Method and apparatus for separable multi-dimensional linearizer scheme

Abstract

Embodiments of a linearization system and method of operation thereof are disclosed. In one embodiment, a method of operation of a linearization system for a radio node for a wireless network comprises obtaining a plurality of input signals (x 1 , …,x P ) for P input dimensions, respectively, for a P-dimensional LUT for compensating for non-linear characteristics of one or more components of the radio node, wherein P is an integer value that is greater than 1. The method further comprises generating a compensation signal based on the plurality of input signals (x 1 , …,x P ) and a plurality of 1-dimensional (1-D) Look-Up Tables (LUTs) that directly model the P-dimensional LUT. The method further comprises applying the compensation signal to a particular signal to provide a compensated signal for further processing by the radio node.

Description

SEPARABLE MULTI-DIMENSIONAL LINEARIZER SCHEME Technical Field

[0001] The present disclosure relates to linearization and, more specifically, to Look- Up Table (LUT) based linearization for a radio node. Background

[0002] A typical radio in modern wireless communication system is composed of a variety of non-linear devices. Because of their non-linear response to input, these non- linear devices often create spurious emissions interfering with other systems using other parts of the frequency spectrum, in addition to reducing their own efficiency in delivering data. A typical example is the Power Amplifier (PA), which is often modelled as parametric Generalized Memory Polynomial (GMP). Knowing the parameters of this parametric GMP model has been successfully used to digitally pre-distort the input signal to mitigate the PA non-linearity effects, thereby producing not only a clean signal but also avoiding out-of-band emissions. Other non-linear devices present in any modern radio include, for example, mixers, oscillators, Digital-to-Analog Convertors (DACs), and Analog-to-Digital Convertors (ADCs).

[0003] A classical way to linearize all these non-linear devices is to use Look-Up Table (LUT) based adaptive linearization architectures in lieu of polynomials which require an excessive number of multiplications. LUT based adaptive linearization architectures offer cost effective efficient structures and can handle a variety of traffic conditions. A LUT based adaptive linearization architecture replaces multiplications with memory.

[0004] Technology trends are gravitating towards multiband-wideband radios. As a result, LUT based adaptive linearization architectures will soon become difficult, if not impractical, to implement as the number of frequency bands increases beyond two frequency bands. With wideband radios, sampling rate requirements for non-linear systems are very much magnified along with the computational processing cost at those sampling rates. Hence, the cost-effective way of processing signals in such systems is to process only targeted regions of the spectrum of much lower bandwidth than the total bandwidth of the multi-band system in order to reduce the sampling rate and hence processing requirements of the system. Multidimensional structures with Multi-InputSingle-Output (MISO) processing architectures targeting much smaller regions of spectrum have been found to be more efficient structures to handle wideband- multiband systems. LUT based adaptive linearization in such MISO processing architectures requires multi-dimensional LUTs. However, a problem arises in that the size of such multi-dimensional LUTs exponentially increases as the number of independent dimensions (e.g., frequency bands) increases. As such, there is a need for systems and methods for LUT based adaptive linearization that address this problem. Summary

[0005] Embodiments of a linearization system and method of operation thereof are disclosed. In one embodiment, a method of operation of a linearization system for aradio node for a wireless network comprises obtaining a plurality of input signals (^^, …,^^) for ^ input dimensions, respectively, for a ^-dimensional LUT for compensating fornon-linear characteristics of one or more components of the radio node, wherein ^ is an integer value that is greater than 1. The method further comprises generating a compensation signal based on the plurality of input signals (^^, …, ^^) and a plurality of 1-dimensional (1-D) Look-Up Tables (LUTs) that directly model the ^-dimensional LUT. The method further comprises applying the compensation signal to a particular signal to provide a compensated signal for further processing by the radio node. By directly modeling the ^-dimensional LUT as an arrangement of 1D LUTs results in a cost effective and efficient implementation of the linearization system.

[0006] In one embodiment, the plurality of 1-D LUTs model the desired multi- dimensional LUT in accordance with: ^^^ ^ where ^^^^, ^^, … , ^^^ is the 1-D LUT for ^th input signal for a ^^^summationpositive integer that is greater than or equal to 1.

[0007] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of frequency band input signals (^^, …, ^^) for ^ frequency bands, respectively, wherein ^ = ^.

[0008] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of frequency band input signals (^^, …, ^^) for ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1 and, for each frequency band input signal (^^) of the plurality of frequency band input signals (^^, …, ^^), one or more delayed versions of the frequency band input signal (^^).

[0009] In one embodiment, the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P-dimensional LUT for one of the ^ frequency bands, the compensation signal generated based on the plurality of input signals (^^, …, ^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is a compensation signal for the one of the ^ frequency bands, and applying the compensation signal to the particular signal comprises applying the compensation signal for the one of the ^ frequency bands to the frequency band input signal for the one of the ^ frequency bands to provide the compensated signal for the one of the ^ frequency bands.

[0010] In one embodiment, the method further comprises, for each additional frequency band of the ^ frequency bands, generating a compensation signal for the additional frequency band based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1-D LUTs that directly model a ^-dimensional LUT for the additional frequency band for compensating for non-linear characteristics of one or more components of the radio node for the additional frequency band and applying the compensation signal for the additional frequency band to the frequency band input signal for the additional frequency band to provide a compensated frequency input signal for the additional frequency ban. The method further comprises combining the compensated frequency band input signals for the ^ frequency bands to provide a final compensated input signal for further processing by the radio node.

[0011] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of beam domain input signals (^^, …, ^^) for ^ beam directions, respectively, wherein ^ = ^.

[0012] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of beam domain input signals (^^, …, ^^) for ^ beam directions, wherein ^ is an integer value that is greater than or equal to 1 and, for each beam domain input signal (^^) of the plurality of beam domain input signals (^^, …, ^^), one or more delayed versions of the beam domain input signal (^^).

[0013] In one embodiment, the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P-dimensional LUT for one of the ^ beam directions, the compensation signal generated based on the plurality of input signals (^^, …, ^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is a compensation signal for the one of the ^ beam direction, and applying the compensation signal to the particular signal comprises applying the compensated signal for the one of the ^ beam directions to the beam domain input signal for the one of the ^ beam directions to provide the compensated signal for the one of the ^ beam directions. In one embodiment, the method further comprises, for each additional beam direction of the ^ beam directions, generating a compensation signal for the additional beam direction based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1-D LUTs that directly model a ^-dimensional LUT for the additional beam direction for compensating for non- linear characteristics of one or more components of the radio node for the additional beam direction and applying the compensation signal for the additional beam direction to the beam domain input signal for the additional beam direction to provide a compensated beam domain input signal for the additional beam direction.

[0014] In one embodiment, the plurality of input signals (^^, …, ^^) consist of, for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1, a plurality of beam domain input signals (^^,^, …, ^^,^) for ^ beam directions for each of the ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1.

[0015] In one embodiment, the plurality of input signals (^^, …, ^^) consist of, for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1, a plurality of beam domain input signals (^^,^, …, ^^,^) for ^ beam directions for each of the ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1 and, for each beam domain input signal (^^,^) of the plurality of beam domain input signals (^^,^, …, ^^,^) for each of the ^ frequency bands, one or more delayed versions of the beam domain input signal (^^,^).

[0016] In one embodiment, the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P-dimensional LUT for one of the ^ beam directions for one of the ^ frequency bands, the compensation signal generated based on the plurality of input signals (^^, …, ^^) and the plurality of 1-D LUTs that directly model the ^-dimensionalLUT is a compensation signal for the one of the ^ beam directions for the one of the ^ frequency bands, and applying the compensation signal to the particular signal comprises applying the compensated signal for the one of the ^ beam directions for the one of the ^ frequency bands to the beam domain input signal for the one of the ^ beam directions for the one of the ^ frequency bands to provide the compensated signal for the one of the ^ beam directions for the one of the ^ frequency bands. In one embodiment, the method further comprises, for each additional frequency band of the ^ frequency bands, generating a compensation signal for the one of the ^ beam directions for the additional frequency band based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1-D LUTs that directly model a ^-dimensional LUT for the one of the ^ beam directions for the additional frequency band for compensating for non-linear characteristics of one or more components of the radio node for the one of the ^ beam directions for the additional frequency band and applying the compensation signal for the one of the ^ beam directions for the additional frequency band to the input signal for the one of the ^ beam directions for the additional frequency band to provide a compensated signal for the one of the ^ beam directions for the additional frequency band. The method further comprises combining the compensated signals for the one of the ^ beam directions for the ^ frequency bands to provide a compensated signal for the one of the ^ beam directions for further processing by the radio node.

[0017] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of transmit branch input signals (^^, …, ^!) for ^ transmit branches of the radio node, respectively, wherein ^ = ^.

[0018] In one embodiment, the plurality of input signals (^^, …, ^^) consist of a plurality of transmit branch input signals (^^, …, ^!) for ^ transmit branches of the radio node, respectively, wherein ^ is an integer value that is greater than or equal to 1 and, for each transmit branch input signal (^^) of the plurality of transmit branch input signals (^^, …, ^!), one or more delayed versions of the transmit branch input signal (^^). In one embodiment, the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P-dimensional LUT for generating a Passive Inter-Modulation (PIM) compensation signal for a receiver of the radio node, the compensation signal generated based on the plurality of input signals (^^, …, ^^) and the plurality of 1-DLUTs that directly model the ^-dimensional LUT is a PIM compensation signal, and applying the compensation signal to the particular signal comprises applying the compensated signal to a received signal received via the receiver of the radio node to provide a compensated receive signal as the compensated signal.

