Advanced Digital Signal Processing Techniques ... - Semantic Scholar

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 6, JUNE 2006

Advanced Digital Signal Processing Techniques for Compensation of Nonlinear Distortion in Wideband Multicarrier Radio Receivers Mikko Valkama, Member, IEEE, Ali Shahed Hagh Ghadam, Student Member, IEEE, Lauri Anttila, Student Member, IEEE, and Markku Renfors, Senior Member, IEEE

Abstract—One of the main trends in the evolution of radio receivers and other wireless device is to implement more and more of the receiver functionalities using digital signal processing (DSP). However, due to practical limitations in the analog-to-digital conversion process, some analog signal processing stages are likely to remain also in the continuation. With the ever-increasing demands for the system performance and supported data rates on one side, and the terminal flexibility and implementation costs on the other, the requirements for these remaining analog front-end stages become extremely challenging to meet. Then, one interesting idea in this context is to apply sophisticated DSP-based techniques to compensate for some of the most fundamental nonidealities of the receiver analog front-ends. In this paper, we focus on developing and demonstrating novel digital techniques to mitigate the effects of harmonic and intermodulation distortion in wideband multicarrier or multichannel receivers using adaptive interference cancellation. The approach in general is practically oriented and largely based on analyzing and processing measured real-world receiver front-end signals. The obtained results indicate that the proposed compensation technique can be used to suppress nonlinear distortion due to receiver front-end sections under realistic signaling assumptions. Index Terms—Adaptive filters, communication system nonlinearities, digital radios, harmonic and intermodulation distortion, radio receivers.

I. INTRODUCTION HE DESIGN and implementation of radio receivers for wireless terminals is currently dictated by the strong needs and push towards flexible and software configurable receiver structures being able to operate over multiple frequency bands and supporting different type waveforms and different air interfaces of the currently existing and also emerging wireless systems [1]–[5]. The terms multimode, multiband, and multistandard radio are commonly used in this context. One key ingredient in building flexible radios is the efficient use of digital signal processing (DSP) [3], [4], [6], [7]. Enabled by the recent advances in DSP techniques, both at the algorithmic and the implementation levels, as well as in the analog-to-digital conversion (ADC) technologies, more and more of the receiver func-

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Manuscript received October 24, 2005; revised February 8, 2006. This work was supported in part by Nokia, by the Finnish Graduate School in Electronics, Telecommunications, and Automation (GETA), by the Nokia Foundation, and by the Academy of Finland under the Advanced Signal Processing Techniques for Future Wireless Communications Transceivers project. The authors are with the Institute of Communications Engineering, Tampere University of Technology, FIN-33101 Tampere, Finland (e-mail: mikko.e. [email protected]). Digital Object Identifier 10.1109/TMTT.2006.875274

tionalities can be implemented using DSP. However, due to the fundamental gap in the used radio frequencies (typically on the order of 1–10 GHz) and supported maximum sampling frequencies (up to a few hundred megahertz, depending on the needed resolution and dynamic range), some receiver analog front-end stages are still needed also in the continuation. This being the case, the performance of the remaining analog signal processing sections is actually one key element in defining and determining the whole receiver performance. One fascinating application area of advanced DSP techniques in receiver signal processing is the possibility to enhance the receiver performance as a whole by mitigating some of the nonidealities of the (remaining) analog front-end stages. One good example in this context is the so-called I/Q imbalance or I/Q mismatch problem and its compensation using DSP. During the last five years or so, much research has been devoted to this issue; see, e.g., [6], [9]–[12], and the references therein, with really promising results in different system scenarios. Another more recent (and also more challenging) topic deals with suppressing the distortion and interference originating from the nonlinear characteristics of the receiver analog front-end. While there has been much research focusing on linearization of transmitter power amplifiers (PAs) during the last ten years or so, digital compensation of receiver nonlinearities in the wideband multichannel or multicarrier context has not received considerable interest so far. This is indeed the central theme in this paper, in the form of mitigating harmonic and/or intermodulation distortion caused by strong blocking type carriers and falling on top of the desired signal band or bands. In general, using the proposed digital compensation technique, the tight design requirements of the receiver analog radio-frequency (RF) front-ends can basically be relaxed in terms of RF filtering and linearity. While there are some further implications on the requirements of the analog-to-digital interface, we strongly believe that the design requirements and implementation complexity of the overall receiver signal processing chain can be relaxed using the proposed techniques. Some preliminary ideas have been considered by the authors in [13] which form the starting point for this paper. Notice also that some related work by other authors has been reported in [14] and [15]; see also [16] and [17]. The work and results presented in this paper can be viewed as a generalization of the ideas in [14], which focuses on canceling second-order interference in cases where the desired signal appears at baseband after the analog front-end downconversion stage. Recently in [18], a hybrid analog–digital calibration technique has also been pro-

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VALKAMA et al.: ADVANCED DSP TECHNIQUES FOR COMPENSATION OF NONLINEAR DISTORTION IN WIDEBAND MULTICARRIER RADIO RECEIVERS

