PRACTICAL PREDISTORTION ARCHITECTURES FOR MULTIBAND RADIOS

Systems and methods for separate digital predistortion (S-DPD) for multi-band radios are disclosed. In one embodiment, a method of operation of a digital predistortion (DPD) actuator system for a radio node for a wireless network comprises receiving a plurality of input signals (x1, . . . , xB) for a plurality of frequency bands (b1, . . . , bB), respectively. The method further comprises, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating a plurality of predistorted signals for the frequency band (bl) based on the plurality of input signals (x1, . . . , xB) and a plurality of Look-Up Tables (LUTs) each having less than B dimensions and combining the plurality of predistorted signals for the frequency band (bl) to provide a combined predistorted signal for the frequency band (bl). In this manner, lower dimensionality LUTs are used, which in turn reduces cost and complexity of the DPD system.

TECHNICAL FIELD

The present disclosure relates to digital predistortion (DPD) for multiband radios.

BACKGROUND

For a wideband High-Power Amplifier (HPA) with Instantaneous Bandwidth (IBW) of, e.g., 1 Gigahertz (GHz) or above, it has been observed that traditional Lookup Table (LUT) based methods for linearization are excessively costly because of higher sample rate requirements. It has been observed that Peven with higher sample rates, LUT based methods for linearization are unable to reach the desired Adjacent Channel Leakage Ratio (ACLR) performance. Separate Digital Predistortion (S-DPD), which is also known as frequency selective Digital Predistortion (DPD), treats each linearization region separately. S-DPD not only offers low sample rate operations but also can reach desired ACLR performance levels. One example of S-DPD is described in U.S. Pat. No. 8,750,410 B2 (hereinafter referred to as “the '410 Patent”).

The basic idea of S-DPD is to formulate a multivariate Generalized Memory Polynomial (GMP) or just Memory Polynomial (MP) for each linearization region and estimate corresponding coefficients independently. Typically, each linearization region covers a transmission frequency band. As such, the terms linearization region and frequency band are used interchangeably herein. After estimating the coefficients for the linearization regions, a portion of each of the S-DPD polynomials can be quantized to a multidimensional LUT. This is usually done by forming either a uniform or non-uniform multidimensional grid of points over the range of inputs, followed by evaluation of the S-DPD polynomials at the grid points. These evaluated points are stored as LUT outputs for each combination of inputs. Using the multidimensional LUT for the S-DPD actuator (or DPD forward calculation) makes it much faster and economical compared to evaluating the polynomial. This approach is known as hybrid LUTs and has proven a cost-effective solution for multiband implementation (see, e.g., Christophe Quindroit, Naveen Naraharisetti, Patrick Roblin, Shahin Gheitanchi, Volker Mauer, Mike Fitton, “FPGA Implementation of Orthogonal 2D Digital Predistortion System for Concurrent Dual-Band Power Amplifiers Based on Time-Division Multiplexing”, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 12, December 2013, p. 4591-4599, which is hereinafter referred to as the “Quindroit Paper”). For instance, a triple band system will have a 3-dimensional hybrid LUT for each of its bands.

The main drawback of S-DPD for linearization is scalability in terms of computational complexity. Dual-band systems are still manageable, and triple-band systems can be built by coalescing two bands into one if they are near in frequency and essentially treating the triple-band system as dual-band system. However, this band reduction fails if the combined bands are not near and for systems with more than three frequency bands. Evaluation of very a high order polynomial soon becomes equally expensive as traditional LUT methods with more than two bands. In addition, though a multidimensional LUT provides a very fast computational alternative to evaluate a polynomial, the memory requirements soon become unmanageable from three frequency bands onwards.

In this regard, the '410 Patent discloses a multi-band power amplifier digital predistortion system that uses a S-DPD architecture. However, this multiband power amplifier digital predistortion system uses the product of two band inputs (see Equations 4-6 of the '410 Patent). As a result, this multiband power amplifier digital predistortion system requires B-dimensional LUTs to support B frequency bands. Again, while such multidimensional LUTs provide a very fast computational alternative to evaluate a polynomial, the memory requirements soon become unmanageable as B increases beyond 2.