[0020] In one embodiment, the plurality of input signals (^^, …, ^^) consist of, for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1, a plurality of transmit branch input signals (^^,^, …, ^^,!) for ^ transmit branches of the radio node for each of the ^ frequency bands, wherein ^ = ^ × ^.

[0021] In one embodiment, the plurality of input signals (^^, …, ^^) consist of, for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1, a plurality of transmit branch input signals (^^,^, …, ^^,!) for ^ transmit branches of the radio node for each of the ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1 and, for each transmit branch input signal (^^,^) of the plurality of transmit branch input signals (^^,^, …, ^^,!) for each of the ^ frequency bands, one or more delayed versions of the transmit branch input signal (^^,!). In one embodiment, the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P-dimensional LUT for generating a PIM compensation signal for a receiver of the radio node, the compensation signal generated based on the plurality of input signals (^^, …, ^^) and the plurality of 1-D LUTs that directly model the ^- dimensional LUT is a PIM compensation signal for a receiver of the radio node, and applying the compensation signal to the particular signal comprises applying the PIM compensation signal to a received signal received via the receiver of the radio node.

[0023] In one embodiment, the method further comprises performing an adaptation procedure whereby values stored by the plurality of LUTs are updated.

[0024] In one embodiment, the method further comprises, for each 1-D LUT of the plurality of 1-D LUTs, obtaining an observation vector (Yi) comprising observed samples of an output signal transmitted by the radio node that correspond to a given input vector comprising samples of the plurality of input signals (^^, …, ^^), computing a delta vector for the 1-D LUT based on a difference between the given input vector (Xi) and the observation vector (Yi), and updating the 1-D LUT based on the delta vector. In one embodiment, the method further comprises performing a plurality of iterations ofthe steps of, for each 1-D LUT of the plurality of 1-D LUTs, obtaining an observation vector (Yi), computing a delta vector, and updating the 1-D LUT.

[0025] Embodiments of a linearization system are also disclosed. In one embodiment, a linearization system for a radio node for a wireless network comprises an actuator system adapted to obtain a plurality of input signals (^^, …, ^^) for ^ input dimensions, respectively, for a ^-dimensional LUT for compensating for non-linear characteristics of one or more components of the radio node, wherein ^ is an integer value that is greater than 1. The actuator system is further adapted to generate a compensation signal based on the plurality of input signals (^^, …, ^^) and a plurality of 1D LUTs that directly model the ^-dimensional LUT and apply the compensation signal to a particular signal to provide a compensated signal for further processing by the radio node.

[0026] In one embodiment, the plurality of 1-D LUTs model the desired multi- dimensional LUT in accordance with: ^^^^^^, ^^, … , ^^^ = ^ ^ ^^,^^^^^ ^^^ ^^^where ^^^^, ^^, … , ^^^ is the P-dimensional LUT and ^^,^^^^^the 1-D LUT for ^th input signal for a ^^^summation where 1≤ ^ ≤ ^ and ^ is a predefined positive integer that is greater than or equal to 1. Brief Description of the Drawings

[0027] The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure, and together with the description serve to explain the principles of the disclosure.

[0028] Figure 1 illustrates a Look-Up Table (LUT)-based linearization system that utilizes a 1-Dimensional (1D) LUT arrangement that directly models a multi-dimensional LUT or multi-dimensional linearization function, in accordance with one embodiment of the present disclosure;

[0029] Figure 2 is a flow chart that illustrates the operation of the LUT-based linearization system of Figure 1, in accordance with one embodiment of the present disclosure;

[0030] Figure 3 illustrates a partial sum that forms a basic unit of a single dimensional complete linearizer;

[0031] Figures 4 and 5 illustrate an example 2-Dimensional (2D) LUT based linearization system for compensating for non-linearities for first and second frequency bands in a two-band radio, in accordance with one embodiment of the present disclosure;

[0032] Figure 6 illustrates a complete LUT based linearization system for a two band system including multiple memory taps per frequency band, in accordance with one example embodiment of the present disclosure;

[0033] Figure 7 illustrates a LUT based linearization system for a first of three frequency bands for three-band radio, in accordance with one example embodiment of the present disclosure;

[0034] Figure 8 illustrates one example of a radio node that includes a Digital Pre- Distortion (DPD) actuator system that uses a Separate DPD (S-DPD) architecture that utilizes LUT based linearization, in accordance with embodiments of the present disclosure;

[0035] Figure 9 illustrates the b-th S-DPD actuator of Figure 8 in more detail, in accordance with one example embodiment of the present disclosure;

[0036] Figure 10 is a flow chart that illustrates the operation of the radio node of Figure 8, in accordance with one embodiment of the present disclosure;

[0037] Figure 11 is a flow chart that illustrates an adaptation process by which values stored in the entries of the 1D LUTs in the 1D LUT arrangement (e.g., 1D LUT arrangement 900 of Figure 9) are determined and, if desired, updated over time, in accordance with one example embodiment of the present disclosure;

[0038] Figure 12 illustrates an example radio node including a beam domain DPD actuator system that utilizes 1D LUT arrangements in accordance with an embodiment of the present disclosure;

[0039] Figure 13 illustrates the d-th beam-domain SDP actuator of the beam domain actuator system of Figure 12, in accordance with one example embodiment of the present disclosure;

[0040] Figure 14 illustrates the b-th 1D LUT arrangement of Figure 13 in more detail, in accordance with one example embodiment of the present disclosure;

[0041] Figure 15 illustrates an example radio node including a Passive Inter- Modulation (PIM) compensator that utilizes one or more 1D LUT arrangements in accordance with an embodiment of the present disclosure; and

[0042] Figure 16 illustrates one example embodiment of the PIM compensator of Figure 15 in which the PIM compensator includes a 1D LUT arrangement that directly models a P-dimensional LUT for generating the PIM compensation signal, in accordance with one example embodiment of the present disclosure. Detailed Description

[0043] The embodiments set forth below represent information to enable those skilled in the art to practice the embodiments and illustrate the best mode of practicing the embodiments. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure.

[0044] As discussed in the Background section above, using multi-dimensional Look- Up Table (LUT) structures for linearization has been proven to be efficient way in terms of performance and cost. However, the memory requirement for such a multi- dimensional LUT based linearization system grows exponentially when the number of independent dimensions increases beyond three. For example, a single-dimensional LUT with 16 bins requires 16 locations only, whereas a 4-dimensional LUT with same 16 bins in each dimension would require 65536 bins.

[0045] Systems and methods are disclosed herein that address the aforementioned challenges with existing multi-dimensional LUT based linearization systems. Embodiments of LUT-based linearization systems are disclosed herein in which a combination of one-dimensional (1D) LUTs is used to directly model a multi-dimensional LUT.

[0046] It should be noted that International Patent Application Publication No. WO 2022 / 185903 entitled PRACTICAL PREDISTORTION ARCHITECTURES FOR MULTIBAND RADIOS, which was published on September 9, 2022, teaches systems and methods that replace a multi-dimensional LUT with 1D LUTs by assuming a Generalized Memory Polynomial (GMP) model explicitly having non-linear combinations of multiple variablesand factoring that GMP model into a series of linear summations of those multiple variables to be compatible with 1D LUTs. However, in the present disclosure, there is no assumption of any model (e.g., no assumption of a GMP model); instead, the desired multi-dimensional linearization function is represented as combination of single variable functions from beginning where each signal variable function is implemented as a 1D LUT. In other words, a desired multi-dimensional LUT is directly modeled by a combination of 1D LUTs. The desired P-dimensional linearization function or P- dimensional LUT ^^^^, ^^, … , ^^^ is represented as a combination of single-dimensional functions or 1D LUTs ^^,^^^^^ as follows: ^^^^^^, ^^, … , ^^^ = ^ ^ ^^,^^^^^ (1)^^^ ^^^where: • ^^^^, ^^, … , ^^^ is a P-dimensional function or P-dimensional LUT where each dimension can be either an input variable itself or a delayed sample of an input variable, e.g., one can have ^^^$^ = ^^^$ − &^,^^ where ^^^$^ is the original / current sample of an input variable for dimension 1, ^^^$ − &^,^^ is a delayed version of the same sample of the input variable that is delayed by &^,^relative to of ^^^$^. The number of dimensions, ^, is an integer value that is greater than 1. • ^^,^^^^^ is a 1D function or 1D LUT for the ^-th dimension for the ^-thHere, ^ is a dimension index where ^ = 1, … , ^, ^ is summation index where ^ = 1, … , ^ and ^ is a predefined orinteger value that is greaterequal to 1. The value of ^ is, in some embodiments, predefined or predetermined according to the non-linearity of the device for which linearization is being performed.

[0047] In other words, non-linear systems are usually represented as parametric models of a GMP. However, for embodiments of the present disclosure, a model agnostic system is assumed in which the desired multi-dimensional linearization function or multi-dimensional LUT is represented by a combination of single variable functions or 1D LUTs.

[0048] In addition, the formulation supports algorithms that are directly formulated using 1D LUTs without any further necessity to apply function conversion to LUTs andusing interpolation to enhance performance. Equation (23) below describes a multidimensional function. To be implemented in digital hardware, this function needs to be sampled and values then inserted into a multidimensional matrix or cube. In addition, normally one would need a denser grid of sample values than what is represented by a multi-dimensional matrix / cube, so some sort of multi-dimensional interpolation then has to be performed. With embodiments of the proposed solution, one can avoid this, since the formulation from start on involves 1D LUTs. If needed 1D interpolation can be done with much less effort than multi-dimensional interpolation, as a general rule.

