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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1

Reference Receiver Enhanced Digital Linearizationof Wideband Direct-Conversion Receivers

Jaakko Marttila, Markus Allén, Marko Kosunen,Member, IEEEKari Stadius,Member, IEEEJussi Ryynänen,Member, IEEEand Mikko Valkama,Senior Member, IEEE

Abstract—This paper proposes two digital receiver (RX) lin-earization and I/Q correction solutions, where an additionalreference RX (ref-RX) chain is adopted in order to obtain a morelinear observation, in particular, of the strong incoming signals.This is accomplished with reduced RF gain in the ref-RX inorder to avoid nonlinear distortion therein. In digital domain,the signal observed by the ref-RX is exploited in linearizingthe main RX. This allows combining the sensitivity of the mainRX and the linearity of the lower-gain ref-RX. The proposeddigital processing solutions for implementing the linearization arefeed-forward interference cancellation and nonlinearity inversion,which are both adapted blindly, without a priori informationof the received signals or RX nonlinearity characteristics. Thelinearization solutions enable flexible suppression of nonlineardistortion stemming from both the RF and analog basebandcomponents of different orders. Especially wideband multi-carrier RXs, where significant demands are set for the RXlinearity and I/Q matching, are targeted. Using comprehensiveRF measurements and realistic base-station scale components,an RX blocker tolerance improvement of 23dB and weakcarrier signal-to-noise-and-distortion ratio gain of 19dB aredemonstrated with combined linearization and I/Q correction.

Index Terms—adaptive signal processing, direct-conversionreceiver, interference cancellation, intermodulation distortion,I/Q imbalance, linearization techniques, mirror-frequency inter-ference, nonlinear distortion, radio receiver.

I. I NTRODUCTION

W IDEBAND multi-carrier or multi-channel direct-conversion receivers (DCRs) are becoming increas-

ingly popular while the cost and size of a single receiver(RX) chain are dropping due to advances in circuit design andunderlying process technologies. Also multi-operator and/ormulti-technology scenarios, where signals of multiple opera-tors and potentially of multiple radio access networks are allreceived simultaneously with a single wideband RX hardwareare becoming more common. In such conditions, the powerrange of the strong and weak carriers inside, e.g.,100MHzreception band, can be up to60–70 dBs [1]–[3]. This is es-pecially emphasized in future ultra-dense networks [4], wherethe strong, blocking mobile transmitters can be in very closeproximity of the base-station (BS) RX [3] while the weak car-riers are received through multiple shadowing obstacles. This

This work was supported by Nokia Networks and the Finnish FundingAgency for Technology and Innovation (Tekes).

J. Marttila, M. Allén and M. Valkama are with the Department of Elec-tronics and Communications Engineering, Tampere University of Technology,Korkeakoulunkatu 1, 33720 Tampere, Finland. E-mail: [email protected],[email protected] and [email protected].

M. Kosunen, K. Stadius and J. Ryynänen are with Department of Micro- andNanosciences, Aalto University School of Electrical Engineering, Otakaari 5,02150 Espoo, Finland. E-mail: [email protected], [email protected],[email protected]

sets stringent requirements for the RX linearity. Improving thelinearity by analog means is challenging, especially with strictlimitations for the design and implementation costs, circuit sizeand power consumption [5]–[7]. However, the requirementsfor analog hardware can be effectively alleviated by meansof digital signal processing (DSP) [8]–[13]. This allows thereceived signal quality to be enhanced after the analog RXwith digital post-processing solutions.

A widely-adopted DCR [5], [14] is illustrated at concep-tual level in Fig. 1, where the most important nonlineardistortion and mirror-frequency interference (MFI) sources arehighlighted. To reflect the overall distortion characteristics asaccurately as possible, the nonlinear distortion modelinginthis paper covers arbitrary-order nonlinearities both in theRF as well as the baseband (BB) components. In addition tothe actual nonlinear distortion products, MFI components areinduced by the in-phase/quadrature (I/Q) mismatches of thedown-converting mixers and other analog components in theBB I and Q rails [8]. Hence, to account for all these distortionproducts, we derive the overall nonlinear behavioral modelfor the RX, employing elementary nonlinear transformationsof the complex-valued signal and its complex-conjugate.

Two alternative DSP solutions are then derived using thebehavioral model in order to either (i) cancel or (ii ) invertall the essential nonlinear distortion effects due to the ana-log hardware. The first method is called reference-receiver-enhanced adaptive interference cancellation (RR-AIC), wherean estimate of the nonlinear distortion is generated basedon the more linear reference receiver (ref-RX) observationand then subtracted from the main RX signal. In the secondmethod, called reference-receiver-aided nonlinearity inversion(RR-INV), an explicit inverse for the overall nonlinearityof the DCR is pursued, using the ref-RX observation as acalibration signal.

The rest of this paper is organized as follows. Section IIpresents the prior-art and highlights the novelty of the pro-posed solutions. In Section III, arbitrary-order modelingofnonlinear distortion and MFI appearing in wideband DCRsis carried out. Building on this modeling, Sections IV andV propose then two linearization solutions based on thedistortion cancellation and nonlinearity inversion ideas, respec-tively. Therein, also digital parameter estimation and learningsolutions are addressed. True RF measurements are presentedand analyzed in Section VI, comparing the performance of theproposed solutions to the state-of-the-art. Section VII furtherdiscusses the benefits and costs of the proposed solutions.Finally, conclusions are drawn in Section VIII.


II. PRIOR-ART IN DIGITAL RECEIVER L INEARIZATION

RX linearization through post-processing has been ad-dressed to some extent already in the existing literature. In[12], [15], the nonlinear distortion estimate is generatedon theanalog RF and then digitized with separate RX chains. Thisneeds specific RX hardware with analog cubing and squaringoperators, does not consider the modeling or suppression ofthe BB nonlinearities and only approximately estimates higherthan third-order distortion. In addition, analog implementationof the cubing and squaring operators contains inherent inac-curacies. Also [13] considers adopting an additional RX chainbut aims only at suppressing the intermodulation distortion(IMD) appearing at the RF, and thus neglects the effects of BBnonlinearities and I/Q mismatch. Furthermore, only computersimulations based results are reported.

In addition, some single-RX based adaptive interferencecancellation (AIC) methods for RX linearization have beenproposed, e.g., in [16]–[22]. In these works, the referencefor the nonlinear distortion estimation and cancellation isgenerated from the main received signal through simple linearfiltering. This inherently gives only approximate distortionestimates, because the inband portion of the nonlinear distor-tion degrades the quality of the reference signal. In addition,knowledge of the blocker center frequencies and bandwidthsneed to be obtained and the filters for picking these blockersneed to be either designed and optimized in real-time orstored in a filter bank to be able to consider different signalscenarios. In [23], on the other hand, a single-RX based digitalpost-inverse solution for nonlinear distortion suppression isdescribed. The proposed solution, however, is not able toconsider frequency-selective nature of the distortion inducedby the analog hardware. In addition, the precision of thediscrete-cosine-transform applied is limiting the suppressionperformance and robustness of the adaptation.

A reference analog-to-digital converter (ADC) based solu-tion for suppressing the ADC nonlinearities only is proposedin [24]. However, the nonlinearities of the preceding RX front-end are not considered in any manner.

A post-inverse linearization solution with offline calibration,where the transmitter of the transceiver unit is used to feedin the calibration signal in order to find the parametersof the post-inverse nonlinearity is proposed in [25]. This,however, requires specific calibration periods and thus limitsthe adaptability and flexibility of the solution.