posed which uses certain feedback from the receiver digital parts back to the analog sections. The feedback signal is used to adjust the I/Q mixer parameters in order to push down the observed nonlinear distortion components. The mitigation techniques proposed in this paper are based on purely digital processing of the received signal and can be used to suppress nonlinear distortion of varying orders while the desired signal can basically be located anywhere within the available spectrum. To our knowledge, there exists no other all-digital technique in the state-of-the-art literature able to mitigate nonlinear distortion due to other carrier signals. Thus, in this sense, the research reported here can be seen as rather groundbreaking. Furthermore, in a wider context, we also strongly believe that bringing the radio engineering and signal processing communities even closer together than they are nowadays will play a key role in all the future developments of advanced wireless communications systems. This is a big motivation behind this paper as well. Thus in addition to some signal model developments, the approach here is rather practically oriented, being based on analyzing and processing measured analog front-end signals. The organization of the rest of this paper is as follows. The basic front-end model utilizing wideband I/Q downconversion is described in Section II, together with the fundamentals of nonlinear distortion effects under consideration. Essential signal models describing the nature of the nonlinear distortion from complex I/Q signals point of view are given. Then based on these models, in Section III, the basic idea of the proposed adaptive interference canceller based compensation structure is described, together with detailed discussions of some main practical issues in different system scenarios. Section IV shows some simulation and measurement examples, and conclusions are drawn in Section V. II. WIDEBAND I/Q DOWNCONVERSION-BASED FRONT-END AND NONLINEAR DISTORTION EFFECTS A. I/Q Processing Principles Understanding the true nature of bandpass signals and systems is the key in building efficient radio transmitters and receivers. In addition to the basic envelope and phase representation, the so-called I/Q (in-phase/quadrature) interpretation forms the basis for various spectrally efficient modulation and demodulation techniques [19]. More generally, I/Q processing can be used in the receiver and transmitter front-ends for efficient down-/upconversion processing, independently of the applied modulation technique. Given a general bandpass signal

(1) the (formal) baseband equivalent can be recovered by multiplying the modulated signal with a comand low-pass filtering. This is ilplex exponential lustrated in Fig. 1, which also depicts the practical implementation structure based on two parallel real signals. In the receiver architecture context, the differences come basically from the interpretation of the downconverted signal structure. In general,

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Fig. 1. Basic I/Q downconversion principle in terms of: (a) complex signals and (b) parallel real signals.

both the direct-conversion [20]–[23] and low intermediate frequency (IF) [20], [24] receivers utilize the I/Q downconversion principle and are discussed in more detail in the following. B. Architectural Aspects The so called direct-conversion or homodyne receiver is based on the idea of I/Q downconverting the channel of interest from RF directly to baseband [20]–[23]. Thus in a basic single-channel context, the downconverted signal after low-pass filtering is basically ready for modulation-specific processing such as equalization and detection. This is in general an interesting approach in a sense that eliminating the use of any IFs results in rather simple front-end processing, especially in terms of the needed RF/IF filtering. Another closely related receiver architecture, termed low-IF [20], [24], uses I/Q downconversion to a low but nonzero IF. Thus here a further downconversion from IF to baseband is basically needed before detection, depending somewhat on the actual data modulation. In the basic scenarios, this can be done digitally after sampling the signal at low intermediate frequency. In a wider context, with multiple frequency channels to be detected, a generalization of the previous principles leads to a structure where the whole band of interest is I/Q downconverted as a whole. This is also the main scope of this paper. In this case, either the direct-conversion or low-IF model applies to individual channels but the concept itself is simply referred to as wideband or multicarrier I/Q downconversion in the continuation. As an example, a collection of four wideband code-division multiple-access (WCDMA) carriers with individual channel bandwidth of around 5 MHz could be downconverted to low IFs of around 2.5 and 7.5 MHz, respectively, to illustrate the principle. This could be a valid setup, e.g., on the base station side in a mobile cellular network. In this context, in general, it is also important to recognize that, especially from the nonlinear distortion point of view, the location of the preliminary band-limitation filtering in the analog front-end chain has a big impact on the effective interference profile. As an ultimate example, with as simple an RF section as possible (with minimal amount of filtering), also some strong out-of-band blocking carriers are likely to

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Fig. 2. Self-mixing of (a) LO and (b) the input signal.

enter the front-end amplification and mixing stages introducing strong harmonic and/or intermodulation interference on top of the interesting signals. This is one of the challenging working assumptions in the continuation. C. Nonlinear Distortion and Other Nonidealities Generally speaking, when the dynamic range of the signal passing through the receiver front-end stages to the digital side increases, also the possible effects of many of the front-end nonidealities become more challenging [1], [3], [4], [21]. Even though the focus in this paper is on nonlinear distortion effects, some other closely related nonidealities are also discussed shortly in the following. 1) DC Offsets: Due to the weak isolation between the local oscillator (LO), RF input signals, and front-end amplification stages (e.g., LNA), self-mixing of the LO signal and the input signal itself can generate spurious signal components at or around dc [20], [21], [24]. This is illustrated in Fig. 2. These spurs are generally called dc offsets (static and/or dynamic) and can easily degrade the quality of the weak desired signal if located at the same frequency range. Most typically this is the case in the basic direct-conversion scenarios where the desired signal appears at baseband after front-end downconversion, and thus some compensation of the dc offsets is needed. In the case of dynamic dc offsets, due to self-mixing of the incoming RF signals, this problem can be seen as a special case (with second-order interference model) of the nonlinear distortion considered in this paper. This is indeed the approach in [14] and [15]. 2) I/Q Mismatch: One important practical problem in analog I/Q processing is the relative amplitude and phase matching of the I and Q signal branches [6], [10], [11], [21], [24]. This applies basically both to the I/Q downconversion stage as well as to the branch components (low-pass filters, etc.). In practical implementations, especially in highly integrated ones, amplitude and phase mismatches on the order of 1–5% and 1–5 are commonlystatedfeasible [21],[24].TheneteffectoftheI/Q mismatch is that the image or mirror frequency attenuation of the analog front-end is compromised. The previous imbalance levels correspond to around 25–40 dB image attenuation. Thus the I/Q mismatch is a major problem especially in wideband I/Q downconversion-based concepts where the power level differences of the individual frequency channels acting as images of each other can easily be, depending on the system specifications, in the 30–50 dB range or even up to 80–100 dB [1], [3], [24].