[0049] Thus, embodiments of the present disclosure express a desired multi- dimensional linearization function or multi-dimensional LUT in terms of a product of single variable functions. These functions also cover the concept of discrete single variable LUTs. Further, by representing the desired multi-dimensional linearization function or multi-dimensional LUT as a sum of single-variable product of LUTs, adaptation schemes to compute or otherwise determine the LUT entries can be re-used from simpler 1D-solutions.

[0050] Embodiments of the present disclosure provides advantages over existing technology. For example, one advantage of representing any multivariable non-linear model as a combination of 1D LUTs is that it provides a cost effective and efficient implementation in any practical system such as, e.g., a radio for a wireless communication system. A further advantage is that computational schemes can be performed directly in the LUT-plane without involvement of any algebraic functions that would have to be either implemented or simplified through interpolation.

[0051] Moreover, a large advantage over using a multi-dimensional LUT is that considerably less storage or memory is required. For a presumed 5thorder non-linearity, only retaining odd orders, an embodiment of the present disclosure will require (5+1) / 2 = 3 terms in a power series. So, for a P-dimensional application, one would need to populate 3 x P x B entries, where B is LUT bin resolution and P is the table dimension. In comparison, a full multi-dimensional LUT for non-linear correction would require BPentries. The ratio BP / (3xPxB) becomes 2.7x, 28x, 341x, 4400x for a 2D, 3D, 4D, and a 5D LUT table, respectively, for B=16 bins. Thus, for a triple-band configuration, the memory savings provided by using an embodiment of the present disclosure ascompared to a conventional multi-dimensional LUT based linearization system will be 28-fold for a reasonable 16-bins per dimension.

[0052] In addition, as the formulation relies on a LUT formulation from start on, both the activation functionality (e.g., DPD) and the adaptation scheme used to adapt the LUTs are easily implementable in digital circuitry such as, e.g., a Field Programmable Gate Array (FPGA) or as a targeted solution in an Application Specific Integrated Circuit (ASIC). By using embodiments of the present disclosure, existing digital schemes for 1D LUTs can be reused to comply with the more complex situation of having a multi-band system.

[0053] Figure 1 illustrates a LUT-based linearization system 100 in accordance with one embodiment of the present disclosure. Optional elements are represented by dashed lines. As illustrated, the LUT-based linearization system 100 includes a 1D LUT arrangement 102 that directly models a desired P-dimensional linearization function orP-dimensional LUT ^^^^, ^^, … , ^^^ as a combination of 1D LUTs 104(k)(p), ^^,^^^^^, for^ = 1, … , ^ and ^ = 1, … , ^, in accordance with Equation (1) above. Asforeach value of ^ = 1, 2,input signals ^^, ^^, … , ^^, or magnitudes of the input signals^^, ^^, … , ^^, are input into the 1D LUTs ^^,^^^^^, ^^,^^^^^, …, ^^,^^^^^, respectively. Theoutput signals from the 1D LUTs ^^,^^^^^, ^^,^^^^^, …, ^^,^^^^^are multiplied together via multiplier circuitry 106(k). The outputs of the K multiplier circuitries 106(1) to 106(K) are summed by summation circuitry 108 to provide a compensation signal. This compensation signal corresponds to the output of the desired P-dimensional linearization function or P-dimensional LUT that is directly modeled by the 1D LUT arrangement 102. The compensation signal may then be applied to a signal to be compensated (denoted in Figure 1 as “xIN”) via, e.g., multiplier circuitry 110 to provide a compensated signal (denoted in Figure 1 as “y”).

[0054] Figure 2 is a flow chart that illustrates the operation of the LUT-based linearization system 100 of Figure 1 in accordance with one embodiment of the present disclosure. As illustrated, the LUT-based linearization system 100, and in particular the 1D LUT arrangement 102, obtains the input signals ^^, ^^, … , ^^that correspond to the P-dimensions (step 200). The LUT-based linearization system 100, and in particular the1D LUT arrangement 102, generates a compensation signal based on the input signals^^, ^^, … , ^^ and the combination of 1D LUTs that directly model the desired P-dimensional linearization function or P-dimensional LUT ^^^^, ^^, … , ^^^. Optionally, thecompensation signal is applied to (e.g., multiplied with or subtracted from) a particular signal (e.g., one of the input signals ^^, ^^, … , ^^to some other input signal (e.g., a received signal in the case of Passive Inter-Modulation (PIM) compensation as described in one example embodiment below) (step 204).

[0055] The input signals and how the compensation signal is applied will vary depending on the particular implementation or application of the LUT-based linearization system 100. For example, in one embodiment, the LUT-based linearization system 100 is a DPD system including S-DPD for each of multiple (^) frequency bands where ^ = ^ such that the input signals ^^, ^^, … , ^^consist of frequency band input signals ^^, ^^, … , ^^, each being an input signal for the corresponding -th frequency band ( = 1,2, … , ^). In this case, the compensation signal generated in step 202 is a compensation signal for one of the frequency bands, and the compensation signal is, in step 204, applied to the frequency band input signal for that frequency band to provide a compensated frequency band input signal for that frequency band. Steps 200-206 may be separately performed for each of the ^ frequency bands. Further, in one embodiment, the compensated frequency band input signals may be combined (e.g., upconverted to appropriate intermediate frequencies and then summed) to provide a compensated multi-band input signal that is then processed by a multi-band transmitter (e.g., DAC, upconversion to radio frequency, amplification by a PA, etc.) for transmission.

[0056] In another embodiment, the LUT-based linearization system 100 is a DPD system including S-DPD for each of multiple (^) frequency bands and having a memory depth of ) such that the input signals ^^, ^^, … , ^^consist of frequency band input signals ^^, ^^, … , ^^, each being an input signal for the corresponding -th frequency band ( = 1,2, … , ^), as well as ) delayed versions of each of the frequency band input signals. Thus, in this example, ^ = ^ × ). In this case, the compensation signal generated in step 202 is a compensation signal for one of the frequency bands, and the compensation signal is, in step 204, applied to the frequency band input signal for that frequency band to provide a compensated frequency band input signal for that frequency band. Steps 200-206 may be separately performed for each of the ^ frequency bands. Further, in one embodiment, the compensated frequency band input signals may be combined (e.g., upconverted to appropriate intermediate frequencies and then summed) to provide a compensated multi-band input signal that is thenprocessed by a multi-band transmitter (e.g., DAC, upconversion to radio frequency, amplification by a PA, etc.) for transmission.

[0057] In another embodiment, the LUT-based linearization system 100 is a beam- domain DPD system including S-DPD for each of ^ beam directions where ^ = ^ such that the input signals ^^, ^^, … , ^^consist of beam domain input signals ^^, ^^, … , ^^, each being an input signal for the corresponding &-th beam direction (& = 1,2, … , ^). In this case, the compensation signal generated in step 202 is a compensation forone of the beam directions, and the compensation signal is, in step 204, the beam domain input signal for that beam direction to provide a compensated beam domain input signal for that beam direction. Steps 200-206 may be separately performed for each of the ^ beam directions.

[0058] In another embodiment, the LUT-based linearization system 100 is a beam- domain DPD system including S-DPD for each of ^ beam directions and having a memory depth of ) such that the input signals ^^, ^^, … , ^^consist of beam domain input signals ^^, ^^, … , ^^, each being an input signal for the corresponding &-th frequency band (& = 1,2, … , ^), as well as ) delayed versions of each of the beam domain input signals.this example, ^ = ^ × ). In this case, the compensation signal generated in step 202 is a compensation signal for one of the beam directions, and the compensation signal is, in step 204, applied to the beam domain input signal for that beam direction to provide a compensated beam domain input signal for that beam direction. Steps 200-206 may be separately performed for each of the ^ beam directions.

[0059] In another embodiment, the LUT-based linearization system 100 is a multi- band beam-domain DPD system including S-DPD for each of ^ frequency bands for each of ^ beam directions where ^ = ^ × ^ such that the input signals ^^, ^^, … , ^^consist of, for each -th frequency band, beam domain input signals ^^,^, ^^,^, … , ^^,^, each being an input signal for the -th frequency band for the corresponding &-th beam direction (& = 1,2, … , ^). In this case, the compensation signal generated in step 202 is a compensationone of the frequency bands for one of the beam directions, and the compensation signal is, in step 204, applied to the input signal for that frequency band for that beam direction to provide a compensated input signal for that frequency band for that beam direction. Steps 200-206 may be separately performed for each of the ^ frequency bands for each of the ^ beam directions. For each beamdirection, the compensated input signals for the ^ frequency bands for that beam direction may be combined (e.g., upconverted to appropriate intermediate frequencies and then summed) to provide a compensated multi-band beam domain input signal that is then processed by a transmitter (e.g., beam domain to antenna domain conversion and, for each antenna, or transmit, branch of a multi-antenna transmitter, DAC, upconversion to radio frequency, amplification by a PA, etc.) for transmission.

