage medium 230. The processing circuitry 210 may thus be configured to from the storage medium 230 fetch instructions as provided by a functional module 210a:210d and to execute these instructions, thereby performing any steps as disclosed herein. The receiver device 200 may be provided as a standalone device or as a part of at least one further device. For example, as disclosed above, the receiver device 200 might be, or be part of, a network equipment, an access node, or a user equipment. In case the receiver device 200 is, or is part of, a network equipment or an access node, the network equipment or an access node, may either be part of the same network part (such as the radio access network or the core network) or may be spread between at least two such network parts. In general terms, instructions that are required to be performed in real time may be performed in a device, or node, operatively closer to the cell than instructions that are not required to be performed in real time. A first portion of the instructions performed by the receiver device 200 may be executed in a first device, and a second portion of the of the instructions performed by the receiver device 200 may be executed in a second device; the herein disclosed embodiments are not limited to any particular number of devices on which the instructions performed by the receiver device 200 may be executed. Hence, the methods according to the herein disclosed embodiments are suitable to be performed by a receiver device 200 residing in a cloud computational environment. Therefore, although a single processing circuitry 210 is illustrated in Fig.5 the processing circuitry 210 may be distributed among a plurality of devices, or nodes. The same applies to the functional modules 210a:210d of Fig.6 and the computer program 720 of Fig.7. Some (radio) access network architectures define network nodes (or gNBs) comprising multiple component parts or nodes: a central unit (CU), one or more distributed units (DUs), and one or more radio units (RUs). The protocol layer stack of the network node is divided between the CU, the DUs and the RUs, with one or more lower layers of the stack implemented in the RUs, and one or more higher layers of the stack implemented in the CU and / or DUs. The CU is coupled to the DUs via a fronthaul higher layer split (HLS) network; the CU / DUs are connected to the RUs via a fronthaul lower-layer split (LLS) network. The DU may be combined with the CU in some embodiments, where a combined DU / CU may be referred to as a CU or simply a baseband unit. A communication link for communication of user data messages or packets between the RU and the baseband unit, CU, or DU is referred to as a fronthaul network or interface. Messages or packets may be transmitted from the network node in the downlink (i.e., from the CU to the RU) or received by the network node in the uplink (i.e., from the RU to the CU). Fig.7 shows one example of a computer program product 710 comprising computer readable storage medium 730. On this computer readable storage medium 730, a computer program 720 can be stored, which computer program 720 can cause the processing circuitry 210 and thereto operatively coupled entities and devices, such as the communications interface 220 and the storage medium 230, to execute methods according to embodiments described herein. The computer program 720 and / or computer program product 710 may thus provide means for performing any steps as herein disclosed. In the example of Fig.7, the computer program product 710 is illustrated as an optical disc, such as a CD (compact disc) or a DVD (digital versatile disc) or a Blu-Ray disc. The computer program product 710 could also be embodied as a memory, such as a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), or an electrically erasable programmable read-only memory (EEPROM) and more particularly as a non-volatile storage medium of a device in an external memory such as a USB (Universal Serial Bus) memory or a Flash memory, such as a compact Flash memory. Thus, while the computer program 720 is here schematically shown as a track on the depicted optical disk, the computer program 720 can be stored in any way which is suitable for the computer program product 710. The inventive concept has mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the inventive concept, as defined by the appended patent claims.

Claims

CLAIMS 1. A method for compensating for nonlinear distortion, the method being performed by a receiver device (200), the method comprising: receiving (S102), at an input of the receiver device (200), a signal ^^′ over a wireless channel ^^ from an output of a transmitter device (100), the signal comprising pilot symbols and data symbols; estimating (S104) nonlinear distortion of the signal, wherein the estimating is based on a signal model comprising characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device (100) and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device (200), wherein each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^; and compensating (S106) the signal for the estimated nonlinear distortion.

2. The method according to claim 1, wherein, in the signal model,is used by the non-linear transformation to obtain the characteristics of the signal3. The method according to claim 1 or 2, wherein, in the signal model, an approximation of the signal ^^−1^^^^ is used by the non-linear transformation to obtain the characteristics of the signal ^^−1^^^^.

4. The method according to any preceding claim, wherein, in the signal model, the characteristics of the signal represent a cumulative distribution function, CDF, of the signal5. The method according to any preceding claim, wherein, in the signal model, the characteristics of the signal ^^−1^^^^ represent a cumulative distribution function, CDF, of the approximation of the signal ^^−1^^^^.

6. The method according any preceding claim, wherein, in the signal model, the characteristics of the signal is free from nonlinear distortion.

7. The method according to any preceding claim, wherein, in the signal model, the characteristics of the signal and the characteristics of the signal ^^−1^^^^ are jointly estimated.

8. The method according to any preceding claim, wherein, in the signal model, the data symbols are treated as having unknown values.

9. The method according to any preceding claim, wherein, in the signal model and as part of estimating the nonlinear distortion, the data symbols are replaced by an estimate of the data symbols based on the signal as received at the input of the receiver device (200).