U.S. Pat. No. 8,948,301 B2 (hereinafter referred to as “the '301 Patent”) discloses a DPD system that works on radio frequency (RF) signals and, as such, requires a high sampling rate. Further, this DPD system also requires B-dimensional LUTs to support B frequency bands, which may result in unmanageable memory requirements as B increases beyond 2.

SUMMARY

Systems and methods for reduced dimensionality separate digital predistortion (S-DPD) for multi-band radios are disclosed. In one embodiment, a method of operation of a digital predistortion (DPD) actuator system for a radio node for a wireless network comprises receiving a plurality of input signals (x1, . . . , xB) for a plurality of frequency bands (b1, . . . , bB), respectively. The method further comprises, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating a plurality of predistorted signals for the frequency band (bl) based on the plurality of input signals (x1, . . . , xB) and a plurality of Look-Up Tables (LUTs) each having less than B dimensions and combining the plurality of predistorted signals for the frequency band (bl) to provide a combined predistorted signal for the frequency band (bl). In this manner, lower dimensionality LUTs are used as compared to traditional S-DPD, which in turn reduces cost and complexity of the DPD system.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of at least one combination of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of at least two combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating (1002) a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of at least one combination of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of at least two combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, generating a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), the at least a subset of the set of values {q, q+1, . . . , B−2} consists of at least one value from the set of values {q, q+1, . . . , B−2}. In another embodiment, for at least one frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), the at least a subset of the set of values {q, q+1, . . . , B−2} consists of at least two values from the set of values {q, q+1, . . . , B−2}. In another embodiment, for at least one frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), the at least a subset of the set of values {q, q+1, . . . , B−2} consists of all values from the set of values {q, q+1, . . . , B−2}.

In one embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is different for at least two of the plurality of frequency bands (b1, . . . , bB). In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is the same for all of the plurality of frequency bands (b1, . . . , bB).

In one embodiment, for at least one frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) further comprises generating a predistorted signal for the frequency band (bl) in a manner that takes into account only a single frequency band at a time.

In one embodiment, for at least one frequency band (bl) of the plurality of frequency bands (b1, . . . , bB), generating the plurality of predistorted signals for the frequency band (bl) further comprises generating a predistorted signal for the frequency band (bl) based on a summation of magnitudes of the plurality of input signals (x1, . . . , xB) for the plurality of frequency bands (b1, . . . , bB) and a single-dimension LUT for the frequency band (bl).

Corresponding embodiments of a DPD actuator system for a radio node for a wireless network comprises a plurality of S-DPD actuators for a plurality of frequency bands (b1, . . . , bB), respectively. Each S-DPD actuator of the plurality of S-DPD actuators is configured to: receive a plurality of input signals (x1, . . . , xB) for the plurality of frequency bands (b1, . . . , bB), respectively; generate a plurality of predistorted signals for a frequency band (bl) of the plurality of frequency bands (b1, . . . , bB) based on the plurality of input signals (x1, . . . , xB) and a plurality of LUTs each having less than B dimensions; and combine the plurality of predistorted signals for the frequency band (bl) to provide a combined predistorted signal for the frequency band (bl).

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of at least one combination of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of at least two combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) input signals for a set of frequency band combinations that consists of all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of at least one combination of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of at least two combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, each S-DPD actuator of the plurality of S-DPD actuators comprises, for each value of r from at least a subset of a set of values {q, q+1, . . . , B−2} where 1≤q≤B−2, a sub-DPD actuator configured to generate a predistorted input signal for the frequency band (bl) for the value of r, based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations.