[0060] In another embodiment, the LUT-based linearization system 100 is a multi- band beam-domain DPD system including S-DPD for each of ^ frequency bands for each of ^ beam directions and a memory depth of ). In this case, ^ = ^ × ^ × ) such that the input signals ^^, ^^, … , ^^consist of, for each -th frequency band, beam domain input signals ^^,^, ^^,^, … , ^^,^, each being an input signal for the -th frequency band for the corresponding &-th beam direction (& = 1,2, … , ^), as well as one or more delayed versions of each of the beam domain input signals for that frequency band. In this case, the compensation signal generated in step 202 is a compensation signal for one of the frequency bands for one of the beam directions, and the compensation signal is, in step 204, applied to the input signal for that frequency band for that beam direction to provide a compensated input signal for that frequency band for that beam direction. Steps 200-206 may be separately performed for each of the ^ frequency bands for each of the ^ beam directions. For each beam direction, the compensated input signals for the ^ frequency bands for that beam direction may be combined (e.g., upconverted to appropriate intermediate frequencies and then summed) to provide a compensated multi-band beam domain input signal that is then processed by a transmitter (e.g., beam domain to antenna domain conversion and, for each antenna, or transmit, branch of a multi-antenna transmitter, DAC, upconversion to radio frequency, amplification by a PA, etc.) for transmission.

[0061] In another embodiment, the LUT-based linearization system 100 is PIM compensation system for a radio for a wireless communication system, where the PIM compensation system generates a PIM compensation signal that is applied in the receiver to compensation for PIM due to one or more PIM sources in the radio. In one example of this embodiment, the input signals ^^, ^^, … , ^^consist of transmit branch input signals ^^, ^^, … , ^!where ^^is the transmit branch input signal for the *-th transmit branch and * is a transmit branch index (* = 1,2, … ^) where ^ is the number of transmit branches). In this case, ^ = ^. The compensation signal generated in step202 is a PIM compensation signal, and the compensation signal is, in step 204, applied to (e.g., subtracted from) a received signal to provide a compensated received signal. As with DPD, the PIM compensation case may be extended to include ^ frequency band input signals for each transmit branch, ) delayed versions of the transmit branch input signals, or ^ frequency band input signals for each transmit branch together with ) delayed version of each of the frequency band input signals for each transmit branch.

[0062] Now, the description will turn to a description of several example applications of the LUT based linearization system 100. Each example application is described under its own sub-heading. Digital Predistortion (DPD)

[0063] In one example application of the LUT based linearization system 100, the LUT based linearization system 100 is used for linearization of multi-band high power- amplifier (HPA) using Separate (S-DPD) (i.e., S-DPD for each of two or more frequency bands of a multi-band signal (e.g., a wideband, multi-carrier signal with multiple carriers each corresponding to a separate frequency band). In this example, the aim is to linearize separately for each of the two or more frequency bands.

[0064] The outline of the activation function to compensate non-linearity effects follows basically the classical formulation when it concerns using one single Look-up Table (LUT). This formulation may further be developed to support multi-dimensional Table look-up. Typically, these multi-dimensional LUTs occur when one applies separate compensation in several bands or for widely separated carriers.

[0065] Then the compensation would be formulated as the band signal being multiplied by a complex function (or LUT) being dependent on the specific band but also depending on the other bands. This would then be repeated for each band compensation. The advantage of applying this approach is that a fairly low processing speed can be maintained. This method is usually called Separate DPD when it comes to DPD.

[0066] The problem to overcome is that this presents a multi-dimensional approach and either a multidimensional function would be needed or an interpolation formulation of this function is necessary. Further, as mentioned in the preface, this would require a memory size to accommodate this N-dimensional table that quite soon exceeds any practically available memory in a digital implementation.

[0067] As an initial approach and as a means of understanding, we start by formulating a separation technique that is suitable for our implementation. It follows theformalism of being able to expand any function in a power series, as:+^^^ = , + ^ / - ,^^ + ,^^ + ,^^ … (2)or expressed in terms of just as set of basis-functions:+^^^ = 01, ^, ^^, ^ / , ...2 (3)

[0068] Along the same path, one could express, for example, a two-dimensional (2D)function with the help of mixed product basis functions as:ℎ^^, 4^ = 01, ^, 4, ^^, 4^, ^4, ^ / , 4 / , ^^4, ^4^...2 (4)

[0069] By defining two separate functions, one for ‘x’ and one for ‘y’, one will see that the product of these two functions will give rise to the same mixed product terms as expressed as above: 5^4^ = 01, 4, 4^, 4 / , ...2 (5) +^^^ × 5^4^ = 01, ^, 4, ^^, 4^, ^4, ^ / , 4 / , ^^4, ^4^...2 (6)

[0070] In order to make this separation of functions possible to use, summation over products of series expansion functions is needed, as follows: ℎ^^, 4^ =∑^^^^+^^^^ ∙ 5^^4^ (7)

[0071] The summation limit ‘K’ is the same number as the series expansion order (i.e., Polynomial degree). This summation is needed in general since, otherwise, one cannot freely define the coefficients in the 2D-expansion of h(x,y). It would be understood also by the knowledgeable engineer that an extension into a multi-variable space follows the same path as for the 2D-formulation as expressed above.

[0072] 1D-Formulation:

[0073] Let us start with a formulation of the basic 1D LUT formulation to both compute the LUT itself and how to apply the LUT in an activation formulation. In the 1D case, it would be fairly clear as to how to apply the correction according to the specific table entry based on the specific magnitude of the signal for each complex signal sample. 48 = ^ ∙(8)the delayed input sample ^89^:and some arbitrary function of absolute value ^89^<over multiple data- delay &^and address-delay &=(i.e., in the case of memory depth greater than 1),usually implemented as a 1D LUT and represented as ^^;^89^<;^. Input samples ^89^:and ^89^<are delayed by data-delay &^and address-delay &=from current sample ^8. In Figure 3, the partial sum is shown and forms the basic unit of single dimensional complete linearizer.

[0075] In the following description, for sake of clarity, references to delayed samples are omitted unless necessary, and the description focuses mainly on memoryless structures. Note, however, that any of the structures can easily be extended to include memory effects by introducing delays as shown in Figure 3. These delays are usually found by calibration for specific devices and are not the subject of the present disclosure.

[0076] 2D-Formulation:

[0077] For the 2D formation, two frequency bands are considered. The 2D formation for the first band response is: 418= ^18∙ ^^^|^18|,|^28|^(9) The 2D formulation for the second band response is: 428= ^28∙ ^^^|^18|,|^28|^(10)

[0078] In the 2D-formulation, in principle, the 2D-tables could be extended in a series of 1D table multiplications, by which one could write: ^ =∙ ^ ∙From this, a^ ^

[0079] 400 for compensating for non-linearities for a first frequency band (from among two total frequency bands of a multi-band radio), in accordance with one embodiment of the present disclosure. In accordance with Equations (11) and (13) above, the 2D LUT based linearization system 400 produces a compensation signal ^′^for the firstfrequency band and applies this compensation signal to the frequency band input signal^^ for the first frequency band to provide a compensated frequency band input signal 4^for the first frequency band. Note that only a single memory tap is shown in this example. More specifically, as illustrated, for each value of ^ = 1, 2, … ^,band input signals ^^, ^^for the two frequency bands, or more specifically magnitudes of the frequency band input signals ^^, ^^for the two frequency bands, are input into 1D LUTs ^1^,^^^^ and ^1^,^^^^, respectively, which may be referenced herein as 1DLUTs 402(k)(1) and 402(k)(2). The output signals from the 1D LUTs ^1^,^^^^ and^1^,^^^^ are multiplied together via multiplier circuitry 404(k). The outputs of the Kmultiplier circuitries 404(1) to 404(K) are summed by summation circuitry 406 to provide the compensation signal ^′^for the first frequency band. This compensation signal ^′^for the first frequency band corresponds to the output of the desired P- dimensional linearization function or P-dimensional LUT that is directly modeled by the 1D LUT arrangement. The compensation signal ^′^for the first frequency band is then applied to the frequency band input signal ^^for the first frequency band via multiplier circuitry 408 to provide the compensated frequency band input signal 4^for the first frequency band.

[0080] Figure 5 illustrates an example 2D LUT based linearization system 500 for compensating for non-linearities for the second frequency band (from among the two total frequency bands of the multi-band radio), in accordance with one embodiment of the present disclosure. In accordance with Equations (12) and (14) above, the 2D LUT based linearization system 500 produces a compensation signal ^′^for the secondfrequency band and applies this compensation signal to the frequency band input signal^^ for the second frequency band to provide a compensated frequency band inputsignal 4^for the second frequency band. Note that only a single memory tap is shown in this example. More specifically, as illustrated, for each value of ^ = 1, 2, … ^, frequency band input signals ^^, ^^for the two frequency bands, or more specifically magnitudes of the frequency band input signals ^^, ^^for the two frequency bands, are input into 1D LUTs ^2^,^^^^ and ^2^,^^^^, respectively, which may be referenced hereinas 1D LUTs 502(k)(1) and 502(k)(2). The output signals from the 1D LUTs ^2^,^^^^ and^2^,^^^^ are multiplied together via multiplier circuitry 504(k). The outputs of the Kmultiplier circuitries 504(1) to 504(K) are summed by summation circuitry 506 toprovide the compensation signal ^′^for the second frequency band. This compensation signal ^′^for the second frequency band corresponds to the output of the desired P- dimensional linearization function or P-dimensional LUT that is directly modeled by the 1D LUT arrangement. The compensation signal ^′^for the second frequency band is then applied to the frequency band input signal ^^for the second frequency band via multiplier circuitry 508 to provide the compensated frequency band input signal 4^for the second frequency band.

