Abstract:
Apparatus for amplifying an input signal having an input signal power includes a power amplifier, which is adapted to amplify an intermediate signal so as to generate an output signal, and which is characterized by a non-linearity. A non-linear filter is coupled to decompose the input signal into a series of input signal components, each such component proportional to a product of the input signal by a respective integer power of the input signal power, and is adapted to filter the signal components responsively to the non-linearity so as to generate the intermediate signal for input to the power amplifier.

Description:
FIELD OF THE INVENTION 
   The present invention relates generally to high-performance amplifiers for communications applications, and specifically to correction of amplifier non-linearities using predistortion. 
   BACKGROUND OF THE INVENTION 
   Modern mobile communication systems use multiple channels, closely spaced over an assigned frequency band. In order to avoid intermodulation products and spectral regrowth, both in and out of band, it is essential that radio frequency (RF) power amplifier circuits used in these systems be highly linear. A high level of linearity is also required in single-channel transmitters which transmit a wideband, variable-envelope signal, such as a CDMA signal. 
   A major source of non-linearity is distortion, which occurs due to non-linear amplitude and phase response of the amplifier, particularly as power nears the saturation level. Third-order distortion non-linearities typically give the strongest intermodulation products, but higher-order products can be significant. One method of correcting for amplifier distortion, and thus improving linearity, is predistortion, in which a controlled, non-linear distortion is applied to the amplifier input signals. Predistortion circuitry is designed to give non-linear amplitude and phase characteristics complementary to the distortion generated by the amplifier itself, so that ideally, the distortion is canceled in the amplifier output over the entire signal bandwidth. A feedback connection is generally provided from the amplifier output to the predistortion circuitry, for use in adjusting predistortion coefficients for optimal linearization. 
   Various schemes have been proposed for digital-domain predistortion of RF power amplifier input signals. For example, U.S. Pat. No. 6,141,390, whose disclosure is incorporated herein by reference, describes a system that uses a straight inverse modeling scheme with orthogonal predictor variables to determine the inverse of the distortion caused by a power amplifier of a RF transmitter. The predistorter system determines complex predistorter coefficients based on the inverse modeling scheme, and stores the coefficients in a look-up table (LUT). The coefficients from the LUT are then used as the tap weights of a non-linear digital filter implementing the predistorter. 
   Another digital predistortion system is described in U.S. Pat. Nos. 6,549,067 and 6,580,320, whose disclosures are also incorporated herein by reference. A predistortion circuit samples the input to a non-linear amplifier, and multiplies the input by itself using mixers in order to generate various orders of distortion. Filters/time delay means are incorporated into the paths that generate the orders of distortion in order to produce phase and/or amplitude variation with frequency. The distortion orders are summed to provide the predistortion. The filter/time delay means can be implemented by adaptive filters in digital signal processing (DSP) circuits, which sample the output of the amplifier being linearized in order to obtain feedback for adapting the filter(s). The in-phase and quadrature parts of the input are separately digitally predistorted. 
   SUMMARY OF THE INVENTION 
   Embodiments of the present invention provide an improved digital predistortion circuit, which operates on the input signal to a non-linear power amplifier in order to linearize the amplifier output and in addition performs linear equalization. The predistortion circuit comprises a non-linear filter, which includes a power expander for decomposing the input baseband signal, X, into a series of signal components. Each of the components is proportional to a product of the input signal by an integer power of the input signal power envelope |X| 2 . These signal components are filtered, using filter coefficients that are adaptively determined in response to the non-linearity of the power amplifier. The filtered signal components are then combined to provide an intermediate, predistorted signal for input to the power amplifier. This decomposition of signal non-linearity in terms of the input signal power gives a faithful model of the non-linear characteristics of the power amplifier and allows the non-linearity to be corrected by the predistortion circuit with low computational complexity, relative to methods known in the art. 
   In some embodiments of the present invention, the filter coefficients are determined by an adaptation circuit, which operates by inverse modeling of the power amplifier non-linearity. The output of the power amplifier is sampled and decomposed by a power expander in the adaptation circuit, as in the non-linear filter. The components of the sampled output signal are then filtered by the adaptation circuit in a similar manner to the filtering applied by the non-linear filter to the input signal. The filter coefficients in the adaptation circuit are adjusted by an adaptive process until the filter output matches the intermediate signal that is generated by the non-linear filter (as input to the power amplifier). These adapted filter coefficients, representing the inverse of the amplifier non-linearity, are then applied by the non-linear filter in order to provide the appropriate predistortion to the intermediate signal. 