10. The method according to any preceding claim, wherein the signal model is transparent with respect to locations of the pilot symbols in the signal as received at the input of the receiver device (200).

11. The method according to any preceding claim, wherein the signal comprises ^^pilotnumber of pilot signals, wherein the signal model is representable by a system of equations, and wherein the nonlinear distortion is estimated from ^^pilotnumber of the equations.

12. The method according to any preceding claim, wherein, in the signal model and as part of estimating the nonlinear distortion, the data symbols are iteratively estimated.

13. The method according to claim 12, wherein a sequence of decisions is taken on at least some of the data symbols when the data symbols are iteratively estimated.

14. The method according to claim 13, wherein the sequence of decisions is represented by branches in a tree structure, where each branch in the tree structure represents one of the decisions, and wherein, in the signal model and as part of estimating the nonlinear distortion, the data symbols are represented by the branches, that according to a performance criterion, yield best performance.

15. The method according to any preceding claim, wherein the nonlinear distortion is estimated using a minimum mean square error estimator or a least squares estimator.

16. The method according to any preceding claim, wherein, in the signal model, the received signal ^^ is modeled as a linear combination of the transmitted signal and the channel transfer function, a nonlinear function of the received signal, and a model of the channel transfer function.

17. The method according to any preceding claim, wherein, in the signal model, the received signal ^^′ is modeled by ^^, where ^^ is expressed as:where ^^ is a frequency domain representation of the wireless channel, ^^ is the signal as transmitted, ^^0is again parameter, ^^Tx and ^^Rx are nonlinear distortion parameters, ^^^^^̂^ = diag{^^^^−1^̂^}, ^^^̂^ = diag{^^−1^̂^}, ^̂^ represents a frequency-domain approximation of the time-domain signal ^^−1^^, ^^ represents approximation noise, ^^ represents noise of the wireless channel, ^^ is a discrete Fourier transform, and ^^−1is an inverse discrete Fourier transform.

18. The method according to any of claims 1 to 16, wherein, in the signal model, the received signal ^^′ is modeled by ^^, where ^^ is expressed as: ^^^^ = ^^0^^^^^^ + ^^^^Rx^^Rx + ^^^^Tx^^Tx + ^^^^ + ^^^^where ^^ is a frequency domain representation of the wireless channel, ^^ is the signal as transmitted, ^^0is a gain parameter, ^^Txand ^^Rxare nonlinear distortion parameters, ^^Rxis a matrix containing columns of different orders and time-shifts of ^^−1^^^̂^, ^^Txis a matrix containing columns of different orders and time-shifts of ^^−1^̂^, ^̂^ represents a frequency-domain approximation of the time-domain signal ^^−1^^, ^^ represents approximationnoise, ^^ represents noise of the wireless channel, and ^^ is an ^^pilot × ^^ matrix where all elements of each rowof ^^ is zero except one element, where ^^pilotis number of pilot symbols and ^^ is number of total symbols in the received signal ^^.

19. The method according to any preceding claim, wherein the receiver device (200) is, or is part of, a network equipment, an access node, or a user equipment.

20. A receiver device (200) for compensating for nonlinear distortion, the receiver device (200) comprising processing circuitry (210), the processing circuitry being configured to cause the receiver device (200) to: receive, at an input of the receiver device (200), a signal ^^′ over a wireless channel ^^ from an output of a transmitter device (100), the signal comprising pilot symbols and data symbols; estimate nonlinear distortion of the signal, wherein the estimating is based on a signal model comprising characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device (100) and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device (200), wherein each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^; and compensate the signal for the estimated nonlinear distortion.

21. A receiver device (200) for compensating for nonlinear distortion, the receiver device (200) comprising: a receive module (210a) configured to receive, at an input of the receiver device (200), a signal ^^′ over a wireless channel ^^ from an output of a transmitter device (100), the signal comprising pilot symbols and data symbols; an estimate module (210b) configured to estimate nonlinear distortion of the signal, wherein the estimating is based on a signal model comprising characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device (100) and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device (200), wherein each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^; and a compensate module (210c) configured to compensate the signal for the estimated nonlinear distortion.

22. The receiver device (200) according to claim 20 or 21, further being configured to perform the method according to any of claims 2 to 19.

23. A computer program (720) for compensating for nonlinear distortion, the computer program comprising computer code which, when run on processing circuitry (210) of a receiver device (200), causes the receiver device (200) to: receive (S102), at an input of the receiver device (200), a signal ^^′ over a wireless channel ^^ from an output of a transmitter device (100), the signal comprising pilot symbols and data symbols; estimate (S104) nonlinear distortion of the signal, wherein the estimating is based on a signal model comprising characteristics of a complete time-domain version of the signal, ^^−1^^, at the output of the transmitter device (100) and characteristics of a time-domain version of the signal, ^^−1^^^^, at the input of the receiver device (200), wherein each of characteristics is obtained using a non-linear transformation of the signal ^^−1^^^^; and compensate (S106) the signal for the estimated nonlinear distortion.

24. A computer program product (710) comprising a computer program (720) according to claim 23, and a computer readable storage medium (730) on which the computer program is stored.

Images