[0081] Figure 6 illustrates a complete LUT based linearization system 600 for a two band system, in accordance with one example embodiment of the present disclosure. In this example, the LUT based linearization system 600 includes the 2D linearization systems 400 and 500 of Figures 4 and 5, each extended to multiple memory taps. As illustrated, for the first frequency band, the LUT based linearization system 600 includes multiple instances of the linearization system 400 of Figure 4 – one for each of )^memory taps, which are referenced in Figure 6 as LUT based linearization systems 400- 1 to 400-M1for the first frequency band. The )^compensated frequency band input signals for the first frequency band (denoted4^,^to 4^,@^are combined by summation circuitry 600-1 to provide a compensated frequency band input signal 4^for the first frequency band. The compensated frequency band input signal 4^for the first frequency band is upsampled to a desired sampling rate for the multi-band system by upsampling circuitry 602-1 and upconverted to the desired frequency (e.g., a desired intermediate frequency that corresponds to the correct location in the frequency domain of the compensated frequency band input signal for the first frequency band within the multi-band system) by mixer 604-1. Likewise, for the second frequency band, the LUT based linearization system 600 includes multiple instances of the linearization system 500 of Figure 5 – one for each of )^memory taps, which are referenced in Figure 6 asLUT based linearization systems 500-1 to 500-M2 for the second frequency band. The)^ compensated frequency band input signals for the second frequency band (denotedas 4^,^to 4^,@^are combined by summation circuitry 600-2 to provide a compensated frequency band input signal 4^for the second frequency band. The compensated frequency band input signal 4^for the second frequency band is upsampled to a desired sampling rate for the multi-band system by upsampling circuitry 602-2 and upconverted to the desired frequency (e.g., a desired intermediate frequency that corresponds to the correct location in the frequency domain of the compensated frequency band inputsignal for the second frequency band within the multi-band system) by mixer 604-2. The resulting signals are combined by summation circuitry 606 to provide the compensated multi-band input signal, which may then be further processed by a wideband transmitter chain and ultimately transmitted.

[0082] Note that, for a complete expansion, in the mathematical sense, this would mean a summation K over as many vector combinations as there are entries in the LUT themselves. So, seemingly this would not actually mean any reduction in saved memory space, since again it would require N2cells in the 2D table to be stored. For a 16-bin entry 2D table, this would mean 256 cells. However, in reality, the degree of freedom when talking about non-linearity would be only in the order of about 7. Furthermore, the non-linearities usually only occur in terms of the odd-order terms. So, even if the non-linearity has an order of 7, there are only 3 terms to take care of. That means, in the 2D-case, this would require 3x2x16 = 96 cells, which would mean a 2.5x reduction in necessary storage size as compared to using a conventional multi-dimensional LUT based linearization system.

[0083] 3D-Formulation:

[0084] Likewise, for a 3D LUT or 3D linearization function, which would mean support for three frequency bands, the required number of LUT entries using a conventional 3D LUT would be 163= 4096 and, for a 4D (or 4 band) case (4D), the required number of LUT entries using a conventical 4D LUT would be 164= 65536 entries. But in a practical sense and with the same argument as above for the 2D case, the table size when using embodiments of the present disclosure would be in the order of 3x3x16 = 144 and 3x4x16 = 192 for the 3D and 4D case, respectively.

[0085] The 3D formulation can be expressed as follows: ^ ^

[0086] The output signals (i.e., the compensated frequency band input signals in the case of S-DPD) applying this linearizer on the three (baseband) frequency band input signals would then be: ^418 = ^18 ∙ ^ ^1^,^^|^18|^∙ ^1^,^^|^28|^∙ ^1^, / ^|^38|^(18)an a memory tap. In accordance with Equations (15) and (18) above, the LUT based linearization system 700 produces a compensation signal ^′^for the first frequency band and applies this compensation signal to the frequency band input signal ^^for the first frequency band to provide a compensated frequency band input signal 4^for the first frequency band. More specifically, as illustrated, for each value of ^ = 1, 2, … ^, frequency band input signals ^^, ^^, ^ / for the three frequency bands, or more specifically magnitudes of the frequency band input signals ^^, ^^, ^ / for the three frequency bands, are input into 1D LUTs ^1^,^^^^, ^1^,^^^^, and ^1^, / ^^^, respectively, which may be referenced herein as1D LUTs 702(k)(1), 702(k)(2), and 702(k)(3). The output signals from the 1D LUTs^1^,^^^^, ^1^,^^^^, and ^1^, / ^^^ are multiplied together via multiplier circuitry 704(k).The outputs of the K multiplier circuitries 704(1) to 704(K) are summed by summation circuitry 706 to provide the compensation signal ^′^for the first frequency band. This compensation signal ^′^for the first frequency band corresponds to the output of the desired 3-dimensional linearization function or 3-dimensional LUT that is directly modeled by the 1D LUT arrangement. The compensation signal ^′^for the first frequency band is then applied to the frequency band input signal ^^for the first frequency band via multiplier circuitry 708 to provide the compensated frequency band input signal 4^for the first frequency band.

[0088] Note that the complete linearization system for the three frequency bands would include LUT based linearization systems similar to that of Figure 7 for each of the three frequency bands. The resulting compensated frequency band input signals for thethree bands may be upsampled, upconverted to respective desired frequencies, and combined in a manner similar to that described above for the two frequency band case.

[0089] Comparison to 3-Band Non-Linearity:

[0090] To start with, let us say that the non-linearity follows a common baseband polynomial expansion: +^^^ = ^ ∙ ^B- + B^|^|^+ B^|^|C+ ⋯ ^ (21) Then, as an example, by defining a triple band signal configuration, consisting of band signals x1, x2, and x3, we have through expansion that: ^ = ^^∙ EFGH^+ ^^∙ EFGI^+ ^ / ∙ EFGJ^(22) Using this expansion in the general expression for the non-linear PA as above will give the following expansion for the various frequency bands: +^^^ = ^ ^B + B | |^ | |^ | |^ FGH^^ - ^K ^^ + 2   ^^ + 2   ^ / M^ ∙ E +will be simple combinations of intermodulation products falling on the main cardinal carrier frequencies ω1, ω2 and ω3. The analysis for more band combinations follows the same path: the main contribution to the Intermodulation (IM) in each band can be expressed quite generally as a multiplication of a multidimensional table times the complex signal at that specific frequency band. 4^= ^^∙ ^^^|^^|, |^^|, |^ / |, |^C|, ... ^ ∙ EFGH^(24) etc.,this can be written in base-band form as Equation (28) for dimension ^ ∈^1, ^^.@S4^^$^ = ^ ^^^$ − &^,R^R^^(28) ∙^^R^;^^^$ − ,^,R,^^;, ;^^^$ − ,^,R,^^;, … , ;^^^$ − ,^,R,^^;^where there^index, &^,Risthe data- ,^,R,^,^,R,^delays of all dimensions applicable to this dimension ^. Also ^^R^∙^is the ^-dimensional LUT for memory tap T for dimension ^.

[0092] For some of the following description, the simpler formulation and restriction to memory-less three dimensions is considered. However, the more general case is also described below.

[0093] Iterative algorithm for LUT adaptation

[0094] One can employ an iterative algorithm that extracts the Look-up Table entries directly, without any intermediate use of functions that would be interpolated at a later stage. The procedure that is suggested follows an alternate approach where the first LUT is updated first, and then the others follow while keeping the other LUTs constant.

[0095] Assume, for simplicity and understanding, dropping off the memory delay and using only a limited number of indices, that the correction for one particular output into a particular frequency range can simply be written down as: ^ ^∙ ^ ^ = Wsamples ^^in detail in section 2.7.1.6) and ^1^,^, ^1^,^and ^1^, / constitute thebeing used for dimension 1 with the interaction from itself and other dimensions. For the simplicity and clarification, the number of dimensions is kept being 3 at the moment, therefore we postulate 3 LUTs for this configuration. However, we need in general several (K) of these multiplications in the summation. The multiplication Operator ‘ ^’ represents the Hadamard product which describes a term-wise multiplication.

[0096] In order to solve this equation in a for example Gauss-Newton approach (combining LMS and Iterative adaption), we may start by inserting a small disturbance (△ ^1^) in one of the LUTs, let us say the first LUT T1 for specifically T11, while wekeep all the other LUTs fixed. Note that vector Y^is target and W^is the observation based on which we adapt the LUTs. ^ZU^∙△ ^1^,^^ ^1^,^^ ^1^, / [+^U^∙ ^1^,^^ ^1^,^^ ^1^, / = Y^(30)means means approach, we may extract △ ^1^as: △ ^1^,^= ^U^]U^^9^U^]∙ ^Y^− W^^ ⊘ ^1^,^⊘ ^1^, / (33)Note that U^]U^gives non-zero elements in the diagonal; therefore, inverting U^]U^is a simple operation.

[0098] In this formulation, we have focused on the LUT that is in the direction of the main signal (x1) dedicated to its specific frequency band or region or dimension. It is worthwhile to indicate the update procedure in one of the two other signal directions, for example for LUT T2 that takes care of the second dimension interaction to the first dimension. The solution is similar as described in Eqn. (33) △ ^1^,^= ^U^]U^^9^U^]∙ ^Y^− W^^ ⊘ ^1^,^⊘ ^1^, / (34)△ ^1^, / =^U^]U^^9^U^]∙^Y^− W^^⊘ ^1^,^⊘ ^1^,^(35) So the^1^,^← ^1^,^+ _ ∙△ ^1^,^(36)

[0100] In the same spirit, updating the other LUTs follows the same procedure: ^1^,`← ^1^,`+ _ ∙△ ^1^,` (37)^2^,`← ^2^,`+ _ ∙△ ^2^,`(38) ^3^,`← ^3^,`+ _ ∙△ ^3^,` (39)where ‘k’ indicates the polynomial order for the linearizer, ‘r’ indicates the dimension (or band) interacting with the main dimension including itself.