In one embodiment, for each S-DPD actuator of the plurality of S-DPD actuators, the at least a subset of the set of values {q, q+1, . . . , B−2} consists of at least one value from the set of values {q, q+1, . . . , B−2}. In another embodiment, for each S-DPD actuator of the plurality of S-DPD actuators, the at least a subset of the set of values {q, q+1, . . . , B−2} consists of at least two values from the set of values {q, q+1, . . . , B−2}. In another embodiment, for each S-DPD actuator of the plurality of S-DPD actuators, the at least a subset of the set of values {q, q+1, . . . , B−2} consists of all values from the set of values {q, q+1, . . . , B−2}.

In one embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is different for at least two of the plurality of frequency bands (b1, . . . , bB). In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is the same for all of the plurality of frequency bands (b1, . . . , bB).

In one embodiment, for at least one S-DPD actuator of the plurality of S-DPD actuators, the at least one S-DPD actuator further comprises a sub-DPD actuator configured to generate a predistorted signal for the frequency band (bl) in a manner that takes into account only a single frequency band at a time.

In one embodiment, for at least one S-DPD actuator of the plurality of S-DPD actuators, the at least one S-DPD actuator further comprises a sub-DPD actuator configured to generate a predistorted signal for the frequency band (bl) based on a summation of magnitudes of the plurality of input signals for the plurality of frequency bands (b1, . . . , bB) and a single-dimension LUT for the frequency band (bl).

DETAILED DESCRIPTION

Systems and methods are disclosed herein that provide an effective Separate Digital Predistortion (S-DPD) architecture for a multiband system. Embodiments of the present disclosure provide a S-DPD system that utilizes reduced dimensionality hybrid Lookup Tables (LUT). In one embodiment, a S-DPD system is provided that uses B−q dimensional hybrid LUTs, where q={1, 2, . . . , B−2}. In another embodiment, a S-DPD system is provided that uses one-dimensional hybrid LUTs. In both embodiments, a summation over several lower dimension hybrid LUTs it utilized to provide the desired predistorted signal. Depending on the desired performance of linearization and available resources, one can choose between two options with lower dimensions by using the proposed architectures. The main advantage of lower dimensionality LUTs is cost and power.

Before describing embodiments of the present disclosure, it is beneficial to first describe a traditional S-DPD. In this regard,FIG.1illustrates a radio node100that includes a DPD system102that uses a traditional S-DPD architecture. As illustrated, the DPD system102includes multiple S-DPD actuators104-1through104-B for B respective frequency bands (b1, . . . , bB), where B is greater than or equal to 2. As discussed below in detail, each S-DPD actuator104-l(for the l-th frequency band) receives input signals (x1, . . . , xB) (i.e., complex baseband input signals) for the B frequency bands and generates a predistorted signal for the l-th frequency band based on the received input signals (x1, . . . , xB) and a S-DPD actuator mechanism (e.g., memory polynomial or LUT scheme). In this example, the predistorted signals for the B frequency bands are processed by a radio unit106of the radio unit100to provide a radio frequency (RF) signal for transmission. Specifically, in this example, the predistorted signals for the B frequency bands a digitally upconverted by a digital upconverter108, converted to analog by an RF digital-to-analog converter (DAC)110, and amplified by a power amplifier (PA)112.

As will be appreciated by those of skill in the art, the S-DPD actuators104-1through104-B are trained by a DPD adaptor114based on the input signals (x1, . . . , xB) and feedback signals for the B frequency bands received via a radio transmit observation receiver (TOR)116. In this example, the TOR116includes a RF analog-to-digital converter (ADC)118coupled to an output of the PA112via a coupler120and a bandpass filter bank122that filters the output of the RF ADC118to provide the feedback signals (i.e., complex baseband feedback signals) for the B frequency bands. Note that both the radio front end106and the TOR116may include additional or alternative component that are not illustrated inFIG.1, as will be appreciated by those of ordinary skill in the art.

The operation of the S-DPD actuators104-1through104-B is described below in terms of a memory polynomial (MP); however, one can easily extend the formulation for different variants of Volterra series such as a Generalized Memory Polynomial (GMP). Let us use xl(n) to represent input signals (i.e., input samples), where l∈ (1, B) represents the frequency band index. The output signal (i.e., output samples) from the l-th S-DPD104-lis denoted by zl(n). Note that n refers to a time-index. The maximum non-linear order of the S-DPD104-lis denoted by P. Memory taps are denoted by the set={Q0, Q1, Q2, . . . QM} with Q0=0. The cardinality ofis M+1.