3) Nonlinear Distortion: Any nonlinearities in the signal path obviously distort the information bearing signals traveling through the system. Typical sources of nonlinear distortion in receivers and transmitters are, e.g., amplifiers and mixers [1]–[4], [8]. There are two main aspects in this context in general: 1) the self-distortion of any individual modulated signal and 2) the spurious interference components stemming from other signals, such as harmonic and intermodulation distortion, falling on top of the desired signal band. The focus in this paper is on the latter aspects in the wideband I/Q downconversion-based receiver context where the RF front-end provides only preliminary band limitation. Thus the spurious distortion components of strong signals can easily hit the desired signal band, and the target is to mitigate these effects using sophisticated DSP. D. Harmonic and Intermodulation Distortion in Multicarrier I/Q Downconversion-Based Receivers 1) Basic Polynomial Model: For analysis purposes, the model for the nonlinear component or components under study is assumed to be a memoryless polynomial of the form (2) and denote the input and output signals, respecwhere tively. Excitement of such an element by a signal with two frequency components, say, and , results in two groups of freand quencies at the output—the harmonics of the form and the intermodulation (or cross-modulation) frequen, , as is well-known cies in the literature [1]–[4], [7]–[9]. From the receiver perspective, as long as these components are not in the band of interest, they can basically be eliminated using ordinary linear filtering. However, when a multicarrier or multichannel signal experiences this type of behavior, harmonic and/or intermodulation components are indeed likely to hit a desired band or bands, and this calls for more sophisticated methods rather than just linear filtering. Fig. 3 shows an example how second-order intermodulation of and fall on top of the detwo blocking type carriers at sired signal, which in this example is located at baseband (after the downconversion stage). 2) Exact Distortion Profiles and Nature of Interference With Complex I/Q Signals: Typically in the literature, the harmonic and intermodulation distortion is considered only from the previous single-tone or two-tone sinusoidal model point of view. In other words, the true nature of the distortion components from the complex I/Q signal point of view has not been consistently considered. Here, to address these aspects in more details and build general understanding, we take a more generalized approach and assume that a true modulated yet arbitrary bandpass signal of the form will pass through a memoryless and denote the actual envelope and nonlinearity. Here phase functions, and the corresponding I and Q signals appear and , respectively. as Since the overall focus in this paper is on the effects of the distortion caused by other signals on top of the desired one, this incoming signal models the blocking carrier and the actual desired signal is ignored for a moment. While the physical com-


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. Then substituting again and yields

, and rearranging the terms

(4)

Fig. 3. Frequency-domain illustration of second-order intermodulation distortion due to two strong carriers.

ponents (mixers, low-noise amplifiers, etc.) process the two parallel real signals (I and Q), interpreting the resulting signal dispoint of tortion from the composite complex signal view is the final goal of our analysis. To our knowledge, no exact treatment of these issues using an arbitrary bandpass signal formulation is available in the state-of-the-art literature so far. This also forms the basis for the actual digital compensation principle to be introduced in Section III. First consider the case of memoryless second-order distortion. Assuming that the distortion profiles are mutually idenand tical in the I and Q branches (polynomial coefficients ), the resulting complex signal is formally of the form . Now, letting and and combining the terms yields after some rather straightforward manipulations

Now it is very interesting to observe that the third-order distortion component appears only at the opposite side of the spectrum (here at 3 ), compared to the incoming signal located at . Again it can be shown that this actually holds for any odd-order (3,5, ) distortion component. There is also another crucial difference compared to the earlier second-order model in (3), related to the spurious signal component(s) at the original center frequency . While the second-order case is free from this “self-distortion,” such a spurious component is indeed there in the third-order case as given by (4). This aspect is recognized at the basic single-tone analysis level in the literature but not explicitly in the general case of complex bandpass signals as is done here. This also has some implications on the operation of the proposed compensation structure in Section III, as will be discussed in more detail later. Another interesting further development at the signal modeling level is related to the assumption of identical nonlinearities in the I and Q branches. Obviously this is unlikely to hold exactly in practice since the two branches and the related signal processing elements are indeed parallel separate physical components which can never be exactly identical. To model this, we assume that the polynomial coefficients are , , in the , , in the Q branch. Here , , I branch and model the differences in the behavior of the linear, second-order, and third-order terms between the I and Q. Progressing otherwise similarly as in the earlier signal derivations, the resulting complex signals can now be written as

(3) Based on (3), it can be concluded that the distortion profile is identical on both sides of the spectrum, independently of the original location of the incoming signal. In other words, in obvithe complex model, the sign of the center frequency ously defines the exact location of the received signal but the second-order interference is in any case present on both sides, at 2 and 2 , as can easily be concluded based on (3). Even though not proven here explicitly, it can be shown by further generalizing the previous derivation that similar symmetry holds for any even-order (2,4, ) distortion component in general. Next consider the case of third-order nonlinear distortion. Again assuming identical polynomial models (now coefficients and ) for the I and Q branches, the resulting complex signal is formally of the form

(5) in the second-order case, and

(6)

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in the corresponding third-order case. Based on (5) and (6), it is obvious that the distortion profile is now even more challenging compared to the earlier cases of identical I and Q nonlinearities. Here the relative I/Q difference effect is actually similar to the basic I/Q mismatch case (discussed in Section II-C). In other words, the I and Q differences cause crosstalk of the negative and positive (mirror) frequencies, thus clearly affecting also the possible location of the distortion components when interpreted at the complex signal level. As an example, with identical nonlinearities, the third-order component is fully located around 3 but the imbalances cause some interference energy to appear also around 3 , when interpreted for the comsignal. plex The previous models cover basically the case of having only one dominant interfering carrier. Next these models are extended to cover also the joint behavior of two strong incoming carriers. Thus the ideal complex I/Q model is of the form where , and , denote the individual envelopes and phases, respectively. Obviously, both signals give rise to similar distortion components as in (3)–(6), “individually,” and the following models below state only the additional cross-modulation distortion terms. Here, to simplify to notations to some extent, the case of identical distortion profiles for the I and Q paths is assumed, and the linear signal terms are also neglected for brevity. Now in case of second-order distortion affecting the I and Q, the resulting complex distortion components due to cross-modulation are given by