[0101] Extension to any dimensions:

[0102] Combining Equation (28) with Equation (1) and using ^ 1D-LUTs as described above, one can write as Equation (40).@S^ ^ 4^^$^ =^^^^$ − &^,R^∙^ ^^^R,^,a^;^a^$ − ,^,R,a^;^(40)basic structure still remains same as Equation (40), the scalars ^^^$^ and 4^^$^ are replaced by column vectors Y^and W^respectively containing block of samples, and theoutput of LUTs ^^R,^,a^∙^ by the complete table ^^R,^,a along with interpolation matrixU^,=S,b,c derived from ;^a^$ − ,^,R,a^;. Hence in matrix form one can write as Equation(41). ^ ^vector multiplication of its indexed vectors. The matrix Ua,=S,b,chas same number of rows as Y^,^bor dYa,=S,b,cd, and same number ofbins in the LUTs ^^R,^,a. The entries ofderived from;^a^$ − ,^,R,a^;and depends on the order of interpolation used.

[0104] For example, for zeroth order interpolation each row of Ua,=S,b,cwill containzeros except for the column f = g;hc^89=S,b,c^;i∙ ^, where it will1. The operation⌊∙⌋ is used to get the;^a^$ − ,^,R,a^;, and ^ is number of binsin the LUT ^^R,^,a.

[0105] As another example for 1storder interpolation matrix will contain all zeros in each row except two columns f =g;hc^89=S,b,c^;i∙ ^ and f + 1, where it will have ^1 − +^and + respectively where + = − − g;^a^$ − ,^,R,a^;i being the fractional part of the sample value.

[0106] Higher order interpolation will have more populated columns in each row, but usually the matrix Ua,=S,b,cis well known in the art of DPD and is sparse matrix.

[0107] As an optimization without any significant loss in performance, one can use higher order interpolation matrix for band ^ but use zeroth-order interpolation for all other bands o ≠ ^. In addition to that one can use = 1 in Equation (41). Usingthese and further dropping memory terms temporarily for sake of simplicity one can write Equation (41) as Equations (42) and (43). ^^W^ = Y^ ^ ^ ^ ^^Ua ∙ ^^^,a^(42)one LUT at a time. If there is correction for u^^LUT value ^^`,^for dimension ^, denoted by △ ^^`,^, so that target is Y^then Equation (430 can be re-written asEquation (44), where to reduce symbols, we have used U^v = ^Y^^U^^, and ^^^v,a= Ua∙^^^,a.^ ^^observable), one can write Equations (44) and (45) and solving for △ ^^^,^we will have Equation (46). ^ ^division (denoted by ⊘) used in eqn. (48).

[0111] ^(9^ æ vö ^^` ^ ^^^37 ),`,^(47). ^^`,^← ^^`,^+ _ △ ^^`,^ (47)Iterating through u and for all dimensions ^, one can converge to a solution linearizing the system.

[0113] Example Embodiments:

[0114] Figure 8 illustrates one example of a radio node 800 that includes a DPD actuator system 802 that uses a S-DPD architecture that utilizes LUT based linearization in accordance with embodiments of the present disclosure. As illustrated, the DPD system 802 includes multiple S-DPD actuators 804-1 through 804-B for B respective frequency bands (bands 1, 2, …, B), where B is greater than or equal to 2 but preferably greater than 2. As discussed below in detail, each S-DPD actuator 804-b (for the b-th frequency band) receives frequency band input signals (x1, …, xB) (i.e., complex baseband input signals) for the B frequency bands (or at least a subset of the input signals) and generates a compensated signal (i.e., a digitally predistorted signal) for the b-th frequency band based on the frequency band input signals (x1, …, xB) and a S-DPD actuator mechanism that utilizes a 1D LUT arrangement that directly models a desired P-dimensional LUT or P-dimensional linearization function, as described above. In this example, the compensated signals for the B frequency bands are processed by a radio unit 806 of the radio node 800 to provide an RF signal for transmission. Specifically, in this example, the compensated signals for the B frequency bands are digitally upconverted and combined by a digital upconverter 808 to provide a multi-band signal. The multi-band signal is converted to analog by an RF DAC 810, possibly further upconverted to a desired RF frequency (not shown), and amplified by a PA 812.

[0115] In this example, the S-DPD actuators 804-1 through 804-B, and more specifically the 1D LUTs utilized by the S-DPD actuators 804-1 through 804-B, are trained by a DPD adaptor 814 based on the frequency band input signals (x1, …, xB) and feedback signals for the B frequency bands received via a Transmit Observation Receiver (TOR) 816. In this example, the TOR 816 includes a RF ADC 818 coupled toan output of the PA 812 via a coupler 820 and a bandpass filter bank 822 that filters the output of the RF ADC 818 to provide the feedback signals (i.e., complex baseband feedback signals) for the B frequency bands. Note that both the radio front end 806 and the TOR 816 may include additional or alternative components that are not illustrated in Figure 8, as will be appreciated by those of ordinary skill in the art.

[0116] Figure 9 illustrates the b-th S-DPD actuator 804-b of Figure 8 in more detail, in accordance with one example embodiment of the present disclosure. As illustrated, the S-DPD actuator 804-b includes a 1D LUT arrangement 900 that directly models a desired P-dimensional LUT or P-dimensional linearization function for the b-th frequency band. In this example, the ^ input signals ^^, ^^,, … , ^^for the 1D LUT arrangement 900include ) different delayed versions of each of the frequency band input signals^^, ^^,, … , ^^ for the ^ frequency bands, where ) is the memory depth and is an integervalue that is greater than or equal to 1. Thus, the ^ input signals can be represented interms of the frequency band input signals as, e.g.,−− −, ^^, ormore specifically magnitudes of the input signals ^^, ^^,, … , ^^, are input into 1D LUTs^^,^,^^^^ to ^^,^,^^^^ for the -th frequency band, respectively, which may be referencedherein as 1D LUTs 902(b)(k)(1) to 902(b)(k)(P). The output signals from the 1D LUTs^^,^,^^^^ to ^^,^,^^^^ are multiplied together via multiplier circuitry 904(k). The outputsof the K multiplier circuitries 904(1) to 904(K) are summed by summation circuitry 906 to provide the compensation signal ^′^for the first frequency band. This compensation signal ^′^for the first frequency band corresponds to the output of the desired P- dimensional linearization function or P-dimensional LUT for the b-th frequency band that is directly modeled by the 1D LUT arrangement. The compensation signal ^′^for the first frequency band is then applied to the frequency band input signal ^^for the first frequency band via multiplier circuitry 908 to provide thefrequency band input signal 4^for the first frequency band.

[0117] It should be noted that the example embodiment of Figure 9 utilizes a slightly different architecture for considering memory effects as compared to that of Figure 6. In the example of Figure 6, each memory tap is considered separately (i.e., a separatecompensated signal is generated for the b-th frequency band for each of the M memory taps where these separate compensated signals are then combined to provide the compensated signal for the b-th frequency band). In contrast, in the example embodiment of Figure 9, the different memory taps are considered together within a single 1D LUT arrangement. Indeed, either architecture may be used for the S-DPD 804-b.

[0118] Figure 10 is a flow chart that illustrates the operation of the radio node 800 of Figure 8 in accordance with one embodiment of the present disclosure. Optional steps are represented by dashed lines. As illustrated, the radio node 800 obtains the frequency band input signals ^^, ^^,, … , ^^for the ^ frequency bands (step 1000). For each b-th frequency band, the DPD actuator system 802 generates a compensated, or predistorted, frequency band input signal 4^(steps 1002-1 to 1002-B). The compensated, or predistorted, frequency band input signals 4^for b=1,…,B may then be further processed by the radio node 800 (step 1004).

[0119] Figure 11 is a flow chart that illustrates an adaptation process by which values stored in the entries of the 1D LUTs in the 1D LUT arrangement (e.g., 1D LUT arrangement 900 of Figure 9) are determined and, if desired, updated over time, in accordance with one example embodiment of the present disclosure. Note that additional details regarding the adaptation process are described above. As illustrated, the 1D LUTs are initialized (e.g., initialized such that all entries in all of the LUTs are set to some predetermined initial value such as, e.g., “1”) (step 1100). A LUT index j is set to 1 (step 1102). Note that, in this example, the 1D LUTs are ordered in some predetermined order (e.g., first based on k, then based on memory index m, and then based on band index b) and associated to respective LUTs based on this ordering. So, j=1, …, ^ × ) × ^. Then, for a given input vector Y^= ^^, ^^, … , ^^containing samples of frequency band input signals ^^, ^^, … , ^^for a particular time instant, a corresponding observation vector W^is obtained via the TOR 816 (step 1102). In this example, the observation vector W^, contains resulting samples of the feedback signals for the ^ frequency bands obtained via the TOR 816.