The output from the S-DPD actuator104-lcan be written as in Equation (1).

Here, αl,m,p1,p2, . . . ,pBrefers to the S-DPD coefficients and p1=(0,(P−1)), with the restriction pb+1∈(0, pb) and pB+1=0. Equation (1) captures that the non-linear modelling of the inverse of the PA112(i.e., the predistortion) can be performed by considering the current and past samples. Past samples are included because of memory effects inherent in electronic devices. The nonlinearity of the PA112creates intermodulation frequencies and that is modelled by the B multiplicative terms and exponents pbin Equation (1). When memory and non-linearities are both absent, Equation (1) becomes simpler i.e., zl(n)=xl(n). Please note that there are B S-DPD actuators104-1through104-B, and the description of the l-th S-DPD actuator104-lis applicable of the S-DPD actuators104-1through104-B.

As known to those of ordinary skill in the art, the DPD adaptor114can use the least square or other adaptive methods to identify S-DPD coefficients. In the S-DPD actuators104-1through104-B, one can use either polynomial based approach as in the Equation (1) or use variants of a LUT based approach as described below.

There are several LUT based approaches that can be possible. One option is to use a traditional LUT both in both the DPD adaptor14and the S-DPD actuators104-1through104-B. This technique is well known. However, this technique is cumbersome when there are more than two frequency bands (i.e., when B>2), especially in the S-DPD actuators104-1through104-B because of the excessive amount of memory required for storing multi-dimensional LUTs. Here, a hybrid LUT approach is considered, which is best suitable for the multiband case. The hybrid LUT architecture for the S-DPD actuator104-lis illustrated inFIG.2. As can be seen fromFIG.2, Equation (1) is precomputed at various points of the complete range of input signals and the results are stored in the dynamic memory of the hardware; hence, the S-DPD actuator104-lrequires a lower number of computations on the fly.

As shown inFIG.2, there are M+1 hybrid LUTs for the S-DPD actuator104-l,each considering B-inputs that are {|x1|, |x2|, . . . , |xB|} and assuming the range of |xl| is divided into K parts. The division can be done taking statistical distribution of |xl| into consideration, like using usual companding methods such as, e.g., A-law or Mu-law used to compress a large dynamic range to more practical limits, or can be done uniformly in which case the size of each interval would be

The size of each hybrid LUT is KB, and there are M+1 hybrid LUTs corresponding to the memory taps for each l-th band.FIG.3illustrates an example of the hybrid LUT architecture ofFIG.2in which there is a single hybrid LUT for a triple band case without memory taps (i.e., M=0).

As can be seen fromFIGS.2and3, when using the hybrid LUT architecture, the memory requirements of the hybrid LUTs used by the S-DPD104-lbecomes large as the number of frequency bands increases beyond 2. Systems and methods are disclosed herein that enable S-DPD using reduced dimensionality hybrid LUTs. In this regard,FIGS.4A and4Billustrate an example of a radio node400that includes a DPD actuator system402that uses a S-DPD architecture with reduced dimensionality hybrid LUTs in accordance with embodiments of the present disclosure.

As illustrated, the DPD system402includes multiple S-DPD actuators404-1through404-B for B respective frequency bands (b1, . . . , bB), where B is greater than or equal to 2 but preferably greater than 2. As discussed below in detail, each S-DPD actuator404-l(for the l-th frequency band) receives 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 predistorted signal for the l-th frequency band based on the received input signals (x1, . . . , xB) and a S-DPD actuator mechanism that utilizes reduced dimensionality hybrid LUTs. In this example, the predistorted signals for the B frequency bands are processed by a radio unit406of the radio unit400to provide a RF signal for transmission. Specifically, in this example, the predistorted signals for the B frequency bands a digitally upconverted by a digital upconverter408, converted to analog by an RF DAC410, and amplified by a PA412.