(7) while the corresponding third-order case appears as

(8) Again the even-order distortion terms appear symmetrically in the complex signal spectrum while such a symmetry does not exist for the odd-order products. Notice also the appearance of

additional self-interference terms [two first terms in (8)] in the third-order case. In general, these models in (3)–(8) will form the basis in the following, when developing a digital interference canceller type structure for reducing the dominant distortion components from the received signal within the band of interest. Notice that further generalization of the signal models to arbitrary number of interfering carriers is also possible, but in our opinion doing that does not add any further intuition, and thus it is not considered here. III. DIGITAL COMPENSATION STRUCTURE BASED ON ADAPTIVE INTERFERENCE CANCELLATION A. Basic Approach The basic philosophy in the following is to suppress harmonic and intermodulation distortion caused by strong blocking signals on top of the desired signal bands. From the complex communications waveforms point of view, the essential distortion models were introduced previously in Section II. Whether the sources of interference are located within or outside the total bandwidth of the specific communication system at hand has naturally some practical relevance but is ignored here for a while and addressed in detail in the next sections. Here we simply assume that a collection of frequency channels is I/Q downconverted as a whole and some of the downconverted strong signals create interference on top of the weaker signals. The detailed individual behavior under second-order and third-order nonlinearities of the blocking signals is given by (3)–(8). In the following, these effects are simply interpreted from the overall signal point of view while developing the compensation principle. The basic compensation structure is presented in Fig. 4. The idea is to consider the detection of the interesting signals on a channel-by-channel basis, such that the band-split filtering stage first separates the desired signal band and all the other signals. These effective filtering functions are denoted by and , respectively, where “ ” refers to “desired” and “ ” to “reference” signal branches. Then the idea is to regenerate the distorting harmonic and intermodulation components by feeding the reference branch signal into a model of the nonlinear process. The purpose of this reference nonlinearity is simply to reproduce the interfering frequencies, with the amplitudes and phases being most likely incorrect. Then an adaptive filtering stage is applied to “scale” the reproduced frequency components properly before being subtracted from the desired signal observation. The adaptive filter coefficients can be adjusted, e.g., to minimize the power of the compensator output using the well-known least mean square (LMS) algorithm or any of its variants [25]. In a practical implementation, the effective processing of second-order, third-order, etc., interference can be carried out individually, by having parallel reference signal branches (reference nonlinearity and adaptive filter stage) for each order of interest. In this way, the needed reference , cubic , etc., polynomials are basically simply quadratic operators, in the simplest case, and the corresponding adaptive filters process each order effects separately. Thus, in general, it should be noted that no detailed model of the nonlinear physical


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Fig. 4. Proposed compensation structure. The upper branch captures the desired signal band and the lower branch generates an interference reference. These two signals are then processed by an adaptive interference canceller to suppress the nonlinear distortion effects from the signal of interest.

front-end is basically needed. The reference nonlinearity section simply regenerates the interfering frequency components, which are then further modified by the online adaptive filter stage, controlling the actual interference cancellation process. In general, by adjusting the band-split filtering stage separating the so-called desired signal from the rest of the spectrum, this method is applicable independently of the position of the desired signal. Notice also that the processing depicted in Fig. 4 is carried out separately for the physical I and Q signal branches. This will be discussed in more detail in Section III-B. One issue basically ignored in the above developments is the possible cross-modulation of the target signal (within the ) and the other signals (within the passband of passband of ). However, since the power of any cross-modulation component in general depends on the relative strengths of all the signals at hand [see (7) and (8) for the two-carrier case], including the target signal itself in this case, it can be concluded that these distortion components are relatively weak, compared to the dominant interference terms, and are thus neglected for simplicity in the continuation. To put it another way, the main focus in this paper is indeed in compensating the dominant distortion effects stemming from the strong out-of-band signals, as stated in the Introduction. It should also be noted that the role of odd-order distortion products is generally slightly more complicated than the corresponding even-order cases. This is because of the “self-interference” inherent to the odd-order processes as stated by (4), (6), and (8). In other words, the reference signal generated in the receiver for interference cancellation is forced to have a small undesired signal component included, causing also some residual error in the compensator output. Notice, however, that this self-interference is, by design, vanishingly small compared to the dominant interference term, when the blocking signal power level is higher than that of the desired signal. This is rather difficult to analyze exactly by analytical means but will be shown by simulations and measurements in Section IV to have only a very negligible effect, if any, on the quality of the compensator output. B. Practical Aspects 1) Signal-Level Compensator Implementation: In the basic developments, as described above, the distortion in the I and Q signal branches is treated and mitigated separately. This is justified since the sources of distortion are also separate physical components (the I and Q mixers, LNAs, etc.). However, based on the derived signal models in (3)–(8), it is also possible to carry out the calculations using the corresponding

signals. This is a strongly implementacomplex tion-specific issue, and at the very hardware level out of the main scope of this paper, but on the other hand important from the signal-level understanding point of view and is also shown to lead to various alternative implementations at signal and system level. So considering the third-order distortion components of a single incoming carrier as a simple example, it was shown earlier that the induced distortion component . When compared is relative to , it is clear to the incoming signal that from the complex signals point of view, proper reference processing (in addition to band-split filtering) is a pure complex cubic operation combined with complex conjugation. Then, the adaptive filter part controlling the actual interference suppression finally takes care of proper scaling (here complex) between the generated reference signal and the interference to be subtracted. Similarly, in the second-order case, with distortion components relative to and , complex squaring in the reference branch can be deployed. In addition to this, complex conjugation is also possibly needed depending which of the two components above are being canceled. The cross-modulation behavior, in turn, is somewhat more complicated from the complex reference signal processing point of view. Considering two incoming interfering carriers and the induced second-order component at [see (7)], it is clear that it cannot be regenerated by direct complex squaring of the basic reference signal. This can, however, be accomplished by either i) additional filtering in the reference and , conjugating the branch separating the carriers other resulting signal, and finally multiplying the signals or ii) considering the squared absolute value of the reference signal and filtering out the proper cross-term. Similar developments can easily be established for the third-order interference case. Based on the above discussions, it is obvious that the basic implementation based on separate mitigation loops in the digital I and Q branches is a more straightforward approach. The alternative implementation based on purely complex signal processing calls for additional filtering in the reference branch, in order to regenerate all the possible in-band interference. One interesting alternative in this context could, however, be based on frequency-domain processing. Thus instead of the basic band-split filtering which separates the desired band and the rest, the total available band could be channelized using fast Fourier transform (FFT) (or some other filter bank) in an