   In some embodiments of the present invention, the non-linear filter also comprises a weighted linear combiner, which generates signal elements having minimal cross-correlation over a given period, as linear combinations of the signal components produced by the power expander. Each of the substantially uncorrelated signal elements is filtered, typically using the filter coefficients determined by the adaptation circuit, which comprises a similar weighted linear combiner. Treatment of the signal elements in this manner is useful in easing the operation of the adaptation technique and attaining faster convergence of the filter coefficients used in the non-linear filter. The adaptation circuit may also be used to adaptively determine weighting coefficients, for use by the linear combiner in generating the signal elements, as well as in selecting the orders (i.e., the integer powers) of the signal components to be generated by the power expander. 
   There is therefore provided, in accordance with an embodiment of the present invention, apparatus for amplifying an input signal having an input signal power, including:
         a power amplifier, which is adapted to amplify an intermediate signal so as to generate an output signal, and which is characterized by a non-linearity; and   a non-linear filter, which is coupled to decompose the input signal into a series of input signal components, each such component proportional to a product of the input signal by a respective integer power of the input signal power, and which is adapted to filter the signal components responsively to the non-linearity so as to generate the intermediate signal for input to the power amplifier.       

   In a disclosed embodiment, the non-linear filter is adapted to combine the input signal components so as to generate substantially uncorrelated input signal elements, and to filter each of the substantially uncorrelated input signal elements so as to compensate for the non-linearity. Typically, the non-linear filter is adapted to generate the substantially uncorrelated input signal elements by linear combination of the input signal components, using weighting coefficients determined so as to minimize a correlation between the signal elements, and to sum the filtered substantially uncorrelated input signal elements in order to generate the intermediate signal. 
   Additionally or alternatively, the apparatus includes an adaptation circuit, which is arranged to decompose the output signal so as to generate substantially uncorrelated output signal components, and to process the substantially uncorrelated output signal components in order to determine filter coefficients to be applied by the non-linear filter in filtering the substantially uncorrelated input signal elements. Typically, the adaptation circuit is arranged to filter the substantially uncorrelated output signal components, and to compare the filtered substantially uncorrelated output signal components to the intermediate signal in order to determine the filter coefficients to be applied by the non-linear filter to each of the substantially uncorrelated input signal components. For this purpose, the adaptation circuit may be arranged to compute successive differences between the intermediate signal and the filtered substantially uncorrelated output signal components, in order to determine a respective error signal for use in adaptively computing the filter coefficients to be applied to each of the substantially uncorrelated input signal components. Additionally or alternatively, the non-linear filter is adapted to generate the substantially uncorrelated input signal elements by linear combination of the input signal components, and the adaptation circuit is arranged to adaptively determine weighting coefficients to be applied by the non-linear filter in generating the substantially uncorrelated input signal elements and to be applied by the adaptation circuit in generating the substantially uncorrelated output signal elements. 
   In further embodiments, the adaptation circuit is coupled to receive and process samples of the output signal so as to produce an inverse model of the non-linearity of the power amplifier, and to determine filter coefficients to be applied by the non-linear filter to the signal components responsively to the inverse model. Typically, the adaptation circuit is arranged to filter the samples of the output signal responsively to the inverse model, and is further coupled to compare the intermediate signal to the filtered samples of the output signal in order to determine the filter coefficients. In one embodiment, the adaptation circuit is arranged to determine the filter coefficients adaptively using a least mean square (LMS) adaptation process, so as to minimize an error signal based on a comparison of the intermediate signal to the filtered samples of the output signal. Additionally or alternatively, the adaptation circuit is further arranged to determine adaptively the input signal components into which the input signal is to be decomposed for filtering by the non-linear filter. 
   In some embodiments, the apparatus includes a sampling channel, which couples the output of the power amplifier to the adaptation circuit, wherein the adaptation circuit includes a channel compensator, which is adjustable so as to compensate for distortion introduced in the samples of the output signal by the sampling channel. In one embodiment, the apparatus includes a calibrator circuit, which is adapted to inject a calibration signal into the sampling channel, so as to determine the distortion introduced in the samples, for use in adjusting the channel compensator. Typically, the calibrator circuit includes a digital logic driver, which generates a square wave of known amplitude and frequency, and a bandpass filter, which filters the square wave so as to provide the calibration signal. 