The solutions proposed in this paper are able to overcomethe limitations of the prior art elaborated above. The proposedsolutions are blind and can be adapted online, during thenormal RX operation. The nonlinear distortion regenerationand suppression are done fully on the digital BB. From theanalog hardware point-of-view, another parallel RX chain isused as a ref-RX. This ref-RX is assumed to have the samereception bandwidth as the main RX. Otherwise, no specificRX design or tailoring is needed. For example, commercialoff-the-shelf dual-RX set-ups can be utilized for this purpose.In general, the proposed solutions enable combining the sen-sitivity of the main RX and the linearity of the lower-gainref-RX in a flexible manner. Furthermore, opposed to [16]–

ADC

ADC

DigitalI/Q

Correctionand

Linear-ization

LO0°

90°

RF Front-End Baseband Processing

LNA

Chan. Eq.DetectionDecoding

Synch.

y n( )x n( )v n( )u n( )

Fig. 1. Conceptual DCR block diagram emphasizing the main sources ofnonlinear distortion and I/Q mismatch together with the employed baseband-equivalent discrete-time mathematical notation.

[22], the receiver linearization solutions proposed in this papercan also facilitate digital out-of-band blocker cancellation, bytuning the ref-RX center-frequency accordingly.

In general, it is known that the down-scaling of the semi-conductor processes and decreasing supply voltages exacer-bates the noise and linearity performance of analog signalprocessing electronics, while largely benefiting DSP imple-mentations from speed and power consumption point-of-view.This trend will make the digital error correction and lin-earization more and more viable solution in the future, butis already used, for example, in linearization of ADCs [26].Furthermore, digital predistortion (DPD), relying on similarbehavioral modeling principles and an additional observationRX, is already widely applied in linearizing transmitter poweramplifiers [27]. Finally, it is noted that there are also someworks in the literature [28]–[31] that consider specificallythe modeling and suppression of the self-interference inducedby the own transmitter, in particular in frequency divisionduplexing devices. While in such scenarios the reference signalfor cancellation is inherently available, the work in this paperconsiders more generic problem setting with arbitrary and un-known strong waveforms entering the RX. These approachescould be potentially combined, for achieving versatile andefficient distortion suppression at the RX.

III. A RBITRARY-ORDER NONLINEARITY MODELING FOR

DIRECT-CONVERSIONRECEIVER

In this section, mathematical modeling of a wideband DCR,illustrated in Fig. 1, is presented. Both the nonlinearities andI/Q mismatches of the analog processing stages are considered.The baseband-equivalent signal model for a DCR is visualizedin Fig. 2, together with illustrative spectral examples showing ascenario where, for simplicity of visualization, only a single re-ceived carrier is depicted, being located at a small intermediatefrequency (IF) after the RF down-conversion stage. In general,arbitrary-order nonlinearities are considered for both the RFand BB, in order to provide a complete and comprehensivebehavioral model of the overall RX.

A. LNA Modeling

The RF low-noise amplifier (LNA) nonlinearities are mod-eled with an odd-order memory polynomial incorporatingseparate memory filters for the different polynomial compo-nents in order to cover different nonlinearity orders and the


Mixer I/Q mbalance odelI M

f f f ffIF fIF fIF-fIF fIF-fIF 3fIF- f3 IF

y( )nx n( )v n( )u n( )

...

...

...

...

...

...

...

RF( )

Ka n%

1( )a n%

3( )a n%

2()× ×

RF 1()

K -

× ×

1( )b n

2( )b n

1,0( )c n%

1,1( )c n%

*()×

...

2,0( )c n%

BB BB,( )

K Kc n%BB*[( ) ]K×

*()×

2()×

RF onlinearity odelN M

BB onlinearity odelN M

Fig. 2. Illustration of cascaded parallel Hammerstein models considering RF and BB nonlinearities as well as mixer and BB I/Qmismatches. The highestnonlinearity orders taken into account for the RF and the BB are KRF andKBB, respectively. Due to the generality of the nonlinearity models, they also takemixer nonlinearities into account. The spectrum illustrations are sketched for BB equivalent signals matching to the mathematical modeling in the paper, andonly a single carrier located at thefIF, after I/Q down-conversion, is shown for visualization purposes.

related memory effects as accurately as possible. This structureis known as parallel Hammerstein model [32], [33] and isillustrated in Fig. 2. The choice of odd-order simplification isjustified by even order distortion falling either on multiples ofthe RF center frequency or around BB, while the interestingsignals at this stage are still at the RF. In addition, also the odd-order harmonic components are excluded based on the sameassumptions [34]. This is a valid approach as long as the centerfrequency is high compared to the instantaneous bandwidth ofthe total signal entering the LNA. However, if the receptionband becomes very wide, e.g., in gigahertz range, in respectto the center frequency, also harmonic distortion should beconsidered.

Mathematically, the odd polynomial orders, considered upto KRF, are gathered intoΩRF, i.e., ΩRF = 1, 3, ...,KRF.With this assumption, the LNA output as a discrete-timebaseband-equivalent model can be expressed as

v(n) =∑

k∈ΩRF

ak(n) ∗1

2k−1

(

kk+12

)

[u(n)u∗(n)](k−1)/2

u(n)

=∑

k∈ΩRF

ak(n) ∗ |u(n)|k−1u(n),

(1)

whereak(n) are the impulse-responses for each odd polyno-mial order in ΩRF taking memory effects into account andu(n) is the original LNA input. Notationwise,∗ and (·)∗

denote convolution and complex-conjugate, respectively.Fur-thermore, the modified filters, denoted byak(n), include alsothe contribution of the scalar scaling coefficients multiplyingthe signal component on the first line of (1). Using theseimpulse-responses instead of scalar coefficients extends themodeling presented in [34] to cover also memory effects. Inaddition, using complex-valued impulse-response taps allowscovering AM/PM characteristics of the amplifiers [35]. ForΩRF, one practical example is third order distortion modeling,ΩRF = 1, 3, where1 represents the linear component. Suchsimplified modeling was earlier assumed, e.g., in [18], [20],[25].

B. I/Q Mixer and Baseband Component Modeling

Next, the LNA output is fed into down-converting I/Qmixers. The finite image-rejection ratio (IRR) of the mixersismodeled by adding a filtered complex-conjugate of the inputsignal to the output of the mixer [8], [36]. In this way, themixer output signal becomes

x(n) =b1v(n) + b2v∗(n), (2)

where b1 and b2 are the scaling coefficients for the directand conjugate branches, being more specifically defined asb1 = (1 + ge−jφ)/2 and b2 = (1 − gejφ)/2, whereg andφ are the gain mismatch and the phase mismatch betweenthe branches, respectively [8], [36]. The nonlinearity of theI/Q mixers and the I/Q mismatches between the BB I and Qcomponent frequency responses are included in the followingBB nonlinearity model and are thus not explicitly included inthe instantaneous mixer I/Q mismatch model in (2).

Finally, the BB I and Q nonlinearities are included in thejoint model. Independent arbitrary order parallel Hammersteinmodels are employed for modeling both the rails in order totake into account also the possible I/Q mismatches betweenthe rails. The nonlinearities can originate from I/Q mixers, BBamplifiers and ADCs. In the BB stage modeling, also evenorder nonlinearities are taken into account, modeling, e.g., theself-mixing problem in the mixer [8]. Similar to the RF, theorders included in the modeling, up toKBB, are representedwith ΩBB. In practice, this can be, e.g.,ΩBB = 1, 2, 3 formodeling second- and third-order BB nonlinear distortion.The


final digitized waveform can thus be expressed as

y(n) =∑

k∈ΩBB

cre,k(n) ∗ xkI (n) + jcim,k(n) ∗ x

kQ(n)

=∑

k∈ΩBB

1

2k

k∑

l=0

[(

cre,k(n) +(−1)

lcim,k(n)

jk−1

)

∗

(

kl

)

xk−l(n)[x∗(n)]l

]

=∑

k∈ΩBB

k∑

l=0

ck,l(n) ∗ xk−l(n)[x∗(n)]

l,

(3)

wherecre,k(n) andcim,k(n) are the impulse responses for eachpolynomial order defined inΩBB for I and Q rails, respectively,taking memory effects into account. In addition,ck,l(n) are themodified filters including also the scalar multipliers on secondline of (3), reflecting the combined responses for each of thecomplex-valued signal components.