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efficient manner. Then the earlier complex signal processing would simply reduce to proper multiplications of the subcarrier signals. Especially if many bands need to be cleaned anyway, this might indeed be more favorable since in the basic approach, parallel band-split filtering stages are basically needed (one per target band). These further developments are, however, out of the main scope of this paper but offer an interesting and relevant topic for future studies. 2) Role of Fading Channel: One obvious issue in any wireless and radio communication system is the role of the actual communication channel. Here in our context, the fading profiles of the individual signals at different carriers simply affect the corresponding incoming power levels. Since some automatic gain control (AGC) is in any case needed in the receiver chain, the desired signal power level can be considered rather stable in the basic developments (given, of course, that the dynamics of the system power control is reasonable with respect to the fading rate). And stable or not, this actually has influence only on the relative strength of the in-band interference (the lower the desired signal level, the more sensitive it obviously is to any in-band interference). Considering then the strength of the interference, it is also obvious that when the power level of the dominant interference source is changing, also the resulting distortion level changes but in a nonlinear manner. In general, this depends strongly on the operating point of the physical component or components giving rise to the distortion. However, since it is assumed that the reference part in the compensation block anyway contains reference nonlinearities with the corresponding characteristics (meaning basically correct nonlinearity orders), identical nonlinear dynamics (as a function of the power level of the incoming blocker) is seen in the reference signal behavior, and the actual adaptive part (interference cancellation coefficients) will basically remain unaffected. Thus it can be concluded that the power changes of the blocking signal do not affect the compensation stage as such, given that the actual nonlinear characteristics of the front-end components are fixed. This has been verified using simulations at a rather preliminary level, but more detailed studies are still needed to explore the dynamic channel effects in more detail, especially with realistic AGC functionalities included in the front-end. This constitutes an important topic for future work. 3) Role of Blocking Signals, Band-Limitation Filtering, and Analog-to-Digital Conversion (ADC) Interface: One important practical aspect in the context of previously proposed compensation structure is the “availability” of the strong interfering signals in the digital domain. At the conceptual level, this poses some limitations to the analog filtering stages controlling the signal bandwidth entering the sampling and ADC stages of the receiver, and thus also the needed resolution and speed of the ADC(s). Generally speaking, the sources of distortion cannot be rejected by the analog filtering stages after having created the interference—otherwise there is no proper reference available in the digital domain for interference cancellation. This in turn means that also the speed and resolution of the sampling and ADC stages have to support, one way or the other, the bandwidth and dynamic range of the “total” signal, consisting of both the interferers, to be mitigated digitally, as well as the desired signal(s).

In the ultimate example where the RF front-end provides only very preliminary band-limitation filtering before the mixing stage, sources of harmonic and intermodulation distortion can basically be also true out-of-band blockers located outside the target system band under consideration. In this case, in order to carry out the compensation processing depicted in Fig. 4, the implications on the needed resolution and speed of the common ADC stage can be rather unrealistic using today’s technologies. One interesting possibility in this context could then be to use two parallel sampling and ADC stages—one for the desired signal band or bands and the other one for capturing the out-of-band blockers. In this case, the requirements for the sampling and ADCs of the desired signal branch are basically determined by the target system specifications, independently of the receiver nonlinear characteristics. The needed resolution in the reference branch, in turn, is likely to be relatively much lower since there is no need to support the weak desired signals here. The total possible bandwidth and thus the needed maximum speed of the reference branch sampling and ADC stage is generally determined by the bandwidth of the RF band-limitation filtering. In a more “basic” scenario, the signals entering the downconversion stage all belong to the target system band, being generally composed of multiple frequency channels with different power levels. Assuming any of these channels can be the desired one and the actual channel selectivity is to be implemented using digital filtering, the requirements for the sampling and ADC stage are determined solely by the target system characteristics and are, again, not affected by the compensation principle or the receiver nonlinear characteristics as such. 4) Frequency-Dependent Effects and Memory: One additional and important practical aspect from the proposed compensator point of view is related to the detailed structure of the nonlinear distortion components. Generally speaking, if the physical process giving rise to the harmonic and intermodulation components to be mitigated digitally is memoryless, also the reference nonlinearities can be ordinary memoryless polynomials and a single coefficient for each polynomial order is sufficient in the adaptive interference cancellation part. If, in turn, there are some memory or frequency-dependent characteristics involved in the nonlinear distortion process, similar features need to be incorporated also in the compensation stage. In practice, this means introducing memory in the reference nonlinearity section (e.g., in terms of Volterra series [26], [27] or related processing) and/or having multitap filters for each polynomial order in the adaptive IC stage. According to the practical signal measurements, as will be demonstrated in more detail in Section IV, processing two consecutive samples (i.e., memory of one sample interval) yields already most of the gain available compared to a purely memoryless compensator. IV. ILLUSTRATIONS AND OBTAINED RESULTS The operation of the proposed compensation principle is illustrated next using both computer simulations as well as measured receiver front-end signals. For illustration purposes, similar type RF waveforms are used in both studies to help in comparing the measured results with the purely simulation