[0120] The DPD adaptor 814 then computes a delta between the input vector Y^and the observation vector W^(step 1106) and updates the values stored in the j-th LUT based on the delta value (step 1108). In one embodiment, this update is performed according to Equation (36) above. If the j-th LUT is not the last LUT (step 1110, NO),the index j is incremented (step 1112) and the process returns to step 1104 and is repeated. Once the last LUT is reached (step 1110, YES), the DPD adaptor 814 determines whether one or more stopping criteria are satisfied (step 1114). The stopping criteria may include, e.g., a convergence criterion and / or a maximum number of repetitions of the adaptation process. If the one or more stopping criteria are not satisfied (step 1114, NO), the process returns to step 1102 and is repeated. Once the one or more stopping criteria are satisfied (step 1114, YES), the adaptation process ends. Beam-Domain DPD

[0121] Another example application of embodiments of the present disclosure (e.g., of the 1D LUT arrangement 102 of Figure 1) is beam-domain DPD in a radio node. In this regard, Figure 12 illustrates an example radio node 1200 including a beam domain DPD actuator system 1202 that utilizes 1D LUT arrangements in accordance with an embodiment of the present disclosure. As illustrated, the beam-domain DPD actuator system 1202 includes multiple beam-domain S-DPD actuators 1204-1 through 1204-D for D respective beam directions (beam directions 1, 2, …, D), where D is greater than or equal to 2 but preferably greater than 2. As discussed below in detail, each beam- domain S-DPD actuator 1204-d (for the d-th beam direction) receives beam domain input signals (x1, …, xD) (i.e., complex baseband input signals) for the D beam directions (or at least a subset of the input signals) and generates a compensated signal (i.e., a digitally predistorted signal) for the d-th beam direction based on the beam domain input signals (x1, …, xD) and a S-DPD actuator mechanism that utilizes a 1D LUT arrangement that directly models a desired P-dimensional LUT or P-dimensional linearization function, as described above. In this example, the compensated signals for the D beam directions are processed by a radio front end 1206 of the radio node 1200 to provide multiple RF signals for transmission via a multi-antenna system. Specifically, in this example, the compensated signals for the D beam directions are converted from the beam domain to the antenna domain by a beam-domain to antenna-domain converter 1208 to thereby provide separate input signals, in the antenna domain, for multiple transmit branches 1210-1 to 1210-T, where T is the number of transmit branches (also referred to as antenna branches). The transmit branches 1210-1 to 1210-T process (e.g., perform DAC, upconversion, amplification, etc.) the respectiveinput signals to output RF signals that are transmitted via respective antennas (not shown).

[0122] In this example, the beam-domain S-DPD actuators 1204-1 through 1204-D, and more specifically the 1D LUTs utilized by the S beam-domain S-DPD actuators 1204-1 through 1204-D, are trained by a DPD adaptor 1212 based on the beam domain band input signals (x1, …, xD) and feedback signals for the D beam directions obtained via TORs 1214-1 to 1214-T and antenna-domain to beam-domain converter 1216. In this example, the TORs 1214-1 to 1214-T are coupled to respective outputs of the transmit branches 1210-1 to 1210-T via couplers 1218-1 to 1218-T.

[0123] Figure 13 illustrates the d-th beam-domain SDP actuator 1204-d in accordance with one example embodiment of the present disclosure. Note that, in this example, both frequency bands and memory depth are illustrated; however, both are not required. In other words, the number of frequency bands ^ may be greater than or equal to 1, and the number of memory taps ) may be greater than or equal to 1. As illustrated, the input signals. As illustrated, the beam-domain S-DPD actuator 1204-d includes a 1D LUT arrangement 1300-b that directly models a desired ^ = ^ × ) dimensional LUT or ^ = ^ × ) dimensional linearization function for the b-th frequency band for the d-th beam direction.

[0124] For each b-th frequency band, the 1D LUT arrangement 1300-b receives a set of ^ input signals ^^, ^^,, … , ^^for the 1D LUT arrangement 1300-b that includes ) different delayed versions of each of the frequency band input signals ^^, ^^,, … , ^^for the d-th beam direction. Thus, the ^ input signals for the 1D LUT arrangement 1300-b can be represented in terms of the frequency band input signals for the d-th beamdirection as, e.g.,^^, ^^,, … , ^^ = ^^^^,^^^^$^, ^^,^,^$^, … , ^^,^^$^, … , ^^,^^$^, ^^,^,^$^, … , ^^,^^$^,^^,^^$ − 1^, ^^,^,^$ − 1^, … , ^^,^^$ − 1^, … , ^^,^^$ − 1^, ^^,^,^$ − 1^, … , ^^,^^$Then, as^^, ^^,, … , ^^, or more specifically magnitudes of the input signals ^^, ^^,, … , ^^, are inputinto 1D LUTs ^^,^,^,^^^^to ^^,^,^,^^^^for the -th frequencythe &-th beam direction, respectively, which may be referenced herein as 1D LUTs 1400(d)(b)(k)(1) to 1400(d)(b)(k)(P). The output signals from the 1D LUTs ^^,^,^,^^^^ to ^^,^,^,^^^^ aremultiplied together via multiplier circuitry 1402(k). The outputs of the K multiplier circuitries 1402(1) to 1404(K) are summed by summation circuitry 1404 to provide the compensation signal ^′^,^for the first frequency band for the &-th beam direction. This compensation signal ^′^,^for the first frequency band for the &-th beam direction corresponds to the output of the desired P-dimensional linearization function or P- dimensional LUT for the b-th frequency band for the d-th beam direction that is directlymodeled by the 1D LUT arrangement. Returning to Figure 13, the compensation signal^′^,^ for the first frequency band for the d-th beam direction is then applied to the beamdomain input signal ^^,^for the first frequency band for the d-th beam direction via multiplier circuitry 1302-b to provide the compensated frequency band input signal 4^,^for the first frequency band for the d-th beam direction. The compensated frequency band input signals 4^,^, … , 4^,^for the ^ frequency bands for the d-th beam direction are frequency shifted to the appropriate frequency locations and combined via frequency shift and combiner circuitry 1304 to provide the compensated beam domain input signal 4^for the d-th beam direction. PIM Compensation

[0125] Another example application of embodiments of the present disclosure (e.g., of the 1D LUT arrangement 102 of Figure 1) is Passive Inter-Modulation (PIM) compensation in receiver of a radio node. In this regard, Figure 15 illustrates an example radio node 1500 including a PIM compensator 1502 that utilizes one or more 1D LUT arrangements in accordance with an embodiment of the present disclosure. In this example, the radio node 1500 includes a radio front end 1504 including multiple transmit branches 1506-1 to 1506-T, where T is the number of transmit branches. The radio node 1500 also includes a receiver 1508. A (digital baseband) received signal that is output by the receiver 1508 suffers from distortion due to PIM resulting from the transmission of signals via the transmit branches 1506-1 to 1506-T and one or more PIM sources (e.g., cables between the transmit branches 1506-1 to 1506-T and associated antennas). The PIM compensator 1502 generates a PIM compensation signal that is applied to (e.g., subtracted from) the received signal so as to compensate for (e.g., cancel out or mitigate) the distortion in the received signal due to PIM.

[0126] The PIM compensator 1502 is, in this embodiment, a LUT based system that utilizes one or more 1D LUT arrangements to directly model associated P-dimensional LUTs. In this regard, Figure 16 illustrates one example embodiment of the PIM compensator 1502 in which the PIM compensator 1502 includes a 1D LUT arrangement 1600 that directly models a P-dimensional LUT for generating the PIM compensationsignal based on ^ input signals ^^, ^^,, … , ^^. In this example, the ^ input signals^^, ^^,, … , ^^ include (baseband digital) transmit input signals ^^, ^^,, … , ^! that are inputto the transmit branches 1506-1 to 1506-T and, optionally, one or more additionaldelayed versions of the transmit input signals ^^, ^^,, … , ^!. Thus, the ^ input signals^^, ^^,, … , ^^ for the 1D LUT arrangement 1600 are, in this example:^^, ^^,, … , ^^ = ^^^$^, ^^,^$^, … , ^!^$^, ^^^$ − 1^, ^^,^$ − 1^, … , ^!^$ − 1^, … , ^^^$^^, ^^,, … , ^^, or more specifically magnitudes of the input signals ^^, ^^,, … , ^^, are inputLUTs ^^,^^^^ to ^^,^^^^, respectively, which may be referenced herein as 1D LUTs 1602(k)(1) to 1602(k)(P). The output signals from the 1D LUTs ^^,^^^^ to ^^,^^^^ are multiplied together via multiplier circuitry 1604(k). The outputs of the K multiplier circuitries 1604(1) to 904(K) are summed by summation circuitry 1606 to provide the PIM compensation signal ^^^@. The compensation signal ^^^@is then applied to the received signal output by the receiver 1508 via a subtractor 1510 to provide a compensated receive signal, which may be further processed (e.g., via baseband processing).

[0128] Any appropriate steps, methods, features, functions, or benefits disclosed herein may be performed through one or more functional units or modules of one or more virtual apparatuses. Each virtual apparatus may comprise a number of these functional units. These functional units may be implemented via processing circuitry, which may include one or more microprocessor or microcontrollers, as well as other digital hardware, which may include Digital Signal Processors (DSPs), special-purpose digital logic, and the like. The processing circuitry may be configured to execute program code stored in memory, which may include one or several types of memory such as Read Only Memory (ROM), Random Access Memory (RAM), cache memory, flash memory devices, optical storage devices, etc. Program code stored in memoryincludes program instructions for executing one or more telecommunications and / or data communications protocols as well as instructions for carrying out one or more of the techniques described herein. In some implementations, the processing circuitry may be used to cause the respective functional unit to perform corresponding functions according to one or more embodiments of the present disclosure.

[0129] While processes in the figures may show a particular order of operations performed by certain embodiments of the present disclosure, it should be understood that such order is exemplary (e.g., alternative embodiments may perform the operations in a different order, combine certain operations, overlap certain operations, etc.).

[0130] Those skilled in the art will recognize improvements and modifications to the embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein.