In this example, the S-DPD actuators404-1through404-B, and more specifically the reduced-dimensionality LUTs utilized by the S-DPD actuators404-1through404-B, are trained by a DPD adaptor414based on the input signals (x1, . . . , xB) and feedback signals for the B frequency bands received via a TOR416. In this example, the TOR416includes a RF ADC418coupled to an output of the PA412via a coupler420and a bandpass filter bank422that filters the output of the RF ADC418to provide the feedback signals (i.e., complex baseband feedback signals) for the B frequency bands. Note that both the radio front end406and the TOR416may include additional or alternative component that are not illustrated inFIG.4, as will be appreciated by those of ordinary skill in the art.

The operation of the S-DPD actuators404-1through404-B is described below in terms of a memory polynomial (MP); however, one can easily extend the formulation for different variants of Volterra series such as a Generalized Memory Polynomial (GMP). Let us use xl(n) to represent input signals (i.e., input samples), where l∈(1, B) represents the frequency band index. The output signal (i.e., output samples) from the l-th S-DPD404-lis denoted by zl(n). Note that n refers to a time-index. The maximum non-linear order of the S-DPD404-lis denoted by P. Memory taps are denoted by the set={Q0, Q1, Q2, . . . QM} with Q0=0. The cardinality ofis M+1. The output from the S-DPD actuator404-lcan be written as in Equation (1). However, as discussed below, the S-DPD actuator404-ldecomposes the B-dimensional LUT problem into the summation of multiple lower-dimensional LUT problems.

In one embodiment, the S-DPD actuators404-1through404-B perform digital predistortion based on a S-DPD scheme that uses B−q dimensional hybrid LUTs. This S-DPD scheme is also referred to herein as B−q dimensional S-DPD. The B−q dimensional S-DPD reduces the size of the hybrid LUTs from B-dimensions to B−q dimensions, where q={1, 2, . . . , B−2}. In this regard,FIG.4Billustrates one embodiment of the l-th S-DPD actuator404-l.Unlike in traditional S-DPD, the S-DPD actuator404-lincludes several low-dimensional DPD actuators, which are referred to herein as “sub-DPD actuators”. In other words, the conventional B-dimensional hybrid LUT problem is decomposed into the summation of multiple lower-dimensional hybrid LUT problems. These lower-dimensional hybrid LUT problems include, as described below, one or more B−q dimensional hybrid LUT problems. One advantage of this approach as compared to the tensor product approach described in the Quindroit Paper is that the predistorted output signals from the sub-DPDs are added, instead of multiplied. As such, the proposed S-DPD architecture significantly reduces the computational cost in the S-DPD actuator404-l.

As illustrated inFIG.4B, the S-DPD actuator404-l(i.e., the S-DPD actuator for the l-th frequency band) includes a sub-DPD actuator424-lthat takes into account a single frequency band at a time. The S-DPD actuator404-lalso includes multiple sub-DPD actuators for different numbers of two or more frequency bands, which are denoted generally as sub-DPD actuators426-l-(B−r), where the values of r are the values in the set {q, q+1, . . . , B−2}. Thus, in this example, the sub-DPD actuators426-l-(B−r) include a sub-DPD actuator426-l-(B−q) for B−q frequency bands, a sub-DPD actuator426-l-(B−q−1) for B−q−1 frequency bands, . . . , and sub-DPD actuator426-l-(2). In addition, the S-DPD actuator404-lincludes a sub-DPD actuator428-lfor an envelope of input signals. Note that the sub-DPD actuators424-land428-lare optional. Also note that not all of the sub-DPD actuators426-l-(B−r) are required. The S-DPD actuator404-lincludes the sub-DPD actuator(s)426-l-(B−r) for at least one, at least two, or all values of r from the set {q, q+1, . . . , B−2}, where q is a value in the range of and including 1 to B−2. The details of each of the sub-DPD actuators424-l,426-l-(B−r), and428-lare described. The predistorted signals output by the sub-DPD actuators424-l,426-l-(B−r), and428-lare combined (e.g., summed) by combiner430to provide a combined predistorted output signal output by the S-DPD404-l.