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based ones. The measurement environment consists of commercially available state-of-the-art signal generators and discrete front-end components like mixers, filters, splitters, and combiners. After the receiver analog front-end, the downconverted and filtered I and Q signals are sampled and A/D converted and stored into memory for further digital processing. The receiver digital part, including the proposed compensation structure as well as final channel selectivity and demodulation functions, is here implemented offline using MATLAB. A. RF Waveforms and Front-End Characteristics In these experiments, the desired signal is quadrature phaseshift keying (QPSK) modulated with 800 kHz symbol rate and located at 103 MHz RF carrier. The pulse-shape is a raised-cosine pulse with 30% rolloff, yielding roughly 1-MHz RF bandwidth. Notice that “downscaled” RF frequencies on the order of 100 MHz are used simply to facilitate the measurement system implementation (cabling requirements, etc.) and do not play any other role here. I/Q downconversion with 100 MHz LO signal(s) translates the desired signal to 3 MHz IF. When experimenting with second-order distortion effects, there is a strong sinusoidal blocker at 98.6 MHz RF frequency. This results in second-order harmonic distortion component on top of the desired signal at 2.8 MHz (after I/Q downconversion) to be mitigated digitally. In case of third-order distortion experiments, a strong AM blocker at 98.95 MHz RF center frequency is used with 100 kHz modulating tone and 20% modulation index. This yields altogether third-order harmonics at 2.85, 3.15, and 3.45 MHz, as well as third-order intermodulation at 2.95, 3.05, 3.25, and 3.35 MHz, which all fall on top of the desired signal at IF. After I/Q downconverting the signals down to IF, the I and Q signals are low-pass filtered, sampled, and digitized. The sampling frequency in the I and Q branches is here 32 MHz and the resolution of the used ADCs is 14 bits. The available sample memory per captured I/Q data block is 265 ksamples. In the basic experiments, the power difference of the strong blocking signal and the desired one is set to 40 dB to model a typical yet difficult example case. B. Computer Simulation Results To illustrate the basic idea of the proposed compensation principle, purely computer simulation based results are presented first. As stated in Section IV-A, both second- and third-order distortion effects are examined. The obtained results are illustrated in Figs. 5 and 6, in terms of the downconverted complex signal spectrum as well as demodulated desired signal at symbol rate without and with digital compensation. Here, in carrying out the simulations, a purely instantaneous polynomial has been used as a model for the nonlinear process, and thus also the compensation stage is memoryless. The adaptation of the IC coefficients is implemented using the well-known LMS algorithm [25]. As illustrated in Fig. 5, the strong sinusoidal blocker creates considerable second-order harmonic distortion on top of the desired signal, seen as the peak in the spectrum at 2.8 MHz. Also in case of third-order distortion (Fig. 6), the induced harmonic and intermodulation components of the used AM blocking signal create strong interference on top of the desired signal. Without

Fig. 5. Top: Simulated spectrum of the downconverted complex signal with second-order distortion. The desired signal is QPSK modulated and located at 3 MHz IF. Bottom: Baseband desired signal observations at symbol rate without and with compensation.

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Fig. 6. Top: Simulated spectrum of the downconverted complex signal with third-order distortion. The desired signal is QPSK modulated and located at 3 MHz IF. Bottom: Baseband desired signal observations at symbol rate without and with compensation.

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compensation, the demodulated desired signal is useless as such in both cases. However, by using the proposed compensator, virtually all the essential interference can be suppressed, resulting in close-to perfect QPSK signal constellations as can be seen in the figures. C. Laboratory Measurement Results Next the corresponding results obtained using actual laboratory signal measurements are reported. For illustration and comparison purposes, exactly the same RF waveform setups as in the computer simulations are used, and were described in Section IV-A. Fig. 7 shows the measured IF signal spectrum with sinusoidal blocking signal, evidencing again clear second-order harmonic distortion on top of the desired signal. Mirror frequency “aliasing” between the positive and negative

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Fig. 7. Top: Measured IF signal spectrum with sinusoidal blocker. The desired signal is QPSK modulated and located at 3 MHz IF. Bottom: Baseband desired signal observations at symbol rate without and with compensation.

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Fig. 8. Example realization of the adaptive IC coefficients.

frequencies in the complex signal spectrum due to I/Q imbalance is also evident. Furthermore, the measured spectrum also verifies the signal analysis models, including the symmetric and nonsymmetric natures of the even- and odd-order distortion components. In this case when processing measured signals, one sample memory (two consecutive samples) is incorporated in the digital compensation stage to account for the possible (yet unknown) memory effects of the measured receiver analog front-end. In general, remarkable similarity between the simulated and measured results can be established by comparing the final demodulated symbol rate constellations of Figs. 5 and 7, in terms of the compensated (“cleaned”) signal. Fig. 8 shows example realizations of the adaptive filter coefficients during the compensator adaptation, evidencing clean convergence in roughly 20 000 iterations or so with the selected step-size values. In general, the selection of the step-size affects both the convergence rate and the average steady-state performance. Notice that if sufficient computational resources are

Fig. 9. Top: Measured IF signal spectrum with AM blocker. The desired signal is QPSK modulated and located at 3 MHz IF. Bottom: Baseband desired signal observations at symbol rate without and with compensation.

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available, reiteration over the same received data block can also be used in practice. Furthermore, once the convergence is established, it is likely sufficient to update the coefficients only rather rarely, in order to keep track of the possible effects of changing nonlinear characteristics. The corresponding results with third-order distortion profile and AM modulated blocking signal are depicted in Fig. 9. Now, as described in Section IV-A, there are altogether seven third-order distortion components falling on top of the desired signal band, causing a catastrophic effect on the demodulated desired signal as can be seen in the figure. However, when processed using the proposed digital compensation stage, again a close-to ideal QPSK constellation is obtained. Thus in general it can be concluded that nonlinear distortion effects due to strong blocking type signals can be efficiently suppressed using the proposed compensation scheme. The in-band carrier-to-interference (C/I) ratio in these measurements is generally around 0 dB when no compensation is used. The C/I levels in the 0 dB range were selected to represent a really challenging operation environment in general. By using the proposed compensation technique, most of the essential in-band interference is removed, resulting in roughly 29 and 25 dB C/I figures after compensation in the second-order and third-order distortion cases, respectively. In order to get further insight into the operation of the proposed compensator, especially when considerable additive noise is present in the signals, a new set of measurements is carried out. For illustration purposes, the focus is on the previous second-order interference case, with considerable amount of additive white (over the whole measurement bandwidth) noise being included in the measurements. The in-band signal-to-noise ratio (SNR) ranges roughly from 0 to 10 dB. The noisy signals are then processed using the compensator and both the uncompensated and compensated signals are detected, in a symbol-by-symbol manner, and the corresponding detection error rates are evaluated. In this case, the original RF power of the interfering carrier is slightly decreased, compared


