 Research
 Open Access
Automatic leaking carrier canceller adjustment techniques
 Gregor Lasser^{1}Email author,
 Robert Langwieser^{2} and
 Christoph F Mecklenbräuker^{2}
https://doi.org/10.1186/1687396320138
© Lasser et al.; licensee Springer. 2013
 Received: 31 December 2012
 Accepted: 21 March 2013
 Published: 7 May 2013
Abstract
In this contribution, four automatic adjustment algorithms for leakage carrier cancellation in radio frequency identification (RFID) readers are compared: full search, gradient search, fast and direct I/Q algorithms. Further, we propose two enhanced adjustment procedures.
First, we analytically calculate the performance of the fast adjustment algorithm in the presence of noise and derive its theoretical bias. We compare the theoretical results with the numerical results from accompanying simulations. Further, we evaluate the performance of these algorithms based on realworld measurements acquired with our RFID testbed.
Finally, we propose and discuss the merits of two enhanced adjustment procedures based on the fast adjustment algorithm. The fast adjustment procedure with bipolar probing signals achieves the isolation gain of the (much slower) gradient search algorithm at the expense of a mean penalty of 0.48 dB. We observe that the fast adjustment aided gradient algorithm requires 72% less steps than the gradient search algorithm in our measurements.
Keywords
 Fast Algorithm
 Gradient Algorithm
 Power Detector
 Error Vector Magnitude
 Leakage Signal
1 Introduction
Radio frequency identification (RFID) is a technique to remotely identify and detect objects that are branded with a special transponder called RFID tag [1]. RFID systems operate at several frequency bands and use different methods to transfer data and energy between an RFID reader and the tags. In this work, we will focus on RFID systems that use electromagnetic waves for communications, especially ultrahigh frequency (UHF) RFID systems.
An RFID tag consists of an antenna that is connected to an electronic circuit, which in most cases is built on an integrated circuit. Many RFID systems use the socalled passive or semipassive tags that do not use an internal power source to communicate with the RFID reader. They instead use backscattering, a technique which is based on the fact that the amplitude and phase of the waves scattered from an antenna depend on the antenna termination impedance. Thus, the tag sends data to the reader by modulating the impedance that the tag chip presents to the antenna terminals [2, 3]. While this backscattering technique, seen from the tag, enables remotely powered communication, it necessitates a constant carrier signal to be transmitted from the RFID reader during the tag to reader data transfer [4–6]. Therefore, the RFID reader has to transmit a carrier signal while it simultaneously receives a weak backscattered signal from the tag. To separate transmit an receive paths, readers either use separate transmit and receive antennas or use circulators or directional couplers. In analogy to radar systems, the first case is called bistatic, while the second one is called monostatic. Still, both system concepts struggle with low transmitter to receiver isolations [7]. This demands for receivers with very large dynamic ranges, which enhance costs, both on the analog front end as well as on the analog to digital converters. To reduce these demands, many authors [6, 8–17] as well as commercial monolithic RFID reader chip manufacturers [18, 19] propose or use active leakage cancellation techniques. These techniques, which originate in radar [20, 21], extract a part of the transmit signal, adjust it in amplitude and phase and inject it at the receiver. When the amplitude is adjusted to be equal and the phase to be opposite of the leakage signal, the deliberately added signal and the leakage signal cancel. While there exist many publications on hardware implementations of these leaking carrier cancellers (LCCs), few exist on adjustment algorithms to adapt them. However, adaption is critical [22, 23] because typical RFID scenarios like warehouses and conveyor belts change permanently and therefore cannot be adjusted statically.
In this paper, we will accomplish the following:

Present a comparison of four adjustment algorithms regarding their demands on hardware linearity, detector type and LCC calibration, and their setting speed,

Analytically and numerically analyse the noise performance of the fast algorithm including a bias derivation,

Practically compare the fast algorithm with the gradient search algorithm using our RFID testbed,

Present an enhancement to the fast algorithm, which both gives better results under nonlinear detector conditions as well as a better noise performance,

Report on observed step number reductions using the result of the fast algorithm for initialising the gradient algorithm: 72% reduction on average in our experiment.
The paper is structured as follows: In Section 2, we will describe the principals of leakage cancellation based on a generic RFID reader model. We will then present four automatic LCC adjustment routines and compare them regarding hardware demands and speed. This will be discussed in the context of detector types and positions with regard to our generic reader. In Section 3, we will provide a noise analysis for the fast algorithm which includes analytic and numeric results. Measurements on our RFID testbed will be described in Section 4. Finally, we will present two enhanced adjustment procedures based on the practical findings of the measurements, and we will compare them with the algorithms described before.