Claims

Claims 1. A method of operation of a linearization system for a radio node for a wireless network, the method comprising: obtaining (200) a plurality of input signals (^^, …, ^^) for ^ input dimensions, respectively, for a ^-dimensional LUT for compensating for non-linear characteristics of one or more components of the radio node, wherein ^ is an integer value that is greater than 1; generating (202) a compensation signal based on the plurality of input signals (^^, …, ^^) and a plurality of 1-dimensional, 1-D, Look-Up Tables, LUTs, that directly model the ^-dimensional LUT; and applying (204) the compensation signal to a particular signal to provide a compensated signal for further processing by the radio node.

2. The method of claim 1, wherein the plurality of 1-D LUTs model the desired multi-dimensional LUT in accordance with: ^^… ^^^ =^ ^where^^^^, ^^, … , ^^^ is the P-dimensional LUT; and ^^,^^^^^ the 1-D LUT for ^th input signal for a ^^^summation where 1≤ ^ ≤ ^ and ^ is a predefined positive integer that is greater than or equal to 1.

3. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of a plurality of frequency band input signals (^^, …, ^^) for ^ frequency bands, respectively, wherein ^ = ^.

4. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: a plurality of frequency band input signals (^^, …, ^^) for ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1; andfor each frequency band input signal (^^) of the plurality of frequency band input signals (^^, …, ^^), one or more delayed versions of the frequency band input signal (^^).

5. The method of claim 3 or 4, wherein: the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P- dimensional LUT for one of the ^ frequency bands; the compensation signal generated based on the plurality of input signals (^^, …,^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is acompensation signal for the one of the ^ frequency bands; and applying the compensation signal to the particular signal comprises applying the compensation signal for the one of the ^ frequency bands to the frequency band input signal for the one of the ^ frequency bands to provide the compensated signal for the one of the ^ frequency bands.

6. The method of claim 5, further comprising: • for each additional frequency band of the ^ frequency bands: o generating a compensation signal for the additional frequency band based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1- D LUTs that directly model a ^-dimensional LUT for the additional frequency band for compensating for non-linear characteristics of one or more components of the radio node for the additional frequency band; and o applying the compensation signal for the additional frequency band to the frequency band input signal for the additional frequency band to provide a compensated frequency input signal for the additional frequency band; and • combining the compensated frequency band input signals for the ^ frequency bands to provide a final compensated input signal for further processing by the radio node.

7. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of a plurality of beam domain input signals (^^, …, ^^) for ^ beam directions, respectively, wherein ^ = ^.

8. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: a plurality of beam domain input signals (^^, …, ^^) for ^ beam directions, wherein ^ is an integer value that is greater than or equal to 1; and for each beam domain input signal (^^) of the plurality of beam domain input signals (^^, …, ^^), one or more delayed versions of the beam domain input signal (^^).

9. The method of claim 7 or 8, wherein: the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P- dimensional LUT for one of the ^ beam directions; the compensation signal generated based on the plurality of input signals (^^, …,^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is acompensation signal for the one of the ^ beam directions; and applying the compensation signal to the particular signal comprises applying the compensated signal for the one of the ^ beam directions to the beam domain input signal for the one of the ^ beam directions to provide the compensated signal for the one of the ^ beam directions.

10. The method of claim 9, further comprising: • for each additional beam direction of the ^ beam directions: o generating a compensation signal for the additional beam direction based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1- D LUTs that directly model a ^-dimensional LUT for the additional beam direction for compensating for non-linear characteristics of one or more components of the radio node for the additional beam direction; and o applying the compensation signal for the additional beam direction to the beam domain input signal for the additional beam direction to provide a compensated beam domain input signal for the additional beam direction.

11. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1: a plurality of beam domain input signals (^^,^, …, ^^,^) for ^ beam directions for each of the ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1.

12. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1: a plurality of beam domain input signals (^^,^, …, ^^,^) for ^ beam directions for each of the ^ frequency bands, wherein an integer value thatis greater than or equal to 1; and for each beam domain input signal (^^,^) of the plurality of beam domain input signals (^^,^, …, ^^,^) for each of the ^ frequency bands, one or more delayed versions of the beam domain input signal (^^,^).

13. The method of claim 11 or 12, wherein: the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P- dimensional LUT for one of the ^ beam directions for one of the ^ frequency bands; the compensation signal generated based on the plurality of input signals (^^, …,^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is acompensation signal for the one of the ^ beam directions for the one of the ^ frequency bands; and applying the compensation signal to the particular signal comprises applying the compensated signal for the one of the ^ beam directions for the one of the ^ frequency bands to the beam domain input signal for the one of the ^ beam directions for the one of the ^ frequency bands to provide the compensated signal for the one of the ^ beam directions for the one of the ^ frequency bands.

14. The method of claim 13 further comprising: • for each additional frequency band of the ^ frequency bands: o generating a compensation signal for the one of the ^ beam directions for the additional frequency band based on the plurality of input signals (^^, …, ^^) and an additional plurality of 1-D LUTs that directly model a ^- dimensional LUT for the one of the ^ beam directions for the additional frequency band for compensating for non-linear characteristics of one or more components of the radio node for the one of the ^ beam directions for the additional frequency band; and o applying the compensation signal for the one of the ^ beam directions for the additional frequency band to the input signal for the one of the ^ beam directions for the additional frequency band to provide a compensated signal for the one of the ^ beam directions for the additional frequency band; and •combining the compensated signals for the one of the ^ beam directions for the^frequency bands to provide a compensated signal for the one of the ^ beamdirections for further processing by the radio node.

15. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of a plurality of transmit branch input signals (^^, …, ^!) for ^ transmit branches of the radio node, respectively, wherein ^ = ^.

16. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: a plurality of transmit branch input signals (^^, …, ^!) for ^ transmit branches of the radio node, respectively, wherein ^ is an integer value that is greater than or equal to 1; and for each transmit branch input signal (^^) of the plurality of transmit branch input signals (^^, …, ^!), one or more delayed versions of the transmit branch input signal (^^).

17. The method of claim 15 or 16, wherein:the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P- dimensional LUT for generating a Passive Inter-Modulation, PIM, compensation signal for a receiver of the radio node; the compensation signal generated based on the plurality of input signals (^^, …,^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is a PIMcompensation signal; and applying the compensation signal to the particular signal comprises applying the compensated signal to a received signal received via the receiver of the radio node to provide a compensated receive signal as the compensated signal.

18. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1: a plurality of transmit branch input signals (^^,^, …, ^^,!) for ^ transmit branches of the radio node for each of the ^ frequency bands, wherein ^ =^× ^.

19. The method of claim 1 or 2, wherein the plurality of input signals (^^, …, ^^) consist of: for each -th frequency band of ^ frequency bands wherein ^ is an integer value that is greater than 1: a plurality of transmit branch input signals (^^,^, …, ^^,!) for ^ transmit branches of the radio node for each of the ^ frequency bands, wherein ^ is an integer value that is greater than or equal to 1; and for each transmit branch input signal (^^,^) of the plurality of transmit branch input signals (^^,^, …, ^^,!) for eachthe ^ frequency bands, one or more delayed versions of the transmit branch input signal (^^,!< / sub>).

20. The method of claim 18 or 19, wherein:the ^-dimensional LUT directly modeled by the plurality of 1-D LUTs is a P- dimensional LUT for generating a Passive Inter-Modulation, PIM, compensation signal for a receiver of the radio node; the compensation signal generated based on the plurality of input signals (^^, …,^^) and the plurality of 1-D LUTs that directly model the ^-dimensional LUT is a PIMcompensation signal for a receiver of the radio node; and applying the compensation signal to the particular signal comprises applying the PIM compensation signal to a received signal received via the receiver of the radio node.

21. The method of any of claims 1 to 20, further comprising performing an adaptation procedure whereby values stored by the plurality of LUTs are updated.

22. The method of any of claims 1 to 20, further comprising, for each 1-D LUT of the plurality of 1-D LUTs: obtaining (1104) an observation vector (Yi) comprising observed samples of an output signal transmitted by the radio node that correspond to a given input vector comprising samples of the plurality of input signals (^^, …, ^^); computing (1106) a delta vector for the 1-D LUT based on a difference between the given input vector (Xi) and the observation vector (Yi); and updating (1108) the 1-D LUT based on the delta vector.

23. The method of claim 22, further comprising performing (1102-1114) a plurality of iterations of the steps of, for each 1-D LUT of the plurality of 1-D LUTs, obtaining (1104) an observation vector (Yi), computing (1106) a delta vector, and updating (1108) the 1-D LUT.

24. A linearization system for a radio node for a wireless network, the digital predistortion actuator system comprising: • an actuator system adapted to: o obtain a plurality of input signals (^^, …, ^^) for ^ input dimensions, respectively, for a ^-dimensional LUT for compensating for non-linearcharacteristics of one or more components of the radio node, wherein ^ is an integer value that is greater than 1; o generate a compensation signal based on the plurality of input signals (^^, …, ^^) and a plurality of 1-dimensional, 1-D, Look-Up Tables, LUTs, that directly model the ^-dimensional LUT; and o apply the compensation signal to a particular signal to provide a compensated signal for further processing by the radio node.

25. The linearization system of claim 24, wherein the plurality of 1-D LUTs model the desired multi-dimensional LUT in accordance with: ^^^^^^, ^^, … , ^^^ = ^ ^ ^^,^^^^^ where^^^^, ^^, … , ^^^is the P-dimensional LUT; and ^^,^^^^^the 1-D LUT for ^th input signal for a ^^^summation where 1≤ ^ ≤ ^ and ^ is a predefined positive integer that is greater than or equal to 1.

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