Fig. 10. Symbol error rate performance with measured signals as a function of additive noise level. QPSK modulated desired signal and sinusoidal blocker. The in-band C/I ratio is around 6 dB without compensation.

to earlier experiments, such that the in-band carrier-to-interference ratio is roughly 6 dB without compensation. Otherwise, with the earlier setup, the error rate of the uncompensated signal would have been almost constant, independently of the actual additive noise level. The obtained results are shown in Fig. 10. For reference we also evaluate the error rate performance with the blocking signal turned off, in order to get proper reference against which to compare the error rates of the uncompensated and compensated signals. Here, as also earlier when experimenting and illustrating the symbol rate signals, all the synchronization (symbol timing recovery, carrier phase, and frequency offset estimation and compensation) information is obtained by digitally processing the observed signal. Thus there will also be some residual error and distortion in the signal entering the data detection due to finite accuracy of the used synchronization techniques. This explains the gap of 0.7–0.8 dB between the measured reference and theoretical reference curves in Fig. 10. However, the most important message is that the detection error rate of the compensated system is practically identical to that of the measured reference. The difference at raw (uncoded) error rates on the order of 10 –10 is only around 0.2–0.25 dB. This gives further confidence on the proposed compensation technique, in the sense that reliable operation is demonstrated under very low SNRs. This is crucial in any practical system, and especially in CDMA type systems where the typical chip-level SNRs indeed range around 0 dB. V. CONCLUSION AND FURTHER DISCUSSIONS This paper has demonstrated that the effects of nonlinearities produced by the analog front-end sections of communications receivers can be compensated by advanced digital signal processing techniques, at least up to a certain degree, in the general multicarrier or multichannel direct-conversion receiver context. The key ingredient for such techniques is developing proper signal models and understanding for the imperfections at signal level, after which fairly standard adaptive signal pro-

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cessing algorithms can be applied. The proposed methods are generally blind, i.e., no training signals or knowledge of the detailed waveform structure nor the nature of the nonlinear process is utilized. Basically only the statistical independence or lack of correlation of the signals at different frequency bands is assumed, which is indeed typically satisfied and justified by physically independent signal sources. Also certain cross-effects between the target signal and the interfering carriers are ignored at signal modeling level, the contribution of which can safely be assumed to be much smaller than the main interference effects. This means that the same principal structures and algorithms can basically be used for various types of communication waveforms in general. The main limitation of the proposed basic approach is that a wideband observation of the received signal is basically required, which would lead to rather challenging requirements for the sampling and ADC process if only a single (common) ADC is utilized. A solution based on utilizing a lower resolution wideband reference branch was then proposed as a practical alternative, but more detailed studies are still needed to verify the idea more thoroughly. This constitutes an interesting and important topic for future work. Furthermore, it is obvious that various other practical issues still need to be explored before being able to use these ideas in practical receiver implementations, but core understanding and principal operation have now been established, as demonstrated using practical laboratory signal measurements. Additional topics for future work include more detailed performance evaluations using the laboratory measurements system and building a field-programmable gate-array (FPGA) prototype for the receiver digital front-end including the compensation stage. At algorithm level, the idea of using frequency-domain processing based on FFT bins (or some other filter bank type transform) will also be investigated. The nonlinearity compensation methods proposed in this paper, as well as earlier developments for compensation of the I/Q imbalance effects, are examples of new opportunities that clever use of DSP can offer in communications receiver design. Being able to compensate for different nonidealities of the analog RF sections basically relieves the specifications for those parts, e.g., by helping to reduce the power consumption of the corresponding analog blocks. Thus cheaper very large-scale integration (VLSI) technologies and more simple receiver architectures can be utilized than in the traditional radio implementations, thereby facilitating flexible multimode, multiband receiver design for future wireless communications systems. Also philosophically, we strongly believe that bringing the radio engineering and signal processing communities even closer together, e.g., through the type of developments reported here, will open up new possibilities and increased synergy benefits for the design and implementation of radio transceivers in the future. ACKNOWLEDGMENT The authors would like to thank A. Asp and J. Suviola with the Institute of Communications Engineering, Tampere University of Technology, Tampere, Finland, for their help in carrying out the practical signal measurements. Also all the technical discussions with H. Somerma, H.-O. Scheck, K. Nikkanen, and

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J. Kämäräinen, all with Nokia Networks, Espoo, Finland, are gratefully acknowledged.

[27] W. J. Rugh, Nonlinear System Theory. Baltimore, MD: Johns Hopkins Univ. Press, 1981.