   Typically, the input signal and the intermediate signal are baseband signals, and the apparatus includes an upconverter for upconverting the intermediate signal to a radio frequency (RF) for input to the power amplifier, and wherein the non-linear filter is adapted to apply a low-pass filtering function to the signal components. 
   There is also provided, in accordance with an embodiment of the present invention, a method for amplifying an input signal having an input signal power, using a power amplifier characterized by a non-linearity, the method including:
         decomposing the input signal into a series of input signal components, each such component proportional to a product of the input signal by a respective integer power of the input signal power;   filtering the signal components responsively to the non-linearity so as to generate an intermediate signal for input to the power amplifier; and   amplifying the intermediate signal using the power amplifier.       

   There is additionally provided, in accordance with an embodiment of the present invention, a receiver, including:
         a sampling channel, which is adapted to receive and digitize an analog input signal, so as to generate a sequence of digital samples of the input signal;   a calibration circuit, which includes:
           a digital logic device, which is adapted to generate a square wave of known amplitude and frequency; and   a bandpass filter, which is coupled to filter the square wave so as to provide a calibration signal for input to the sampling channel, for use in measuring a distortion introduced by the sampling channel; and   
           a channel compensator, which is coupled to operate on the digital samples so as to compensate for the distortion measured using the calibration circuit.       

   Typically, the digital logic device comprises a temperature-compensated emitter-coupled logic (ECL) device, and the bandpass filter comprises a printed circuit filter. In a disclosed embodiment, the calibration circuit includes a frequency synthesizer, which is adapted to generate a spectrum of one or more frequency tones for input to the digital logic device, so as to cause the digital logic device to generate the square wave at the known frequency. 
   The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram that schematically illustrates apparatus for RF power amplification, in accordance with an embodiment of the present invention; 
       FIG. 2  is a block diagram that schematically illustrates a non-linear filter, in accordance with an embodiment of the present invention; 
       FIG. 3  is a block diagram that schematically illustrates a power expander, in accordance with an embodiment of the present invention; 
       FIG. 4  is a block diagram that schematically illustrates an adaptation circuit, in accordance with an embodiment of the present invention; 
       FIG. 5  is a block diagram that schematically shows a detail of an adaptation circuit, in accordance with an alternative embodiment of the present invention; and 
       FIG. 6  is a block diagram that schematically illustrates a calibrator circuit for use in calibrating a receiver, in accordance with an embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF EMBODIMENTS 
     FIG. 1  is a block diagram that schematically illustrates apparatus  20  for power amplification of an input signal X(t), in accordance with an embodiment of the present invention. Apparatus  20  is built around a RF power amplifier  22 , which generates a RF output signal U(t). Generally speaking, the input signal X(t) is band-limited and has a limited, known envelope peak-to-average ratio (EPAR). Typically, X(t) is a digital baseband signal, but the input signal to apparatus  20  may alternatively be an intermediate-frequency (IF) signal. Although certain linearization techniques applied in apparatus  20  are described hereinbelow with reference to baseband signal processing, these techniques may also be applied, mutatis mutandis, to IF signals, as will be apparent to those skilled in the art. Similarly, although amplifier  22  is assumed in this embodiment to generate RF output signals for transmission over the air (in a cellular communication network, for example), the principles of the present invention may likewise be applied to linearization of other types of amplifiers, as well as of other types of non-linear circuit elements. 
   Amplifier  22  is characterized by a certain non-linearity, which is typically not known precisely in advance and may change over time. To correct for this non-linearity, a non-linear filter  24  predistorts the input signal X(t), using a non-linear filtering function that is approximately the inverse of the amplifier non-linearity. Filter  24  outputs an intermediate, predistorted signal Y(t). This signal is typically upconverted to a real IF signal by a digital upconverter  25 , which is then converted to analog form by a digital/analog converter (DAC)  26 . The analog IF signal is then upconverted to the appropriate RF range by an upconverter  28 , driven by a local oscillator  30  operating at the appropriate carrier frequency. (Alternatively, the I and Q components of the complex baseband signal may be converted to analog form prior to upconversion. In this case, carrier leakage and I/Q mismatch of the analog circuits are preferably calibrated and corrected for by appropriate digital processing of the baseband signal prior to D/A conversion.) The RF signal is amplified by amplifier  22  to generate the output signal U(t), which is then typically transmitted over the air. 