C. Cascaded Effects of RF and BB Nonlinearities

The signal components resulting from thecascaded effectsof (1)–(3) are gathered into Table I, in terms of the idealRX input signalu(n), in the example case ofΩRF = 1, 3andΩBB = 1, 2, 3, together with short description of eachcomponent. Even though differential signaling is known toreduce even-order distortion components, the second-orderterm is included in the BB part since, e.g., mixer-inducedsecond-order distortion can still be relevant in certain scenarios[37]. These components and the presented modeling form thebasis for developing the linearization approaches described inthe following sections.

In Table I, the first-column components ("Terms") appearpurely due to the nonlinearities. The second-column compo-nents ("Mirror Terms") appear only in case of I/Q mismatcheither in the mixers or the BB I and Q rails. In (2)–(3), thismeans that the respective scaling coefficients and impulse re-sponses go to zero in case of perfect I/Q matching. In addition,if all the orders considered in the BB nonlinearity modelinginclude I/Q mismatch, introducing mixer I/Q mismatch doesnot generate new Mirror Terms but only affects the effectiveresponses of the ones already appearing because of BB I/Qmismatches. It should be noted that the Terms in Table I cannotbe strictly separated into RF distortion and BB distortion,evenwhen the modeling of those stages differs in ways described in(1)–(3). For example, the Term|u(n)|2u(n) is stemming fromboth the third-order RF nonlinearity, described by (1) and thethird-order BB nonlinearity, described by (3). The proportionsof these contributions depend on the characteristics of theexacthardware at hand and, thus, the exact coefficients of (1)–(3).

Generally, the list of distortion components with differingorders considered in the modeling can be obtained by evalu-ating (1)–(3) in symbolic form. This can be carried out eitherwith pen and paper or using software tools, such as MATLABSymbolic Math Toolbox.

Notice that the above modeling results are generic and applyto arbitrary LNA input signalu(n), independently of whether

TABLE ITERMS GENERATED BY THE JOINT NONLINEARITY MODEL IN CASE OF

ΩRF = 1, 3 AND ΩBB = 1, 2, 3

Terms Mirror Terms Interpretation

u(n) u∗(n) Original signal aroundfIF

|u(n)|2 - 2nd-order IMD around BB

u2(n), [u∗(n)]2 - 2nd-order harmonics around±2fIF

|u(n)|2u(n) |u(n)|2u∗(n) 3rd-order IMD aroundfIF

[u∗(n)]3 u3(n) 3rd-order harmonics around−3fIF

|u(n)|4 - 4th-order IMD around BB

|u(n)|2u2,

|u(n)|2[u∗(n)]2- 3rd-order IMD around±fIF

|u(n)|4u(n) |u(n)|4u∗(n) 5th-order IMD aroundfIF

|u(n)|2[u∗(n)]3 |u(n)|2u3(n) 3rd-order IMD around−3fIF

|u(n)|6 - 6th-order IMD around BB

|u(n)|4u2,

|u(n)|4[u∗(n)]2- 5th-order IMD around±2fIF


|u(n)|4[u∗(n)]3 |u(n)|4u3(n) 5th-order IMD around−3fIF


|u(n)|6[u∗(n)]3 |u(n)|6u3(n) 7th-order IMD around−3fIF

receiving a single carrier or multiple carriers, or whetherthe (composite) received signal after I/Q down-conversionislocated strictly at baseband or not. The graphical illustrationin Fig. 2 emphasizes the creation of different distortion termsdue to an individual strong incoming carrier which is locatedat fIF after the I/Q down-conversion stage.

IV. PROPOSEDREFERENCERECEIVER ENHANCED

ADAPTIVE INTERFERENCECANCELLATION (RR-AIC)SOLUTION FOR WIDEBAND L INEARIZATION

In this section, the proposed RR-AIC linearization solutionis described in detail, building on the modeling results of theprevious section. In the RR-AIC another parallel RX, in whichthe RF LNA stage is excluded, is employed as illustrated inFig. 3. Thus, this ref-RX is not creating RF nonlinear distortionand is operating in more linear region when it comes to theI/Q mixer and BB stages. With the ref-RX, only the strongestblockers need to be observed, to be used as a reference signalin the digital linearization processing. Thus, the ref-RX noisefigure and the quantization resolution of the correspondingref-RX ADC are not as critical as for the main RX, who needsto be able to receive also the weak carriers present within thereception band. The weak carriers, however, have only verylittle contribution to the nonlinear distortion appearingin themain RX.

The I/Q correction stage illustrated in Fig. 3 is implementedin both the main RX and the ref-RX based on [36] and appliesadaptive circularity restoring MFI suppression principle. Alsoin the ref-RX, even though it is operated on a more linearregion than the main RX, the MFI contribution might besignificant. In order to achieve as high quality reference signalas possible, it is thus desirable to perform I/Q correction


therein as well. The MFI suppression is generally focusingon the contribution of the possible I/Q mismatch inducedMirror Terms in Table I. This approach is validated by thefact that all the Mirror Terms in Table I can be modeled asBB induced MFI. Thus, the MFI appearing at the last stage ofthe analog front-end is suppressed first in the digital front-end,while the actual nonlinearities are tackled thereafter. The MFIsuppression performance will be demonstrated using the RFmeasurements in Section VI, together with the linearizationperformance. The aim of the actual linearization stage, whichis one of the main contributions in this paper, is to suppressthe remaining nonlinear Terms in Table I.

In Fig. 3, the RR-AIC stages, namely the reference non-linearities, adaptive filtering and interference cancellation areillustrated. These stages aim at regenerating and cancelling thenonlinear distortion induced by the analog RX components.This is based on the mathematical modeling presented inSection III and discussed in more detail in the following. Thedescription in this section follows the signal flow and notationsillustrated in Fig. 3.

A. Reference Nonlinearities

In the reference nonlinearity stage, shown in Fig. 3, ele-mentary nonlinear transformations of the I/Q corrected ref-RXsignal u(n) are generated. Herein, the nonlinearity model isassumed to be a parallel Hammerstein model [32], [33] but,generally, any nonlinearity model can be applied. However,apolynomial model followed by a filtering stage has the benefitof being linear in parameters and is thus very well suitable foradaptive parameter learning. The exact choice of the model inindividual scenarios should be done based on the hardwareat hand and the desired performance/complexity trade-off.For example, a simplified polynomial model followed byscalar adaptive coefficients could be employed, if consideringmemory effects of the analog front-end components is not seennecessary.

In Fig. 3, the reference nonlinearities are denoted withf0(·), f1(·), ..., fP (·), where P is the number of nonlinearterms andf0(·) is a linear function. Thus, the linear componentsignald0(n) and the nonlinear componentsd1(n) to dP (n) areobtained. Here, the reference nonlinearities are chosen basedon the wideband DCR modeling in the previous section. Inpractice, the nonlinear Terms gathered in the first columnof Table I are targeted and the component signals are thusexpressed as

d0(n) = f0(u(n)) = u(n),

d1(n) = f1(u(n)) = u2(n),

d2(n) = f2(u(n)) = [u∗(n)]2,

...

dP (n) = fP (u(n)) = . . .