The sub-DPD actuator424-lonly takes into account one frequency band at a time. The predistorted output signal fl(i)(n) output from the sub-DPD actuator424-lcan be written as follows:

As can be seen from Equation (2), the sub-DPD actuator424-lonly considers one frequency band input xb(n−Qm) when constructing the basis function along with the input xl(n) from l-th frequency band. A hybrid LUT500-lfor the sub-DPD actuator424-lfor one memory tap is shown inFIG.5. As clear fromFIG.5, hybrid LUT500-lin the sub-DPD actuator424-lis a one-dimensional LUT (i.e., it works on one dimension, i.e., one input signal). For the l-th frequency band, there are (M+1) hybrid LUTs500-l,one for each of the memory taps.

The sub-DPD actuator428-lworks on the worst-case envelope i.e., the summation of the magnitudes of the input signals from all B frequency bands. The predistorted signal fl(e)(n) output from the sub-DPD actuator428-lcan be expressed as follows:

FIG.6illustrates a hybrid LUT600-lfor the sub-DPD actuator428-l.While not illustrated, note that, for the l-th frequency band, there are M+1 hybrid LUTs600-l,one for each memory tap. As can be seen inFIG.6, the hybrid LUT600-lfor the sub-DPD actuator428-lis a one-dimensional LUT. Note that the resolution of the LUT600-lis shown the same as before, i.e. K, however, the resolution of the LUT600-lcan be a value other than K.

For the sub-DPD actuators426-l-(B−r), there are r={q, q+1, . . . , B−2} sub-DPD actuators426-l-(B−r) on one example embodiment, one for each value of r. Let us use={1, 2, . . . B} to denote the set of all band indices. The sub-DPD actuator426-l-(B−r) uses a subset of frequency bands to construct the basis functions for the predistortion.

denotes the superset containing setskof all the combinations of B−r frequency bands from the B frequency bangs, where

is a binomial coefficient (i.e., denotes the number of combinations of B−r frequency bands that can be created from the set of B frequency bands). In other words, a setkis drawn fromchoosing B−r elements ork⊂. For instance, when there are three bands, B=3, q=1 one can only have r={1}. In this case, B−r=2 then1={{1, 2}, {1, 3}, {2, 3}}. When B=4, q=1, one can have r={1,2}. So, there are two possibilities i.e., i) B−r=3,1={{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}; ii) B−r=2,2={{1, 2}{1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}. Similarly, when B=4, q=2, one can have r={2} which leads to only one possibility i.e., B−r=2,1={{1, 2}{1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}. Using the defined set notation, the output from the sub-DPD actuator426-l-(B−r) for a particular value of r can be expressed as follows:

A hybrid LUT system700-lfor the sub-DPD actuator426-l-(B−r) for a particular value of r for an example case of triple band (i.e., B=3, q+1, and r=1) is illustrated inFIG.7. In this case, for the l-th frequency band, there are

for the sub-DPD actuator426-l-(B−r), for each memory tap. Thus, using the hybrid LUTs702-l-1to

for the sub-DPD actuator426-l-(B−r) for M+1 memory taps, the output sample of the sub-DPD actuator426-l-(B−r) can be expressed mathematically as:

where LUT1 is the output of the hybrid LUT702-l-1for first frequency band combination, LUT2 is the output of the hybrid LUT702-l-2for the second frequency band combination, and LUT3 is the output of the hybrid LUT702-l-3for the third frequency band combination. As shown inFIG.7, the sub-DPD actuator426-l-(B−r) takes a maximum of B−q dimension input signals (i.e., each hybrid LUT702-1is a B−q dimensional LUT). This proposed architecture is referred to herein as (B−q) dimensional S-DPD.