2 LCC adjustment principles
The LCC consists of a vector modulator and an amplifier. The vector modulator is controlled by the reader control block and enables to adjust the amplitude and phase of the transmit signal sample to cancel the leakage signal in the receiver’s directional coupler. The amplifier compensates for the coupling losses and enables cancellation of strong leakage signals.
Conventional RFID readers rarely have that many detectors as were described before. However, at least one is necessary to implement any LCC adjustment routine, but not every detector position or type supports every algorithm. We use the very general setup described in Figure 1 to exemplify RFID reader implementations with focus on possible LCC control implementations. Besides the location, we distinguish between scalar power detectors and vector detectors which also capture the phase of the incoming signal. The second type requires a reference signal that is either supplied from the reader’s transmitter part or from the ADC sampling clock. We use this generic RFID reader model through the next sections where we describe different automatic LCC adaption techniques, which aim to find the optimum inphase (I) and quadrature (Q) component settings for the LCC.
Our generic model is applicable to stationary RFID readers as well as to handheld devices. The latter usually employ integrated antennas which enable a better control of the typical expected leakage values and potentially a simpler LCC design. To save space and costs, the LCC may also be included in the antenna which was presented in [16]. Besides these differences, all LCC circuits need to be adjusted. While it might be desirable for mobile devices to reduce hardware complexity for smaller packages and lower costs, we will see that there is a tradeoff between adjustment speed and necessary hardware complexity for the different adjustment algorithms. Since handheld readers most likely are moved all the time during their use, permanent and fast adjustment routines are beneficial.
2.1 Full search algorithm
The most primitive way to find the optimum setting for an LCC is by trying all possible LCC settings and picking the one which proved to have the best result. If inphase and quadrature components both have N settings, N^{2} measurements have to be performed. Thus, one obvious drawback of this technique is the large amount of measurements and adjustment steps which need to be performend before the final result is gained. Depending on the speed of the given detector hardware, this corresponds to a large overall scanning time of the LCC which might be inadequate even for moderately changing environments. In these cases, this algorithm may completely fail to find an LCC setting because the slowly moving optimum LCC setting might never be hit during the scanning process. Besides these obvious disadvantages, the full search algorithm has the benefit of accepting any type of power detector as long as it shows a monotone, but not necessary linear inputoutput relation. Here, we mean monotone if the output of the detector is increasing (or remains constant) when the input power is increasing. Even if the receiver is completely overloaded by the leakage signal for most LCC settings, the power detector will provide the lowest output signal at the appropriate LCC setting. Therefore, this algorithm may be used in receiver structures, which do not employ a special power detector for LCC adjustment, and it has very limited demands on receiver linearity. For these reasons, some commercial reader chips use this algorithm [18]. An improvement to reduce the scanning time, which is also implemented in [18], is to divide the algorithm into two steps and to scan only a fraction of all N^{2} setting in the first step. When this subgrid is properly chosen, at least one of the scanned subgrid points is close to the appropriate LCC setting, and therefore, the receiver operates in the linear regime and gives useful power detector readings. In the second step, only the vicinity of the point with the lowest measured remaining LCC power is scanned.
2.2 Gradient search algorithm
where μ is a positive, realvalued constant called the stepsize parameter. Beginning from a starting point that is usually set to zero, c_{0}=0, the gradient search algorithm step by step tries to approach the optimum LCC setting. Setting the stepsize parameter μ is critical for this algorithm to work: If it is too small, many steps are necessary to obtain the final value. Setting it too high results in oscillations, and the algorithm will not converge. A similar problem exists for the deviation value δ that is used to measure the gradient. Choosing δ too large will possibly lead to false gradient measurements when it is applied at close proximity to the optimum value. A small δ implies a small change in power and in the presence of noise an unreliable gradient measure.
Since it is an iterative technique, the gradient search algorithm is well suited for changing environments. Another benefit of this technique are the moderate linearity constraints which it imposes on the reader. As long as the power detector is strictly monotone and the step width is chosen small enough to ensure stability, the algorithm will converge to the optimum LCC setting point. Few authors explicitly state adjustment algorithms, but the authors in [16] are using a gradientbased approach as well as in [12], who describe a similar approach and use a variable step width.