   A portion of the output of amplifier  22  is tapped off and downconverted by a downconverter  32 , which typically operates at a known frequency offset relative to the frequency of upconverter  28 , in order to facilitate the use of a real frequency scheme. In this case, a single analog/digital converter (ADC)  34  may be used to sample and digitize the downconverted output signal. The digitized samples are input to an adaptation circuit  36 , which compares the sampled output signal to the intermediate signal Y(t) in order to estimate the distortion engendered by amplifier  22  (including distortion caused by DAC  26  and upconverter  28 ). In the embodiment described below, adaptation circuit  36  creates an inverse model of this distortion, in order to determine filter coefficients that will transform the output U(t) into the intermediate signal Y(t). These filter coefficients are then applied by non-linear filter  24  to predistort the input signal X(t). A calibrator  38  is used to calibrate the response of the sampling channel leading to the adaptation circuit, as described further hereinbelow. 
     FIG. 2  is a block diagram that schematically shows details of non-linear filter  24 , in accordance with an embodiment of the present invention. A power expander  40  generates power components of input signal X(t), by mixing the input signal with a series of integer powers of the input signal power envelope, |X| 2 . Details of this power expander are shown below in  FIG. 3 . The power expansion is used to model an inverse of the non-linearity of amplifier  22 . Alternatively, other types of expansions, as are known in the art, may be used in place of the power expansion X, X|X| 2 , X|X| 4 , . . . , X|X| 2N  in order to model the amplifier non-linearity. For example, expander  40  may perform a Volterra expansion of the input signal. 
   The power components X, X|X| 2 , X|X| 4 , . . . , X|X| 2N  generated by expander  40  are input to an weighted linear combiner  44 , also referred to as a decorrelator, which generates signal elements V 0 , V 1 , V 2 , . . . , V N  as a linear combination of the power components: 
                   V   i     =       ∑     j   =   0       i   -   1       ⁢       a   ij     ⁢     X   j                 (   1   )               
Typically, the weighting coefficients a ij  are chosen so as to minimize the cross-correlation between the different signal elements V i  over a certain number of samples N+M of the input signal X(t). This correlation condition may be expressed in terms of requiring a ij  to satisfy (for stationary signals) the following condition for all i and for j=0, 1, . . . , i−1:
 
                   a   ij     =     arg   ⁢           ⁢   min   ⁢     {       ∑     k   =     -   N       M     ⁢       w     i   ⁡     (     k   +   N     )         ⁢            r       v   i     ,     v   j         ⁡     (     k   ,     a   ij       )                }               (   2   )               
Here r V     i     ,v     j   (k,a ij ) is the cross-correlation of V i  with V j  at a relative lag k, and W i(k+N)  is a weighting function, which is chosen empirically. This criterion gives signal elements V 0 , V 1 , V 2 , . . . , V N  that are substantially uncorrelated, in the sense that the mutual influence of the different signal elements in the non-linearity of amplifier  22  is minimized.
 
   Alternatively or additionally, power expander  40  and linear combiner  44  may apply other signal correlation functions and criteria, as are known in the art. For example, the signal power components may be combined using Hermite polynomials, or Laguerre functions may be used in place of the power expander and linear combiner. 
   The coefficients a ij  are determined by solving equation (2) using adaptation circuit  36 . The coefficients determined by circuit  36  are then loaded into linear combiner  44 , as well as being used in adaptation circuit  36 , as described below. Periodically, the adaptation circuit may adaptively recompute and update the coefficients. 
   The signal elements V 0 , V 1 , V 2 , . . . , V N  are filtered by respective adaptive filters  46  in order to generate predistorted signal elements Y 0 , Y 1 , Y 2 , . . . , Y N . Filters  46  typically comprise FIR filters, whose filter coefficients are determined by adaptation circuit  36 , as described below. Although combiner  44  and filters  46  are shown, for the sake of conceptual clarity, as separate functional elements in  FIG. 2 , in practice filters  46  may be configured to perform the function of combiner  44 , as well. The predistorted signal elements Y 0 , Y 1 , Y 2 , . . . , Y N  are then summed by an adder  48  to give the predistorted intermediate signal Y(t). 