The description above relates to a (B−q) dimensional S-DPD. Now, an embodiment referred to herein as a one-dimensional S-DPD will be described. For the one-dimensional S-DPD, each of the sub-DPD actuators426-l-(B−r) considers one-dimension input signals. More specifically, for one-dimensional S-DPD, the sub-DPD actuators424-land428-lare the same as described above. However, the sub-DPD actuators426-l-(B−r) operate differently as compared to the (B−r) dimensional S-DPD described above.

For one-dimensional S-DPD, to capture the dependency of different frequency bands in predistorted signal output by the S-DPD actuator404-1output, the sub-DPD actuators426-l-(B−r) operate based on the summation of the magnitudes of the input signals coming from different frequency bands instead of multiplications as in the proposed B−q dimensional S-DPD described above. Thus, for one-dimensional S-DPD, the predistorted signal fl(B−r,e)(n) output by the sub-DPD actuator426-l-(B−r) for a given value of r can be expressed as follows:

Here, the definition ofrandkremains the same as described above. A hybrid LUT system800-lfor the sub-DPD actuator426-l-(B−r) for a given value of r for an example case of triple band (i.e., B=3, q=1, r=1) is illustrated inFIG.8. In this case, for the m-th memory tap, there are

for the sub-DPD actuator426-l-(B−r). Thus, using the hybrid LUTs800-l-1to

for the sub-DPD actuator426-l-(B−r) for M+1 memory taps, the output sample of the sub-DPD actuator426-l-(B−r) can be expressed mathematically as:

where LUT1 is the output of the hybrid LUT802-l-1for first frequency band combination, LUT2 is the output of the hybrid LUT802-l-2for the second frequency band combination, and LUT3 is the output of the hybrid LUT802-l-3for the third frequency band combination. As shown inFIG.8, the sub-DPD actuator426-l-(B−r) takes a maximum of one dimension input signals. In other words, each of the hybrid LUTs802-lis a one-dimensional LUT that is indexed by a sum of the input signals for the respective combination of B−r frequency bands.

FIG.9is a flow chart that illustrates the operation of the DPD actuator system402in accordance with embodiments of the present disclosure. As illustrated, the DPD actuator system402receives B input signals (x1, . . . , xB) for B frequency bands (b1, . . . , bB), respectively (step900). For each frequency band (bl) of the B frequency bands (b1, . . . , bB), the S-DPD404-lfor the frequency band (bl) generates multiple predistorted signals for the frequency band (bl) based on the input signals (x1, . . . , xB) and a multiple LUTs, each having less than B dimensions (step902-l) and combines those predistorted signals for the frequency band (bl) to provide a combined predistorted signal for the frequency band (bl) (step904-l).

FIG.10is a flow chart that illustrates details of step902-lfor the l-th frequency band (bl) in accordance with the (B−q) dimensional S-DPD scheme described above. Optional steps are represented by dashed lines/boxes. Note that while the steps ofFIG.10are shown as being performed in sequential order, some or all of the steps may be performed in parallel. As illustrated, the S-DPD actuator404-l,and more specifically the sub-DPD actuator424-l,for the frequency band (bl) may generate a predistorted signal for the frequency band (bl) in a manner that takes into consideration only a single frequency band at a time (step1000). Here, the details described above for the sub-DPD actuator424-lare applicable.

For each value of r from at least a subset of a set of values {q, q+1, . . . , B−2}, the S-DPD actuator404-l,and more specifically the sub-DPD actuator(s)426-l-(B−r) for the value of r, for the frequency band (bl) generates a predistorted signal based on: (a) input signals for a set of frequency band combinations that consists of at least one combination, at least two combinations, or all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a B−r dimension LUT for each frequency band combination in the set of frequency band combinations (step1002). In one embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is a single value from the set of values {q, q+1, . . . , B−2}. In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is at least two values from the set of values {q, q+1, . . . , B−2}. In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is all of the set of values {q, q+1, . . . , B−2}. Note that number of values of r and/or the value(s) of r used for each of the B frequency bands may be the same or different. Note that the details provided above regarding the sub-DPD actuator(s)426-l-(B−r) are equally applicable here.