2.3 Fast algorithm
The fast algorithm is a new technique which was first published in [25]. In this section, we will give a short description of the principle operation, while in later sections, a noise analysis, numerical simulations and measurement results are presented.
The algorithm gains the optimum LCC setting by obtaining three amplitude measurements. These measurements are very similar to the ones performed to gain the gradient in the gradient algorithm, but in contrast to the gradient algorithm, they do not provide an enhancement in information for the next iteration but immediately provide the correct LCC setting.
where x and y are the unknown I and Q components of the leakage signal.
Thus, the optimum LCC setting is found to be c_{opt}=−x−j y.
In contrast to the techniques described before, the detector has to be linear in amplitude for this algorithm to perform satisfactorily. The benefit of this approach is that it is very fast and may be used for changing environments as long as the leakage channel remains constant during the three measurement steps, which is the same condition as for the gradient algorithm. However, the fast algorithm requires calibration of the LCC settings, which means that for a pure LCC signal the relation between detector readings and LCC setting has to be known. A practical implementation of this calibration is explained in Section 4.1. Based on the calibration, it is possible to generate the appropriate probing signal amplitudes and finally the compensation signal c_{opt} based on Equation 5.
2.4 Direct I/Q algorithm
This is a straightforward technique which requires a receiver equipped with a vector signal detector. Additionally, the LCC settings have to be calibrated with respect to this detector. Once a leakage signal is received, the inphase and quadrature components of this leakage signal are detected in the vector detector. The only necessary step is to set the LCC I and Q values opposite to the leakage signal. The benefit of this approach is extreme speed, when compared to all other techniques. However, it is the technique with the highest hardware demands, both for the detector type and the necessary LCC calibration.
The vector detector may either be implemented in the digital domain as detector C in Figure 1 or as a separate hardware vector detector in positions A or B. The authors of [10] present a receiver structure which employs a dedicated hardware receiver in position A which is suitable for a direct I/Q detection algorithm.
2.5 Comparison of adjustment principles
Comparison of LCC adjustment techniques
Algorithm  Detector type  Linearity constraint  Number of steps  LCC calibration 

Full search  Power  None  N ^{2}  No 
Gradient search  Power  Low  3 to $\frac{3N}{2}$  Minimal 
Fast algorithm  Amplitude  High  3  Yes 
Direct I/Q  I/Q amplitude  High  1  Yes 
2.6 Detector positions
We now discuss the possible detector positions with respect to our principal RFID reader described in Figure 1. Detector A is positioned right at the beginning of the receiver. No active components precede this detector, so only the detector itself is defining its output linearity. Therefore, this position is well suited for algorithms which require a linear detector behaviour like the fast algorithm or the direct I/Q method. However, for the second, a more complex vector detector needs to be implemented. The other two algorithms will also operate properly with this detector.
Detector position B is positioned at the end of the analog receiver chain either at a low intermediate frequency or at the baseband. When compared to detector A, higher signal levels and lower frequencies are present at position B, and therefore, the implementation of the detector itself is less demanding. However, the receiver chain which precedes the detector might degrade the linearity of the detector. Therefore this position is well suited for techniques with low linearity constraint, like the full search algorithm or the gradient search approach.
Detector C in general does not require any additional hardware because it is implemented in a software. It is relatively easily implemented as a vector power detector. The drawback of this detector is the fact that the complete receiver chain including amplifiers, mixers and ADCs is passed before the detector. For linear functionality, this complete chain has to operate in the linear domain as well. This increases the requirements on the whole receiver and at the end makes the use of an LCC questionable  if the receiver operates in a linear fashion under leakage carrier conditions, why bother to implement an LCC? It still makes sense to compensate the leakage in this case because the requirements on dynamic range regarding detecting the weak received tag response under the presence of leakage are very demanding, especially when we concern the necessary ADC resolution.
3 Noise analysis
In this section, we will present a detailed noise analysis for the fast algorithm. We will derive the estimator’s bias and error variance as a function of the carrier to noise ratio (CNR). For the other algorithms, a short description follows.
As the full search algorithm searches the lattice of N^{2} LCC setting points and picks the best one, the final setting error is not only constraint on the CNR at the detector but also on the quantisation error due to the finite number of setting points. For high CNR values, the correct point will be picked with high probability, and the setting error is dominated by the quantisation error which is proportional to $\frac{1}{{N}^{2}}$ ([26], Chap. 5.6). For the low CNR regime or when N is very large, noise limits the detection of the minimum power at the optimum LCC setting point when scanning the complete I/Q plane. Since this null is rather distinct [15, 17], the noise influence is low.