(4)

In general, the nonlinearity modeling in here should matchthe actual main DCR characteristics as accurately as possible.Similar to the choice of the nonlinearity modeling approachin general, also the employed reference nonlinearities should

be optimized based on the performance/complexity trade-off.The optimum set of reference nonlinearities depends also onthe given RX hardware at hand. Thus, giving universal set ofreference nonlinearities is not seen feasible. At the same time,reducing the number of kernels in the following learning stagecan be approached using, for example, principal componentanalysis in similar manner as has been proposed for digital pre-distortion of power amplifier nonlinearities [41]. Furthermore,the role of different nonlinearity components has been studiedin [20] in a simplified two-tone reception scenario, givinginsight to the significance of each component. The role ofthis selection is also illustrated in Section VI together withthe linearization results.

The produced nonlinear components are next fed in parallelto the adaptive filtering stages, as illustrated in Fig. 3. Thisallows individual adaptive weighting for each of the distortioncomponents. The combined, adaptively filtered nonlinear com-ponents yield then the actual estimate of the overall prevailingnonlinear distortion in the received main RX signal. Noticethat the linear component is naturally excluded from theactual cancellation signal but is deliberately included inthegeneration of the error signal for adapting the filters, in order toavoid bias in the adaptive filter coefficients [38] because ofthecorrelation between the nonlinear components and the linearcomponent present in the original main RX signal. Other alter-native option could be to adopt an additional orthogonalizationstage after the generation of the basic reference nonlinearitiesor nonlinear basis functions.

In general, in order to mimic the nonlinearities in the analogfront-end, no harmful aliasing should be allowed in the digitalreference nonlinearities. In this scenario, the harmful aliasingmeans distortion components that alias inside the actual re-ception and cancellation bandwidth. This can be avoided byfirst interpolatingu(n), feeding it to the nonlinear operatorsf1(·), f2(·), ..., fP (·) and then filtering and decimating thegenerated nonlinear components back to the original samplerate. In this way, if non-harmful aliasing is allowed, thenecessary high sample rate isfS,high = [(K + 1)/2]B, whereK and B are the highest polynomial order applied and thereception bandwidth dictated by the ADC and the analogfiltering, respectively [10]. If no aliasing is allowed at all, thenecessary sample rate isfS,high= KB. The need for increasedsample rate is illustrated in Fig. 3 with a dashed-line box.

B. Parameter Learning and Interference Cancellation

The general principle for learning the adaptive filter coef-ficients is to minimize the error power between the sum ofthe adaptively filtered parallel reference nonlinearity outputsignals and the received main RX signal. The intuition behindthe idea is to find a black-box parallel Hammerstein model forthe main RX analog parts and use the nonlinear components ofthe model to cancel the nonlinear distortion from the receivedsignal. This is accomplished by subtracting the adaptivelyfiltered nonlinear components from the received main RXsignal. In general, the adaptive filters are used to find optimalamplitude and phase responses for the nonlinear components,


ADC

-

r -efADC

mainRX

ref-RX

I/Q correctionstage

Referencenonlinearities

Adaptive filtering andinterference cancellation

w0

u d0 d´

y´

^

y u~

I/Qorrectionc

I/Qorrectionc -

d1w1

d

0()f ×

1()f ×

High sample rate

LNA

e

DPLXTX xvu

Fig. 3. Block diagram illustrating the principle of the proposed RR-AIC method for main RX I/Q correction and linearization. The MFI suppression andnonlinearity cancellation stages are cascaded. The I/Q correction stage is implemented based on [36]. The time indexn is omitted from the signal notationfor illustration convenience.

thus creating an optimal estimate of the nonlinear distortioninduced in the main RX analog front-end. In practice, thelearning can build on, e.g., least-squares (LS) block solu-tion, recursive least squares (RLS) or sample-wise least-meansquare (LMS) adaptation [38]. In the following, the LS blocksolution is described in detail, as an illustrative example.Generally, also other learning algorithms can be applied.

First, the set of filtersw0,w1, ...,wP , depicted also inFig. 3, is optimized in the LS sense with the given block ofdata. This block can be, e.g., a frame of the received signal,and its length is denoted byN . The length of each filter isMand hence, e.g.,w1 = [w1(1), w1(2), ..., w1(M)]T. The filtersare obtained by solving the model fitting problem

argminwC

‖DCwC − y′‖2 (5)

for wC= [wT0 ,w

T1 ...,w

TP ]

T such that it minimizes the powerof DCwC−y′, which is the modeling error. This can be inter-preted as fitting the linear component and the nonlinear com-ponents with memory sizeM and individual weights to the I/Qcorrected main RX signal blocky′ = [y′(1), y′(2), ..., y′(N)]T

in LS sense. The matrixDC consists of the linear componentand all the nonlinear transformations obtained via the ref-RX with M separate delays as columns as shown in (8).

The resultingwLSC contains coefficients for all theP + 1

filters wLS0 ,wLS

1 , ...,wLSP , having dimensionsM(P + 1)× 1.

In practice,wLSC is obtained by calculating the pseudo-inverse

of DC [38], giving

wLSC = D+

Cy′

= (DHCDC)

−1DHCy

′.(6)

In general, the interference cancellation is then accom-plished by subtracting the distortion estimate provided bythefilters w′

C = [wT1 ,w

T2 ...,w

TP ]

T from the main RX signaly′,written here as

u = y′ −D′

Cw′

C, (7)

which yields the linearized signalu. Here, opposed to theprevious model fitting stage, the actual cancellation builds onprocessing the nonlinear terms only, i.e.,D′

C is obtained fromDC in (8) by removing the linear signal terms. Furthermore,in the actual online linearization after having estimated thefiltersw1,w2, ...,wP as described above, linearization can becarried out sample by sample without any block-structure.

DC =

d0(1) d0(N) . . . d0(N−M+1) d1(1) . . . d1(N−M+1) . . . dP (1) . . . dP (N−M+1)d0(2) d0(1) d0(N−M+2) d1(2) d1(N−M+2) dP (2) dP (N−M+2)

... d0(2)...

......

......

... d0(N) d1(N) dP (N)d0(1) d1(1) dP (1)d0(2) d1(2) dP (2)

......

...d0(N) d0(N−1) . . . d0(N−M) d1(N) . . . d1(N−M) . . . dP (N) . . . dP (N−M)

(8)


V. PROPOSEDREFERENCERECEIVER ENHANCED

NONLINEARITY INVERSION (RR-INV) SOLUTION FOR

WIDEBAND L INEARIZATION

In case of nonlinearity inversion based main RX lineariza-tion approach, described in this section, the more linear per-ception of the received signal provided by the ref-RX is usedasa calibration signal. This means that the output of the inversenonlinearity, being fed with the main RX signal observation, iseventually mimicking this more linear observation. In thisway,the ref-RX enhances also the performance of the nonlinearityinversion.

In Fig. 4, this approach is illustrated. Therein, the I/Qcorrection stage is first used to suppress mirror-frequencycomponents induced by the I/Q mismatches of both the mainRX and the ref-RX chain analog components. Again, the I/Qcorrection stage is implemented based on [36] and is assumedto tackle the Mirror Terms of Table I, as discussed in the caseof RR-AIC in Section IV. The following inverse nonlinearitystage aims then in suppressing the nonlinear distortion presentin the main RX observation, thus suppressing the remainingnonlinear Terms in Table I.

In the following, the RR-INV processing stages shown inFig. 4 are described in more detail. The description followsthe signal flow and notations of Fig. 4.

A. Inverse Nonlinearity

The actual nonlinearity is implemented as a memory poly-nomial withP +1 separate reference nonlinear transformationstages or basis functionsf0(y′(n)) to fP (y

′(n)), as illustratedin Fig. 4, followed by linear filtersw0,w1, ...,wP . The valueof P is not restricted to be the same as in the interferencecancellation solution discussed in the previous section. Thetarget is generally to find the reference nonlinearities whichinvert the effect of nonlinearity occurring in the main RXfront-end.