   Typically, in order to process the input signal X(t) with sufficient speed, non-linear filter  24  comprises dedicated, hardware-based signal processing elements. For example, filter  24  may be implemented using one or more custom or semi-custom gate arrays and/or programmable digital signal processor chips and/or a dedicated ASIC. On the other hand, the adaptation process carried out by adaptation circuit  36  may proceed off-line, as described below, at substantially lower speeds. Therefore, the functions of adaptation circuit  36  may be implemented in software on a microprocessor. Other hardware and software implementations of the elements of apparatus  20  will be apparent to those skilled in the art and are considered to be within the scope of the present invention. 
     FIG. 3  is a block diagram that schematically shows details of power expander  40 , for operation on the baseband signal X, in accordance with an embodiment of the present invention. This design of the power expander is based on modeling the narrowband RF input signal to amplifier  22  as x(t)=A(t)cos(ωt+φ(t)). This signal can be represented as the upconversion of the complex baseband signal X(t)=A(t)·exp(jφ(t)): 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   Assuming amplifier  22  to be band-limited, the amplifier rejects signals at frequency 2ω 0  and higher, so that only the first harmonic zone is of interest. The first harmonic zone is affected only by odd-order intermodulations. Therefore, for any odd n, 
                           x   n     ⁡     (   t   )       =       ⁢           A   n     ⁡     (   t   )       ⁢       cos   n     ⁡     (       ω   ⁢           ⁢   t     +     φ   ⁡     (   t   )         )         ⁢     ∝   bpf     ⁢         A   n     ⁡     (   t   )       ⁢     cos   ⁡     (       ω   ⁢           ⁢   t     +     φ   ⁡     (   t   )         )                       =       ⁢         A     n   -   1       ⁡     (   t   )       ⁢     x   ⁡     (   t   )                     =       ⁢     Re   ⁢     {       X   ⁡     (   t   )       ⁢     |     n   -   1       ⁢       X   ⁡     (   t   )       ·     exp   ⁡     (     j   ⁢           ⁢   ω   ⁢           ⁢   t     )           }                     (   4   )               
The output signal from the amplifier U(t) can thus be modeled in terms of a power expansion in |X(t)| n−1 X(t).
 
   This model of the amplifier non-linearity is reflected in the structure of power expander  40  shown in  FIG. 3 . The input signal X(t) is passed to a power computation circuit  50 , which multiplies the signal by its complex conjugate to give the power envelope |X| 2 . The input signal is then mixed with the power envelope by a mixer (or multiplier)  52 , to give the third-order power component X|X| 2 . Similar steps of multiplication and mixing proceed to generate the higher-order power components, as shown in the figure. The number of power orders to compute may be determined adaptively by adaptation circuit  36 , based on actual decomposition of the sampled output signal U(t). 
     FIG. 4  is a block diagram that schematically shows details of adaptation circuit  36 , in accordance with an embodiment of the present invention. The sampled, downconverted signals received by circuit  36  from the output of amplifier  22  are delayed by a variable delay line  58 , which is set so as to reduce the length of adaptive filters  66  that are used to process the signals subsequently, as described below. The signals are then filtered by a channel compensator  59 , which compensates for any linear amplitude distortion that is introduced into output signals U(t) by the sampling channel through which the adaptation circuit receives the output samples. This sampling channel typically comprises downconverter  32  and ADC  34 , and may comprise other components, as well. The distortion of the sampling channel may be measured by injecting a known calibration signal at the output of amplifier  22  prior to beginning operation of the amplifier, using calibrator  38 , and measuring the sampled input to the adaptation circuit in response to the known calibration signal. This measurement is then used to calibrate compensator  59 . 
   The sampled, compensated output signals are next separated into power components by a power expander  60 , and are then processed by a weighted linear combiner  64  to yield a set of signal elements V 0 , V 1 , V 2 , . . . , V N  with minimal cross-correlation. These operations are substantially similar to those carried out by expander  40  and linear combiner  44  in non-linear filter  24 , as described above. Note, however, that in adaptation circuit  36 , the signal elements V 0 , V 1 , V 2 , . . . , V N  represent the output signal U(t), rather than the input signal X(t). 