For the gradient search algorithm, the noise influence is uncritical due to its iterative nature. This is of course only true if the step size is chosen small enough to guarantee convergence under noise influence.
The noise analysis for the direct I/Q algorithm is straightforward and we will use it as a reference for the fast algorithm. Since the I and Q components of the leakage signal are directly measured by an appropriate detector, the detector noise variance and bias are equal to the algorithm’s error noise variance and bias.
3.1 Analytic analysis
In this section, we expand the noise free description of the fast algorithm given in Section 2.3 for the case which includes noisy I and Q components. In an actual RFID reader implementation, many parts in the transmitter, channel, receiver, detector and possibly an ADC following the detector contribute to noise which degrades the measurements described in Equations 2 to 4. Depending on the underlying physics of these noise sources and their position in the TXRX chain, their noise has to be modelled in different ways. In the following section, we will focus on strictly white, statistically independent noise that adds to the I and Q components. Further, we focus on the estimation of the inphase component $\widehat{x}$, as these results later may easily be adapted to $\widehat{y}$.
This expectation includes x and an additive bias term. To treat the bias, we specialise our noise model: The noise of both signal components U and V is white and Gaussian and has zero mean μ_{ u }=μ_{ v }=0. The noise variances are ${\sigma}_{u}^{2}$ and ${\sigma}_{v}^{2}$. As stated before, we presume statistical independence of the I and Q noise components.
We see that the proposed fast algorithm acts as a biased estimator. Since the bias is approximately known, it can be compensated if the CNR is known as well. In most RFID applications, leakage carrier compensation is performed to reduce a large leakage signal, so high CNRs are expected. In this case, the bias may be neglected.
3.2 Monte Carlo simulations
4 Measurements
We performed measurements to compare the fast algorithm with the gradient algorithm. These measurements were based on our RFID testbed described in [27], which was controlled via a standard PC. The detailed measurement setup is described in the next section. Further, we will present the results of the pure gradient algorithm, the fast algorithm and two enhanced algorithms based on these two.
4.1 Setup
Both leakage and compensation signals were routed to the front end of our RFID receiver [27] where they combine in the first directional coupler. This summed signal is then fed through a LNA and a LPF and finally reaches the second directional coupler. Here, a part of the received signal is extracted and fed to the internal power detector and an external power metre. The internal logarithmic power detector output is routed to the testbed controller (TBC) where it is used as a source signal for the tested LCC adjustment routines. Except for the LNA chosen for its highly linear operation, it is not affected by nonlinearity of any receiver hardware component and, therefore, is comparable to detector A discussed in Section 2.6. The external power metre was used to obtain measurement data only, but not for use in the adjustment algorithms. The TBC provides 16bit ADCs to capture the power metre output signals and 12bit DACs to control the I/Q channels of CCU1 and CCU2, corresponding to 4,096 possible settings for each channel.
The receiver’s power detector provides a voltage which is logarithmically dependent on the power detector’s input power. Since the fast algorithm demands for a linear amplitude detector, we used a function to convert every voltage measurement from the TBC corresponding to a power measurement from the power detector into a number. This linearising function consists of an exponential function and additionally a multiplicative constant. This constant was chosen to result in most linear amplitude readings with respect to the output of the function. The LCC composed of CCU1 was calibrated with respect to these amplitude measurements by disconnecting the red antenna input signal in Figure 7 and by performing separate sweeps in the I and Q domains, always setting the unswept channel to zero. These sweeps were performed with a step size of 10 corresponding to 410 recorded amplitude measurements per channel. The values obtained in these measurements were stored in a lookup table and aided by interpolation enabled to set the LCC to the correct probing values c_{1} and c_{2} necessary for steps two and three of the fast algorithm and finally to c_{opt} found by Equation 5.
4.2 Measurement results
According to this definition, the isolation gain directly reveals the improvement of the used cancellation algorithm in comparison to a system without LCC usage. When expressed in decibels, the isolation gain ranges from small negative values for badly misadjusted LCCs to large positive values for properly adjusted LCCs.