The exact choice of the basis functions in the inverse nonlin-earity solution depends on the characteristics of the forwardnonlinearity whose distortion effects are to be inverted. Forexample, in case of a nonlinear system described by a simplepower series of increasing polynomial orders, also the inversenonlinearity can take a form of a power series [39]. The orderof this inverse nonlinearity can, however, differ from the orderof the original system. Thus, considering the nonlinearities ina wideband DCR, the applied basis functions are chosen fromTable I also in the case of nonlinearity inversion. With thesereference nonlinearities, theP +1 component signalsd0(n) todP (n) are obtained. Summing the component signals together,after being properly filtered, forms the final linearized signal,as shown in Fig. 4.

Proper oversampling should again be applied before thereference nonlinearities in order to avoid harmful aliasing inthe component signalsd0(n), d1(n)..., dP (n). This is high-lighted in Fig. 4 with a dashed line box indicating the needfor higher sampling rate. The same interpolation factor demandof (K + 1)/2, whereK is the highest considered polynomialorder, discussed in Section IV, applies also herein.

B. Parameter Learning

The general principle for adapting the filters of the inversenonlinearity is to minimize the difference of the output andthe more linear signal observation captured with the ref-RX.The higher linearity of the ref-RX observation is assumedbecause of the reduced RF gain in the ref-RX branch. Theconcept is implemented in practice by subtracting this morelinear blocker observation, denoted asu(n), from the inversenonlinearity outputu(n), resulting in an error signale(n)containing only an estimate of the prevailing nonlinear dis-tortion in u(n). Thus, by adapting the inverse nonlinearityfilters w0,w1, ...,wP such that the power of this error signalis minimized, the inverse nonlinearity output is driven towardsthe more linear ref-RX observation while at the same timemaintaining the better signal-to-noise ratio (SNR) and sensi-tivity of the main RX observation.

Next, we formulate the actual adaptation or parameterlearning processing in more detail, again adopting the blockLS principle as a concrete example. Generally, also other, e.g.,sample-adaptive, learning algorithms can be applied.

The filters w0,w1...,wP , shown in Fig. 4, are foundthrough LS model fitting over the given processing block. Theyare obtained by solving the model fitting problem

argminwI

‖DIwI − u‖2 (9)

for wI = [w0,w1, ...,wP ]T in such a way that the power

of the differenceDIwI − u, which is the adaptation error, isminimized. Formally, the structure of the data matrixDI isidentical to that ofDC in (8). It should be, however, notedthat here the component signals fromd0(n) to dP (n), andthus also the matrixDI, are formed by feeding the receivedmain RX observationy′(n) to the reference nonlinearities, asshown in Fig. 4. In practice, the LS optimum filterswLS

I canbe found by calculating the pseudo-inverse ofDI, expressedhere as

wLSI = D+

I u

= (DHI D)−1

I DHI u.

(10)

In general, after solving forwI, the final output of theinverse nonlinearity is given as

u = DIwI. (11)

This is also the linearized version of the distorted mainRX observationy(n), approximating the original baseband-equivalent RX inputu(n). Naturally, in the actual onlinelinearization after having estimated the filtersw0,w1...,wP

as described above, linearization can be carried out samplebysample without any block-structure.

VI. L INEARIZATION PERFORMANCEDEMONSTRATION

WITH RF MEASUREMENTS

In this section, the performance of the proposed linearizationsolutions is evaluated and demonstrated with true BS RXhardware and RF measurements. In addition, the performanceis compared against previous state-of-the-art. For the single-RX AIC [20] implementation, 100th order digital bandpass


mainRX

ref-RX

ADC

r -efADC -

Filter adaptation

u

d0 u~

I/Qorrectionc

I/Qorrectionc

y

Inverse nonlinearityI/Q correctionstage

w00()f ×

High sample rate

LNA

e

y´DPLX

TX u v x

Fig. 4. Block diagram illustrating the principle of the proposed RR-INV method for main RX I/Q correction and linearization. The MFI suppression andnonlinearity inversion stages are cascaded. The I/Q correction stage is implemented based on [36]. The time indexn is omitted from the signal notation forillustration convenience.

MATLAB

Clock

LNA DUALRX EVB

FPGA

DC

VECTORSIGNAL

GENERATOR

DC DC

LPFRX1

RX2

Fig. 5. The measurement setup illustrating device control with Matlab PCand the measurement flow from the vector signal generator to theFPGAconnected to the PC.

Fig. 6. A photograph of the measurement setup, illustrating the devices usedin the laboratory.

and bandstop filters are designed in order to keep the digitalfront-end complexity realistic. These filters form the bandsplitstage described in [20].

The following measurements replicate two uplink BS multi-carrier reception scenarios [3]. More specifically,10MHz3GPP Long Term Evolution (LTE) uplink single-carrierfrequency-division multiple access (SC-FDMA) waveformswith 16-QAM subcarrier modulation are applied. The mea-sured composite signal is generated with National InstrumentsPXIe-5645R vector signal transceiver. This signal is fed into asplitter, with3.5 dB attenuation, giving the inputs for the mainRX and the ref-RX. In the main RX chain, a HD Communi-cations Cor. HD24089 wideband LNA is employed. The IIP3and the gain of the LNA are−7 dBm and22 dB, respectively.

After the LNA, a state-of-the-art BS-scale wideband dual-RXboard with pre-commercial RX-version of the Analog DevicesAD9371 transceiver is used to down-convert, digitize andcapture the data. The reception bandwidth of both the RXs is100MHz. The measurement set-up is illustrated in more detailin Fig. 5 and shown as a photograph in Fig. 6. For the ref-RX, the received signal is fed without LNA, having thus22 dBlower RF gain compared to the main RX. The measurementsare performed on1750MHz RF center frequency.

For the distortion suppression, the following reference non-linearities and component signals are applied in the RR-AIC

d0(n) = f0(u(n)) = u(n),

d1(n) = f1(u(n)) = u2(n),

d2(n) = f2(u(n)) = [u∗(n)]2,

d3(n) = f3(u(n)) = |u(n)|2,

d4(n) = f4(u(n)) = |u(n)|2u(n),

d5(n) = f5(u(n)) = [u∗(n)]3,

d6(n) = f6(u(n)) = |u(n)|4u(n),

(12)

where the second, third and fifth order nonlinearities areconsidered for optimizing linearization performance. Inthe RR-INV processing, the same reference nonlinearitiesf0(·), f1(·), ..., f6(·) are applied for the received and I/Qcorrected main RX signaly′(n), instead of u(n) used in(12), as illustrated in Fig. 4. These distortion componentsfrom Table I have been chosen based on trials in the RFmeasurements with the utilized RX hardware. The significanceof these components is further studied and demonstratedin Sub-Section VI-C. Two-tap adaptive filters, per nonlinearbasis function, are applied in both the RR-AIC and RR-INV linearization stages in order to consider mild memoryeffects. Furthermore, two-tap filters are also adopted in theI/Q correction stages, building on [36]. This, as well, allowsconsidering mild frequency selectivity in the I/Q mismatchappearing in the measurement setup. The signal-to-noise-and-distortion ratio (SNDR) and uncoded symbol error ratio (SER)results are obtained using the block LS based parameterlearning. These figures of merit are evaluated and averagedover 10 independent measurements each consisting of305 600


TABLE IISIGNAL AND MAJOR DISTORTION COMPONENTS IN NON-OVERLAPPING

NONLINEAR DISTORTION AND MIRROR-FREQUENCY INTERFERENCE

SCENARIO. THE SHOWN CENTER FREQUENCIES REFER TO THEIQDOWN-CONVERTER OUTPUT.