REFERENCES [1] X. Li and M. Ismail, Multi-Standard CMOS Wireless Receivers. Norwell, MA: Kluwer, 2002. [2] C. Chien, Digital Radio Systems on a Chip. Norwell, MA: Kluwer, 2001. [3] W. Tuttlebee, Ed., Software Defined Radio: Enabling Technologies. Chichester, U.K.: Wiley, 2002. [4] P. Kenington, RF and Baseband Techniques for Software Defined Radio. Norwood, MA: Artech House, 2005. [5] M. Brandolini, P. Rossi, D. Manstretta, and F. Svelto, “Toward multi-standard mobile terminals—Fully integrated receivers requirements and architectures,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1026–1038, Mar. 2005. [6] M. Valkama, J. Pirskanen, and M. Renfors, “Signal processing challenges for applying software radio principles in future wireless terminals: an overview,” Int. J. Commun. Syst., vol. 15, pp. 741–769, Oct. 2002. [7] M. E. Frerking, Digital Signal Processing in Communication Systems. New York: Chapman and Hall, 1994. [8] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits. Norwood, MA: Artech House, 2003. [9] J. Tsui, Digital Techniques for Wideband Receivers. Norwood, MA: Artech House, 1995. [10] M. Valkama, “Advanced I/Q signal processing for wideband receivers: Models and algorithms,” Ph.D. dissertation, Tampere Univ. of Technology, Tampere, Finland, 2001. [11] P. Rykaczewski, D. Pienkowski, R. Circa, and B. Steinke, “Signal path optimization in software defined radio systems,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1056–1064, Mar. 2005. [12] G. Fettweis et al., “Dirty RF,” in Proc. Wireless World Res. Forum (WWRF) Meeting 11, Oslo, Norway, Jun. 2004. [13] A. Shahed, M. Valkama, and M. Renfors, “Adaptive compensation of nonlinear distortion in multicarrier direct-conversion receivers,” in Proc. IEEE Radio Wireless Conf. (RAWCON’04), Atlanta, GA, Sep. 2004, pp. 35–38. [14] M. Faulkner, “DC offset and IM2 removal in direct conversion receivers,” in Proc. Inst. Elect. Eng. Commun., Jun. 2002, vol. 149, pp. 179–184. [15] P. Alinikula, H.-O. Scheck, and K.-P. Estola, “Elimination of D.C. offset and spurious AM suppression in a direct conversion receiver,” U.S. Patent 6 115 593, Sep. 5, 2000. [16] S. Laursen, “Second order distortion in CMOS integrated mixers,” Ph.D. dissertation, Aalborg Univ., Aalborg, Denmark, 2001. [17] L. D. Quach and S. P. Stapleton, “A postdistortion receiver for mobile communications,” IEEE Trans. Veh. Technol., vol. 42, no. 6, pp. 604–616, Nov. 1993. [18] K. Dufrene and R. Weigel, “Adaptive IP2 calibration scheme for directconversion receivers,” in Proc. IEEE Radio Wireless Symp. (RWS’06), San Diego, CA, Jan. 2006, pp. 111–114. [19] E. A. Lee and D. G. Messerschmitt, Digital Communication, 2nd ed. Norwell, MA: Kluwer, 1994. [20] S. Mirabbasi and K. Martin, “Classical and modern receiver architectures,” IEEE Commun. Mag., vol. 38, no. 11, pp. 132–139, Nov. 2000. [21] B. Razavi, RF Microelectronics. Upper Saddle River, NJ: PrenticeHall, 1998. [22] ——, “Design considerations for direct-conversion receivers,” IEEE Trans. Circuits Syst. II, vol. 44, no. 6, pp. 428–435, Jun. 1997. [23] A. Abidi, “Direct conversion radio transceivers for digital communications,” IEEE J. Solid-State Circuits, vol. 30, no. 12, pp. 1399–1410, Dec. 1995. [24] J. Crols and M. S. J. Steyaert, CMOS Wireless Transceiver Design. Dordrecht, The Netherlands: Kluwer, 1997. [25] S. Haykin, Adaptive Filter Theory, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 1996. [26] V. J. Mathews and G. L. Sicuranza, Polynomial Signal Processing. New York: Wiley, 2000.

Mikko Valkama (S’00–M’02) was born in Pirkkala, Finland, on November 27, 1975. He received the M.Sc. and Ph.D. degrees (both with honors) in electrical engineering from Tampere University of Technology (TUT), Finland, in 2000 and 2001, respectively. In 2003, he was a Visiting Researcher with the Communications Systems and Signal Processing Institute, San Diego State University, San Diego, CA. Currently, he is a Senior Researcher with the Institute of Communications Engineering, TUT. His general research interests include communications signal processing, estimation and detection techniques, signal processing algorithms for software defined flexible radios, and digital transmission techniques such as different variants of multicarrier modulation methods and orthogonal frequency-division multiplexing. Dr. Valkama received the Best Ph.D. Thesis Award from the Finnish Academy of Science and Letters for his thesis entitled “Advanced I/Q Signal Processing for Wide-Band Receivers: Models and Algorithms” in 2002. He is Publications Chair of the IEEE SPAWC’07 Conference to be held in Helsinki, Finland.

Ali Shahed Hagh Ghadam (S’02) was born in Tehran, Iran, on November 29, 1975. He received the B.Sc. degree from Khajeh Nasir Toosi University, Iran, in 1999, and the M.Sc. degree from Tampere University of Technology (TUT), Finland, in 2003, both in electrical engineering, and is currently working toward the Ph.D. degree at TUT. Since 2001, he has been with TUT as a Researcher. His main research interests are in signal processing algorithms for flexible radio receivers and transmitters.

Lauri Anttila (S’05) was born in Kankaanpää, Finland, on January 2, 1976. He received the M.Sc. degree in electrical engineering from Tampere University of Technology (TUT), Finland, in 2004, where his is currently working toward the Ph.D. degree. Currently, he is a Researcher with the Institute of Communications Engineering at TUT. His main research interests are in signal processing algorithms for flexible radio receivers.

Markku Renfors (S’77–M’82–SM’90) was born in Suoniemi, Finland, on January 21, 1953. He received the Dipl.Eng., Lic.Tech., and Dr.Tech. degrees from Tampere University of Technology (TUT), Finland, in 1978, 1981, and 1982, respectively. He held various research and teaching positions at TUT during 1976–1988. During 1988–1991, he was was a Design Manager in the area of video signal processing, especially for HDTV, with Nokia Research Centre and Nokia Consumer Electronics. Since 1992, he has been a Professor and Head of the Institute of Communications Engineering at TUT. He has been involved in the organization of ISCAS’88 (Symposium Committee Secretary), ICC’01 (Technical Program Vice-Chair, Tutorials), and PIMRC’06 (Technical Program Vice-Chair, Tutorials). His main research areas are multicarrier systems and signal processing algorithms for flexible radio receivers and transmitters.