For comparison, we also implemented a gradient search algorithm according to Section 2.2, where we chose the gradient finding step size to be δ=10 in general and δ=2 for LCC settings close to the optimum LCC setting point. We used a variable step size μ which was adapted proportional to $\sqrt{{\nabla}_{n}}$ according to an empirically chosen factor. Both adaption schemes aided to securely find the optimum LCC setting by reducing the step sizes close to the optimum point. The gradient search algorithm reached isolation gains ranging from 14.7 to 24.7 dB.
5 Enhanced procedures
Based on the practical and theoretical findings, we present two enhancements to the set of algorithms described in Section 2.
5.1 Fast algorithm with bipolar probing signals
Since the fast algorithm in the first step measures the leakage amplitude r, it is immediately clear after the second step if this step should be repeated with a negative probing signal, because the resulting measured amplitude in the second step is smaller than $\sqrt{2}r$ when the I component lies in the beneficial region. Using this conditional remeasurement technique, the fast algorithm’s step count stated in Table 1 is increased from three to three to five, which has an average number of four steps. Of course, it is also possible to always perform all five measurements; then, even averaging of the two estimates of the same I/Q component is possible. This possibly makes sense for leakage signals whose signal power is concentrated in the other I/Q component so that the leakage signal and probing signal are almost orthogonal to each other.
When using this technique of bipolar probing signals, the bias derived in Section 3.1 does not change as long as the statistical properties of the noise components U and V are the same; since then, Equation 15 does not depend on x or y. The variance of the standardised estimation error for medium to high CNR values for this algorithm is smaller than the standard deviation of the regular fast algorithm, as we see from our Monte Carlo simulations in Figure 3. Therefore, this improvement which we had considered to overcome limitations due to the linearity of the amplitude detector also improves the estimation in the case of noiselimited operation.
Based on the measurements presented in Figure 10, we calculate the average isolation gain ratio of the beneficial quadrant shown as the lower left quadrant in Figure 11 and get 0.48 dB. Thus, we conclude that using the bipolar probing method for the fast algorithm, we reach the isolation gain of the gradient algorithm with a mean penalty of only 0.48 dB.
5.2 Fast algorithmaided gradient algorithm
In practical RFID scenarios, many factors limit the performance of the fast algorithm, which are mainly based on nonlinear detector behaviour and imperfect LCC calibration. However, the fast algorithm may be used to aid the gradient algorithm by setting the starting point of the iterative search to the values found by the fast algorithm. We compare this fast algorithmaided gradient algorithm with our standard gradient algorithm using the same measurement setup as described in Section 4.1. Using the monostatic and bistatic antenna scenarios, we compare the necessary number of steps for the algorithms to converge. If we stick to our step definition as stated in Section 2.6, the pure gradient algorithm required 39 to 135 steps, while the aided algorithm for the same scenarios was content with 21 to 60 steps.
6 Conclusions
This contribution discussed the performance of wellknown algorithms and novel enhanced procedures for the automatic adjustment of leakage carrier cancellers in RFID readers. We briefly described three wellknown algorithms and the fast algorithm published in [25] and discussed their requirements on receiver hardware and performance in terms of their step count. Further, we carried out an analytical noise analysis for the fast adjustment algorithm and derived its bias behaviour. The presented analytic approximation of the estimator bias holds for the high CNR regime where the bias is very small and can be safely ignored. The analytical results were compared to numerical simulation studies which were used to show the estimator’s error distribution for varying CNR levels. We found that the bias at low CNR values is negligible in favour of a mode of the error which is close to zero. Thus, it was shown that for both high and low CNR regions, bias compensation of the fast algorithm is not an issue.
We demonstrated the practical performance of the fast adjustment algorithm using our unmodified RFID reader hardware platform. Although this hardware only implements a logarithmic power detector, a systematic scan of the leakage I/Q plane demonstrated that 95% of the measurements show a maximum penalty in isolation gain of 3 dB when compared to the much slower gradient search algorithm. We further proposed and discussed two enhanced procedures based on the fast algorithm. The first procedure is an extension and uses bipolar probing signals, which enables accurate LCC setting with a mean error of 0.48 dB, while the average step count is only increased to four. The second procedure is an enhancement to the gradient search algorithm by setting an improved starting point. This reduces the average step count by 72%.
Declarations
Acknowledgements
This work has been funded by the Christian Doppler Laboratory for Wireless Technologies for Sustainable Mobility. The financial support by the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged. We would further like to thank our colleague Robert Dallinger for the many inspiring and valuable discussions.
Authors’ Affiliations
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