Component Center Freq. BW Power

Weak carrier 1 −40MHz 10MHz −77dBm (RF)

Weak carrier 2 20MHz 10MHz −77dBm (RF)

Blocker 1 10MHz 10MHz swept


Mirror Term 1 −10MHz 10MHz varies


3rd Ord. Spreading 1 10MHz 30MHz varies


3rd Ord. Intermodulation −20MHz 30MHz varies

complex-valued received samples. When sweeping the blockerpower in the measurements, the power step for each blockeris 2 dB.

A. Suppression Quantification for Non-overlapping NonlinearDistortion and Mirror-frequency Interference

In this scenario, two weak LTE uplink carriers are receivedin the presence of two strong blocking carriers. The weakcarriers are placed in such a manner that the other one suffersfrom the MFI and the other one from the nonlinear distortioninduced by the strong carriers. The details of this signalscenario are gathered in Table II.

Snapshot spectral examples are shown in Fig. 7 in orderto illustrate the signal scenario and the major performancedifferences between the solutions. The strong blocking carri-ers, responsible for the dominating distortion componentsinthe black spectra of the original received signal, are locatedafter the RF I/Q down-conversion at the IF center frequenciesof 10MHz and40MHz. The strongest distortion componentsappear thus on the mirror bands, around the original strongcarriers, with triple bandwidth typical for 3rd-order IMD,andaround−20MHz (2×10 MHz − 40 MHz = −20 MHz, 3rd-order IMD). The weak LTE carriers are in this example locatedat the IF center frequencies of−40MHz and20MHz. Thus,MFI stemming from the strong carrier located at40MHz and3rd-order IMD due to the other strong carrier at10MHz arefalling on top of these weak carriers, respectively.

In Fig. 7, it can be observed that the earlier proposed AICprocessing without ref-RX [20] is suppressing the IMD spreadaround the strong carriers poorly compared to the proposedref-RX enhanced approaches. Also 3rd-order IMD around−20MHz remains at slightly higher level compared to theproposed RR-AIC and RR-INV. However, all three solutionsshow clearly improved signal quality at the mirror bands ofthe strong carriers which is best illustrated around−10MHzsignal band, where the image of the10MHz carrier can beseen without underlying weak carrier.

Furthermore, Fig. 8 shows the SNDRs for both the weaksignals (around−40MHz and 20MHz) with different lin-

Frequency (MHz)-50 -40 -30 -20 -10 0 10 20 30 40 50

Pow

er (

dBm

/kH

z)

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

ReceivedSingle-RX AIC [20]RR-AICRR-INV

Fig. 7. The measured spectra of the original received and the linearizedsignals at digital BB/IF, illustrating the performance of the RR-AIC andRR-INV. The blocker powers are−23dBm and weak carrier powers are−77dBm per carrier, when evaluated at the RX input at RF. The weak carriersare located at20MHz and−40MHz.

Received Power per Blocker (dBm)-55 -50 -45 -40 -35 -30 -25 -20

SN

DR

[dB

]

-10

-5

0

5

10

15

20

25

Received, mirror carrierSingle-RX AIC [20], mirror carrierRR-AIC, mirror carrierRR-INV, mirror carrierReceived, neighbor carrierSingle-RX AIC [20], neighbor carrierRR-AIC, neighbor carrierRR-INV, neighbor carrier

Fig. 8. The measured SNDRs of the mirror-band weak carrier around−40MHz ("mirror carrier") and the neighboring-band weak carrieraround20MHz ("neighbor carrier") as functions of the blocker RF powers. Themirror carrier and neighbor carrier SNDRs are presented withsolid and dashedlines, respectively. The weak carrier RF powers are constant −77dBm percarrier.

earization solutions as a function of the blocker power at thesplitter input preceding the main RX LNA. The solid lines inFig. 8 show good improvement in the−40MHz weak carrierSNDR. For example at the14 dB SNDR level,21 dB strongermirror-band blocker is tolerated compared to the originalreceived scenario. As an example, at−27 dBm blocker RFpower level, specified by 3GPP as one test scenario [3], theSNDR of the mirror-band weak carrier is increased from−1 dB to 15 dB with all the studied solutions. Consideringthe weak carrier around−40MHz, it should be noted thatmost of the SNDR gain is achieved by the MFI suppression.

The dashed lines show then the SNDRs for the20MHzweak carrier located close to the10MHz strong carrier. The


black dashed line shows that at this band the SNDR starts tosuffer only at the higher blocker powers, which is typical fornonlinearity dominated distortion profile. As can be observedin Fig. 7, the single-RX AIC [20] is performing poorlycompared to the proposed ref-RX solutions. Between the RR-AIC and RR-INV, the RR-INV is slightly outperforming RR-AIC on most of the practical reception quality range. With thevery highest blocker RF powers studied, the RR-AIC gives2–4 dB higher SNDR compared to RR-INV. Up to the−27 dBmRF blocker power, the performance is practically equal. Again,at the14 dB SNDR level, the blocker tolerance compared to nolinearization at all is improved from the20MHz weak carrierpoint-of-view by 7.0 dB with RR-AIC and7.5 dB with RR-INV. At the same time, at−27 dBm blocker power level, theSNDR of the neighboring band weak carrier is increased from8 dB to 11 dB and 16 dB with the single-RX AIC and boththe ref-RX solutions, respectively. Overall, Fig. 8 shows thatsimilar levels of post-linearization SNDRs can be achievedfor both weak carriers, independent of the differences in pre-linearization SNDR levels.

In Fig. 9, the uncoded SER results for mirror band andneighboring band carriers follow generally the same trendsas observed for the SNDRs. For the mirror band carrier,1%uncoded SER levels are maintained with20–22 dB higherblocker powers compared to the original received signal with-out post-processing. At the same time, for example at the−27 dBm blocker power level the uncoded SER is improvedfrom 80% to below1%. For the neighboring carrier, the single-RX AIC [20] performance is poor also when measured withSER. In parallel, the RR-AIC and RR-INV allow6 dB blockertolerance improvement at1% uncoded SER level. Also in thiscase, SER in−27 dBm blocker case is pushed below1% whenuncompensated SER is27%.

Generally, the results clearly show that the proposed solu-tions outperform the existing state-of-the-art [20], in particularwhen considering the linearization performance at frequenciesclose to the strong carriers.

B. Suppression Quantification for Overlapping Nonlinear Dis-tortion and Mirror-frequency Interference

In this scenario, a single weak carrier is received in thepresence of two blocking carriers such that the MFI and thenonlinear distortion are all falling on the same band togetherwith the weak carrier. From the weak carrier point-of-view,this can be considered as a worst-case scenario. The detailsofthis signal scenario are gathered in Table III.

In Fig. 10, spectral examples in case of a weak LTE carriermasked by overlapping MFI and 3rd-order IMD are illustrated.The overall distortion profile differs in this scenario fromthat of the previous subsection because the strong blockingcarriers are now located at IF center frequencies of10MHzand30MHz instead of10MHz and40MHz that were adoptedin the previous scenario. The weak carrier, in turn, is situatedaround IF center frequency of−10MHz. From the lineariza-tion performance point-of-view, it is again clearly visible in


SE

R

10-2

10-1

100

Received, mirror carrierSingle-RX AIC [20], mirror carrierRR-AIC, mirror carrierRR-INV, mirror carrierReceived, neighbor carrierSingle-RX AIC [20], neighbor carrierRR-AIC, neighbor carrierRR-INV, neighbor carrier

Fig. 9. The measured SERs of the mirror-band weak carrier around−40MHz("mirror carrier") and the neighboring-band weak carrier around 20MHz("neighbor carrier") as functions of the blocker RF powers.The mirror carrierand neighbor carrier SNDRs are presented with solid and dashed lines,respectively. The weak carrier RF powers are constant−77dBm per carrier.