   Each of the signal elements V 0 , V 1 , V 2 , . . . , V N  is processed by a respective adaptive filter  66 , which is typically implemented as a FIR filter with an adaptation controller, as is known in the art. An adder  72  sums the filtered signal elements, and subtracts the intermediate signal Y(t) from the sum to generate an error signal input to filters  66 . Alternatively, each element Y 0 , Y 1 , Y 2 , . . . , Y N  may be subtracted from the output of the corresponding filter  66  to generate a respective error signal. Any suitable adaptation algorithm, such as LMS adaptation, may be applied in generating the coefficients of filters  66 . The adaptation creates an overall, combined filter response that is the inverse of the non-linear response of amplifier  22 . De-correlation of signal elements V 0 , V 1 , V 2 , . . . , V N  by linear combiner  64  is useful in filter adaptation, as it effectively decouples the process of convergence of the individual filters  66 . As a result, the adaptation process is computationally simpler and generally converges more quickly. In order to perform adaptation in circuit  36  on narrowband signals, artificial constraints may be added to the signals that are received from the amplifier output. 
   When the coefficients of filters  66  have converged, adaptation circuit  36  transfers the coefficient values to non-linear filter  24  for application in filters  46 . Adaptation circuit  36  typically continues operating thereafter in order to adapt to any changes that occur in the distortion profile of amplifier  22 . When the adaptation circuit determines that the optimal coefficients have changed substantially from their previous values, it conveys the new coefficient values to non-linear filter  24 . The adaptation circuit may similarly adapt and update the range of powers to be generated by power expander  40  and the weighting coefficients to be applied by linear combiner  44 . 
     FIG. 5  is a block diagram showing elements of adaptation circuit  36 , in accordance with an alternative embodiment of the present invention. In this case, each filter  66  receives its own error signal from a respective adder  74 . The adders are arranged to compute successive differences between the intermediate signal Y(t) and the outputs of the filters. Thus, the error signal to the lowest-order filter (which processes V 0 ) is the difference between the filter output and the intermediate signal Y(t) from non-linear filter  24 . The error signal to the next filter (which processes V 1 ) is the difference between the output of this filter and the error signal to the preceding filter, and so on down the line. This embodiment takes advantage of the de-correlation of signal elements V 0 , V 1 , V 2 , . . . , V N , which renders these elements substantially uncorrelated. 
     FIG. 6  is a block diagram that schematically shows details of calibrator  38 , in accordance with an embodiment of the present invention. Calibrator  38  comprises a crystal oscillator (TCXO)  80 , which generates a output to a frequency synthesizer  82 . In the present embodiment, synthesizer  82  comprises a phase-locked loop (PLL), which generates a pure tone of a desired frequency in the operating range of amplifier  22 . The synthesizer is typically operated at a number of different frequencies during the calibration procedure in order to generate a calibration curve for the sampling channel as a function of the frequency. Alternatively, synthesizer  82  may be configured to generate a pseudo-noise (PN) sequence, typically at a rate of about one-third the center frequency of the amplifier, in order to generate a spectrum of multiple tones simultaneously, with known phases and amplitudes. 
   The frequency signal generated by synthesizer  82  is input to a fast digital logic driver  84 , typically comprising a high-speed ECL (emitter-coupled logic) buffer with temperature compensation. Driver  84  outputs a square wave at the input frequency with short rise and fall times and very stable amplitude. For example, the 100EP16 driver made by ON Semiconductor Corp. (Phoenix, Ariz.) is capable of generating a square wave at 2.1 GHz with amplitude stability &lt;0.1 dB within its specified range of operating temperatures. Alternatively, for higher frequencies, a SiGe device, such as the ON Semiconductor NBSG16 driver, may be used. 
   The output of driver  84  is filtered by a bandpass filter  86 , in order to pass the fundamental frequency and eliminate the harmonics from the square wave. (Alternatively, the filter may be configured to pass the third harmonic, for example, and eliminate the fundamental frequency and higher harmonics.) A printed circuit filter, formed by conducting traces printed on a substrate, as is known in the art, has been found to give good results for this purpose, and is relatively insensitive to temperature variations. Typically, for a center frequency of 2.1 GHz, a filter bandwidth of about 200 MHz has been found to give good results. Variations in the filter response over the operating band of amplifier  22  may be measured in advance, and then applied in calculating the calibration curve of the sampling channel. 
   Calibrator  38  thus gives a very stable calibration signal, of known amplitude and frequency, using inexpensive, off-shelf digital components. The accurate calibration of the sampling channel that can be achieved using this calibrator is particularly important in precisely setting channel compensator  59 , to ensure that adaptation circuit  36  and non-linear filter  24  provide the desired level of linearity correction. Furthermore, this sort of calibrator may also be used to good effect in calibrating sampling channels and receivers of other types. 
   It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.