The S-DPD actuator404-l,and more specifically the sub-DPD actuator428-l,for the frequency band (bl) may generate a predistorted signal for the frequency band (bl) based on a worst-case envelope, i.e., the summation of magnitudes of the input signals from all B frequency bands (step1004). Here, the details described above for the sub-DPD actuator426-lare applicable. As discussed above, the predistorted signals output from steps1000,1002, and1004for the l-th frequency band (bl) are combined (in step904-l) to provide the combined predistorted output signal for the l-th frequency band (bl).

FIG.11is a flow chart that illustrates details of step902-lfor the l-th frequency band (bl) in accordance with the one-dimensional S-DPD scheme described above. Optional steps are represented by dashed lines/boxes. Note that while the steps ofFIG.11are shown as being performed in sequential order, some or all of the steps may be performed in parallel. As illustrated, the S-DPD actuator404-l,and more specifically the sub-DPD actuator424-l,for the frequency band (bl) may generate a predistorted signal for the frequency band (bl) in a manner that takes into consideration only a single frequency band at a time (step1100). Here, the details described above for the sub-DPD actuator424-lare applicable.

For each value of r from at least a subset of a set of values {q, q+1, . . . , B−2}, the S-DPD actuator404-l,and more specifically the sub-DPD actuator(s)426-l-(B−r) for the value of r, for the frequency band (bl) generates a predistorted signal based on: (a) a sum of magnitudes of input signals for a set of frequency band combinations that consists of at least one combination, at least two combinations, or all combinations of B−r frequency bands from among the plurality of frequency bands (b1, . . . , bB) and (b) a set of LUTs that comprises a single-dimension LUT for each frequency band combination in the set of frequency band combinations (step1102). In one embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is a single value from the set of values {q, q+1, . . . , B−2}. In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is at least two values from the set of values {q, q+1, . . . , B−2}. In another embodiment, the at least a subset of the set of values {q, q+1, . . . , B−2} is all of the set of values {q, q+1, . . . , B−2}. Note that the number of values of r and/or the value(s) of r used for each of the B frequency bands may be the same or different. Note that the details provided above regarding the sub-DPD actuator(s)426-l-(B−r) are equally applicable here.

The S-DPD actuator404-l,and more specifically the sub-DPD actuator428-l,for the frequency band (bl) may generate a predistorted signal for the frequency band (bl) based on a worst-case envelope, i.e., the summation of magnitudes of the input signals from all B frequency bands (step1104). Here, the details described above for the sub-DPD actuator426-lare applicable. As discussed above, the predistorted signals output from steps1000,1002, and1004for the l-th frequency band (bl) are combined (in step904-l) to provide the combined predistorted output signal for the l-th frequency band (bl).

The proposed S-DPD architectures disclosed herein provide significant advantages as compared to the existing full-dimensional S-DPD architecture. Here, it is assumed that a hybrid LUT can support K resolution in the hybrid LUT. There are B bands where K>B. The full-dimensional S-DPD, which takes B inputs, requires KBmemory in the hybrid LUT. The proposed B−q dimension S-DPD requires

memory in the hybrid LUT. On the other hand, the proposed one-dimension S-DPD requires only

memory in the hybrid LUT. The above values of memory requirements can be further written in compact form as in Table 1 to compare among themselves.

A simple use case can be made to quantify the implementation advantages of the proposed architectures. Suppose there are three bands B=3, q=1 and hybrid LUT can support 12 resolution that is K=12. The full-dimensional S-DPD requires 123=1728 memory size of S-DPD. For B−q dimension S-DPD, the hybrid LUT requires

memory size S-DPD. On the other hand, one-dimension S-DPD requires only

memory size S-DPD in the hybrid LUT. As a result, keeping same resolution of the LUT, i.e. value of K, our proposed B−q dimension S-DPD requires 28% of the memory required for traditional S-DPD using three-dimensional hybrid LUT, and the proposed one-dimension S-DPD requires just 5% of the memory required for traditional S-DPD using three-dimensional hybrid LUT.