TABLE IIISIGNAL AND MAJOR DISTORTION COMPONENTS IN OVERLAPPING

NONLINEAR DISTORTION AND MIRROR-FREQUENCY INTERFERENCE

SCENARIO. THE SHOWN CENTER FREQUENCIES REFER TO THEIQDOWN-CONVERTER OUTPUT.

Component Center Freq. BW Power

Weak carrier −10MHz 10MHz −77dBm (RF)







3rd Ord. Intermodulation −10MHz 30MHz varies

Fig. 10 that the AIC with main RX only processing [20]suffers from poor performance at the frequencies close to thestrong carriers. Otherwise, the performance of all the studiedsolutions is close to each other in this snapshot example. Itshould be again noted, that the MFI due to the30MHz strongcarrier falling to around−30MHz is pushed down to the noiselevel, which points toward good MFI suppression performancealso at the weak carrier band around−10MHz, where the MFIof the10MHz strong carrier is present. Also the IMD aroundthe weak carrier band seems to be efficiently pushed down.

The actual SNDR of the weak carrier is evaluated andillustrated in Fig. 11 in order to achieve concrete insight onthe distortion levels inside this band. Generally, in Fig. 11, it isvisible that the RR-INV gives most solid SNDR performanceover the whole measured range. All the compared solutionsare, generally speaking, achieving significant improvement inthe weak carrier signal quality. For example, at the previously


Frequency (MHz)-50 -40 -30 -20 -10 0 10 20 30 40 50

Pow

er (

dBm

/kH

z)

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10


Fig. 10. The measured spectra of the original received and thelinearizedsignals at digital BB/IF, illustrating the performance of the RR-AIC andRR-INV in the weak carrier worst-case scenario. The blockerpowers are−23dBm and weak carrier power is−77dBm, when evaluated at the RXinput at RF. The weak carrier is located at−10MHz.


SN

DR

(dB

)

-10

-5

0

5

10

15

20

25


Fig. 11. The measured SNDR of the worst-case weak carrier (around−10MHz) as a function of the blocker RF powers. The weak carrier RFpower is constant−77dBm.

mentioned target SNDR level of14 dB, the RR-INV improvesblocker tolerance of the RX, compared to no linearization, by23 dB and the other two solutions lie within1 dB interval.Furthermore,16 dB post-linearization SNDR is achieved by allthe studied solutions at the blocker power levels of−27 dBmwhile the pre-linearization SNDR is approximately−3 dB,demonstrating thus a significant gain of19 dB. It should benoted that this19 dB gain consists of the combined MFIsuppression and linearization performance that can be achievedwith these solutions.

In Fig. 12, the SERs are shown for the weak carrier. Theuncoded SER performance of the single-RX AIC [20] and theRR-INV are close to each other while the RR-AIC performspoorer with the low blocker powers. Considering again1%uncoded SER level, the single-RX AIC [20] and the RR-INV


SE

R

10-2

10-1

100


Fig. 12. The measured uncoded SER of the worst-case weak carrier (around−10MHz) as a function of the blocker RF powers. The weak carrier RFpower is constant−77dBm.

offer 23 dB improvement in the blocker tolerance, the RR-AICbeing also very close at22 dB. With the −27 dBm blockerpower, all the solutions push the SER level from82% below1% level. In this scenario, the single-RX AIC [20] achievesmarginal edge over RR-AIC and RR-INV by dropping below1% SER level with1 dB higher blocker powers.

Overall, the RR-AIC falls below the RR-INV and the single-RX AIC with the lower blocking carrier power levels andwith lowest power levels is actually slightly decreasing theSNDR level compared to the original received signal. Thiskind of behavior has been documented with such cancellationalgorithms also earlier [25]. However, if, for example, pilot-based estimation of the signal quality indicates good receptionconditions, the linearization processing can and should beswitched off in order to save processing power, at the sametime avoiding these effects.

C. Linearization Performance with Different Reference Non-linearity Subsets

In Fig. 13, the role of chosen reference nonlinearities,given in (12), is illustrated using RR-INV linearization and−23 dBm blocker powers as a concrete example. Further-more, the weak carrier worst case scenario discussed in Sub-Section VI-B and detailed in Table III is used. In the figure,it is visible that includingd4(n) and d6(n) has the biggesteffect on the linearization performance. This indicates thatwith the given hardware, the third- and fifth-order intermodu-lations are the dominant distortion components. This is furtherdemonstrated in Table IV, where examples of the weak carrierSNDR and uncoded SER are given. Herein, also second-ordercomponents and third-order harmonic component in (12) areincluded in the processing in order to maximize the overallperformance on the whole reception band. If lower-complexitysolution is desired, reduced set of reference nonlinearities canbe considered. For example, in addition to linear Termd0(n),solely third- and fifth-order intermodulation Termsd4(n) and


Frequency (MHz)-50 -40 -30 -20 -10 0 10 20 30 40 50

Pow

er (

dBm

/kH

z)

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

Received

Comp. w/ d0 - d

3

Comp. w/ d0 - d

4

Comp. w/ d0 - d

5

Comp. w/ d0 - d

6

Fig. 13. The measured spectra of the original received and thelinearizedsignals at digital BB/IF, illustrating the role of the applied reference nonlin-earities, given in (12). The blocker powers are−23dBm and weak carrierpower is−77dBm, when evaluated at the RX input at RF.

TABLE IVSNDR AND UNCODED SEROF THE WEAK CARRIER WITH VARIED

RR-INV REFERENCE NONLINEARITY SUBSETS AND−23dBm BLOCKER

POWERS IN OVERLAPPING NONLINEAR DISTORTION AND

MIRROR-FREQUENCY INTERFERENCE SCENARIO.

Components Weak Carrier SNDR Weak Carrier SER

Uncompensated −8.8dB 88%

d0, ..., d3 −6.0dB 84%

d0, ..., d4 11dB 7.1%

d0, ..., d5 11dB 7.2%

d0, ..., d6 15dB 1.1%

d6(n) could be employed. On the other hand, if the hardware athand contained even stronger BB nonlinearity, the contributionof the second-order Termsd1(n), d2(n) and d3(n) and thethird-order harmonic Termd5(n) would increase, because theyare tackling exactly this BB distortion. Also cascaded effectsof the RF and BB nonlinearities are covered by the Termsin Table I based on the modeling in (1)–(3). Furthermore,it should be noted, as mentioned in Section III, thatd4(n)and d6(n) are induced both by the RF nonlinearity and theBB nonlinearity. The exact choice of Terms is thus highlyhardware-dependent and exact universal guidelines do notexist, as discussed in Section IV-A. Altogether, the providedRF measurement results successfully demonstrate and verifythe good linearization performance of the proposed solutions.

VII. F URTHER DISCUSSION

The main benefit of the proposed linearization solutions isthe improved distortion suppression performance, as demon-strated in Section VI. However, the ref-RX approach bringsalso additional advantages compared to previous solutions.These are shortly discussed below.

Compared to, e.g., [20], no digital bandpass or bandstop fil-ters are needed for separating the strongest distortion inducing

carriers and removing the blocker inband contribution fromthedistortion estimate, respectively. This simplifies implementa-tion of the digital front-end significantly. Especially because,as noted in Section VI, the response of these filters directlyaffects the linearization performance of the single-RX versionof the AIC. Thus, very high order filters would be needed ifthe linearization performance should be optimized.

Another advantage stemming from the fact that the above-mentioned digital front-end filters can be avoided is that noexact information of the strongest blocking carrier centerfrequencies and bandwidths is needed in the RR-AIC and theRR-INV. The whole main RX observation is processed as iswithout need for bandsplit or other filtering stages, or spectrumsensing for the strongest carriers [20], [21], simplifyingthedigital front-end processing significantly.

The cost of the proposed linearization solutions is theimplementation and power consumption of the ref-RX togetherwith the the digital correction logic proposed herein. It isstillan open question if the current RX systems can tolerate thisoverhead. However, obtaining accurate power consumptionestimates would require implementation on silicon, and evenin such approach, the results would be highly case andprocess dependent. On the other hand, power consumptionestimation based on the amount of operations results com-monly in inaccurate and highly speculative results, and wastherefore not included in this paper. Thus, more detailedcomplexity and power consumption analyses and optimizationin different wideband RX scenarios, e.g., in the context ofcellular networks, are left for future work. Potential complexityreduction techniques for the linearization DSP have beenproposed, especially in the context of the transmitter DPD[40], [41]. They could potentially be applied for the digitalRX linearization for reducing the power consumption of therelated DSP, as the cost of the DSP should not be ignored. Onthe analog side, in general, the ref-RX performance metricsarequite different to the main RX, which is designed for worst-case situation seeking to optimize the challenging combinationof linearity, sensitivity and dynamic range. The ref-RX, inturn, only needs to observe the strong signals and thus, e.g.,the sensitivity requirements are substantially reduced, leadingto simplified and lower-cost implementation prospects. At thesame time, the integrability of the DCR allows also dual-RXchips making efficient implementation of the ref-RX and datatransfer to the BB processing unit possible.

Based on the results presented in Section VI, the proposedRR-INV solution gives the best overall performance in thestudied scenarios. Therein, blocker tolerance improvement of23 dB and weak carrier SNDR gain of19 dB together withuncoded SER improvement from82% to below 1% weredemonstrated in the considered worst-case distortion scenariowith combined suppression of the MFI and the nonlineardistortion. In addition, because in RR-INV no cancellationsignal that should be continuously available is produced fromthe ref-RX received signal, it is possible to run the calibrationof the inverse nonlinearity only periodically. This would allowdecreased power consumption because of the turned-off ref-RX analog components, such as amplifiers and ADCs aswell as the digital parameter learning algorithms. In addition,


in multi-antenna RX scenarios with multiple parallel DCRchains, this opens up potential for linearization and param-eter learning such that only one ref-RX, shared sequentiallybetween the main RXs, is adopted. In such scenarios, thehardware overhead of the adoption of the ref-RX is thus al-ready minimal. Thus, RR-INV is a very potential candidate forlinearizing cellular BS RXs, where wideband multi-operator,multi-technology, multi-carrier reception is a desirablefeature,leading to the aforementioned challenges with very highinband and out-of-band blocker tolerance requirements.

VIII. C ONCLUSION

In this paper, an arbitrary order parallel Hammerstein modelfor wideband DCRs was first developed to characterize theoverall RX nonlinear behavior. The model incorporates theeffects of both RF and BB nonlinearities and I/Q mismatchof the down-conversion mixers and BB I and Q components.The results of this modeling were then applied in developingtwo novel digital post-linearization solutions for suppressingthe nonlinear distortion introduced both at the RF and atthe BB stages of the RX front-end, building on the conceptof adopting a ref-RX to observe the incoming signal withreduced sensitivity but enhanced linearity. The proposed RR-AIC adaptively finds the parameters of the nonlinearity modelof the front-end and provides distortion signal estimate forcancellation. The proposed RR-INV, in turn, finds the inversenonlinearity model which minimizes the distortion powerat the output of the inverse nonlinearity when the wholereceived signal is fed as an input. Both of these solutionscan offer improved performance over the state-of-the-art at acost of a single additional DCR chain while also resulting tosubstantially simplified digital front-end signal processing.

As the actual cost of an additional integrated RX chain isalready pushed down with modern CMOS processes, the RR-AIC and especially the RR-INV offer attractive options forlinearizing cellular wideband multi-operator, multi-technology,multi-carrier BS RXs. In this way, need for expensive high-performance, high-cost analog components can potentiallyberelaxed and the complexity can be moved towards digitaldomain, where the computation power is becoming more andmore cost-effective.

REFERENCES

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Jaakko Marttila was born in Tampere, Finland, onMarch 30, 1982. He received the M.Sc. and D.Sc.degrees in signal processing and communicationsengineering from Tampere University of Technology(TUT), Tampere, Finland, in 2010 and 2014, respec-tively.

He is currently working as a Post-Doctoral Re-searcher at TUT, Department of Electronics andCommunications Engineering. His research interestsare digital compensation of radio receiver nonide-alities and analog-to-digital (AD) conversion tech-

niques for software defined and cognitive radios.

Markus Allén was born in Ypäjä, Finland, on Octo-ber 28, 1985. He received the B.Sc., M.Sc. and D.Sc.degrees in signal processing and communicationsengineering from Tampere University of Technology,Finland, in 2008, 2010 and 2015, respectively.

He is currently with the Department of Electronicsand Communications Engineering at Tampere Uni-versity of Technology as a University Teacher. Hiscurrent research interests include cognitive radios,analog-to-digital converters, receiver front-end non-linearities and their digital mitigation algorithms.

Marko Kosunen (S’97–M’07) received his M.Sc,L.Sc and D.Sc (with honors) degrees from HelsinkiUniversity of Technology, Espoo, Finland, in 1998,2001 and 2006, respectively.

He is currently a Senior Researcher at AaltoUniversity, Department of Micro and Nanosciences.His expertise is in implementation of the wirelesstransceiver DSP algorithms and communication cir-cuits. He is currently working on implementationsof cognitive radio spectrum sensors, digital intensivetransceiver circuits and medical sensor electronics.

Kari Stadius (S’95–M’03) received the M.Sc.,Lic. Tech., and D.Sc. degrees in electrical engi-neering from the Helsinki University of Technology,Helsinki, Finland, in 1994, 1997, and 2010, respec-tively.

He is currently working as a Staff Scientist atthe Department of Micro- and Nanosciences, AaltoUniversity School of Electrical Engineering. Hisresearch interests include the design and analysisof RF transceiver blocks with special emphasis onfrequency synthesis.

Jussi Ryynänen(S’99–M’04) was born in Ilmajoki,Finland, in 1973. He received his Master of Science,Licentiate of Science, and Doctor of Science degreesin electrical engineering from Helsinki Universityof Technology (HUT), Helsinki, Finland, in 1998,2001, and 2004, respectively.

He is currently working as an associate professorat the Department of Micro- and Nanosciences,Aalto University School of Electrical Engineering.His main research interests are integrated transceivercircuits for wireless applications. He has authored or

coauthored over 100 refereed journal and conference papersin the areas ofanalog and RF circuit design. He holds six patents on RF circuits

Mikko Valkama (S’00–M’02–SM’15) was bornin Pirkkala, Finland, on November 27, 1975. Hereceived the M.Sc. and Ph.D. degrees (both withhonours) in electrical engineering (EE) from Tam-pere University of Technology (TUT), Finland, in2000 and 2001, respectively. In 2002 he received theBest Ph.D. Thesis award by the Finnish Academy ofScience and Letters for his dissertation entitled "Ad-vanced I/Q signal processing for wideband receivers:Models and algorithms".

In 2003, he was working as a visiting researcherwith the Communications Systems and Signal Processing Institute at SDSU,San Diego, CA. Currently, he is a Full Professor and Department ViceHead at the Department of Electronics and Communications Engineeringat TUT, Finland. He has been involved in organizing conferences, like theIEEE SPAWC’07 (Publications Chair) held in Helsinki, Finland. His generalresearch interests include communications signal processing, estimation anddetection techniques, signal processing algorithms for software defined flex-ible radios, cognitive radio, digital transmission techniques such as differentvariants of multicarrier modulation methods and OFDM, radio localizationmethods, and radio resource management for ad-hoc and mobile networks.

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