Patent Publication Number: US-8532237-B2

Title: Correction of alternating I/Q imbalance and frequency offset impairments

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to communication systems, and particularly to methods and systems for compensating for In-phase/Quadrature (I/Q) imbalance and frequency offset impairments. 
     BACKGROUND OF THE INVENTION 
     Many Radio Frequency (RF) transmitters and receivers use In-phase/Quadrature (I/Q) configurations, in which a signal is represented by two orthogonal signal components. In some cases, however, the transmitter and/or receiver circuitry introduce I/Q imbalance impairments, which distort the signal and degrade the reception performance. Reception performance may also be degraded by frequency offsets introduced by the transmitter and/or receiver. 
     Various techniques for compensating for I/Q imbalance and frequency offset impairments are known in the art. For example, U.S. Pat. No. 7,433,298, whose disclosure is incorporated herein by reference, describes techniques for correcting residual frequency offset, phase noise and I/Q imbalance in Orthogonal Frequency Division Multiplexing (OFDM) communications. The disclosed techniques compensate for I/Q imbalance based on most likely estimates of the I/Q imbalance between the I and Q components of a baseband signal. Most likely estimates of the common phase error are sometimes used to compensate for the initial channel estimates. 
     PCT International Publication WO 2009/082457, whose disclosure is incorporated herein by reference, describes a signal processing method and system for compensation of I/Q imbalance for a direct conversion packet-switched OFDM communications system. Both frequency-dependent I/Q imbalance and frequency-independent cases are considered, covering both wideband and narrowband modulation. 
     U.S. Pat. No. 7,181,205, whose disclosure is incorporated herein by reference, describes a self-calibration procedure that corrects the amplitude and phase errors of the modulation and demodulation in a transceiver. A test signal is applied to the baseband input of the transmitter, and the output of the modulator is looped back to the input of the demodulator. The amplitude and phase errors of the resulting signal at the baseband output of the receiver are detected, and the contributions of the transmitter and receiver to the errors are separated and resolved into amplitude and phase components. Adjustments are then made to the amplitude and phase balance in the transmit and receive signal paths to correct the errors. 
     SUMMARY OF THE INVENTION 
     An embodiment of the present invention that is described herein provides method for communication, including: 
     receiving a signal, which carries data bits and is distorted by multiple impairments including one or more frequency offsets and one or more In-phase/Quadrature (I/Q) imbalances; 
     producing a corrected signal by applying to the received signal a sequence of corrections to compensate for the impairments, the sequence including a first and a third correction of one correction type and a second correction of another correction type intervening between the first and third corrections in the sequence, the correction types consisting of frequency offset corrections and I/Q imbalance corrections; and 
     extracting the data bits from the corrected signal. 
     In some embodiments, applying the sequence includes applying the corrections for the respective impairments in reverse order to an order in which the impairments distort the signal. In an embodiment, producing the corrected signal includes calculating at least one of the corrections in the sequence based on the extracted data bits. Calculating the corrections may include generating an error signal for setting a given correction in the sequence based on the extracted data bits, processing the error signal so as to reverse a subset of the corrections that are subsequent to the given correction is the sequence, and setting the given correction based on the processed error signal. 
     In a disclosed embodiment, the second correction includes an I/Q imbalance correction and the third correction includes a frequency offset correction, and producing the corrected signal includes calculating an error signal based on the extracted data bits, de-rotating the error signal to compensate for the third correction, and calculating the second correction based on the de-rotated error signal. In another embodiment, the first and third corrections include respective first and second frequency offset corrections, the second correction includes an I/Q imbalance correction, and producing the corrected signal includes applying the first and second frequency offset corrections jointly to the received signal, applying the I/Q imbalance correction to the signal after applying the first and second frequency offset corrections, and rotating the I/Q imbalance correction to compensate for the second frequency offset correction. 
     In another embodiment, the impairments further include at least one I/Q delay mismatch, and producing the corrected signal includes compensating for the I/Q delay mismatch by applying an I/Q delay mismatch correction in the sequence. In yet another embodiment, at least one of the frequency offsets is caused by a deviation between a first reference clock used in a transmitter transmitting the signal and a second reference clock used in a receiver receiving the signal. In still another embodiment, at least one of the frequency offsets is caused by a digital frequency offset in a transmitter transmitting the signal. 
     In some embodiments, the method further includes producing the signal by: 
     in a first transmitter unit, up-converting an input signal to produce an Intermediate Frequency (IF) signal based on a first reference clock, so as to cause a first I/Q imbalance; 
     sending the IF signal from the first transmitter unit to a second transmitter unit; and 
     in the second transmitter unit, down-converting the IF signal based on a second reference clock, and re-up-converting the signal to Radio Frequency (RF), so as to cause a frequency offset, followed by a second I/Q imbalance. 
     In an embodiment, the signal is produced without transferring a clock signal between the first and second transmitter units. 
     In some embodiments, receiving the signal includes: 
     in a first receiver unit; down-converting a Radio Frequency (RF) signal and up-converting the down-converted signal to produce an Intermediate Frequency (IF) signal based on a first reference clock; 
     sending the IF signal from the first receiver unit to a second receiver unit; and 
     in the second receiver unit, down-converting the IF signal based on a second reference clock, so as to cause a frequency offset followed by a second I/Q imbalance. 
     In an embodiment, the signal is received without transferring a clock signal between the first and second receiver units. 
     There is additionally provided, in accordance with an embodiment of the present invention, a communication apparatus, including: 
     compensation circuitry, which is configured to receive a signal that carries data bits and is distorted by multiple impairments including one or more frequency offsets and one or more In-phase/Quadrature (I/Q) imbalances, and to produce a corrected signal by applying to the received signal a sequence of corrections to compensate for the impairments, the sequence including a first and a third correction of one correction type and a second correction of another correction type intervening between the first and third corrections in the sequence, the correction types consisting of frequency offset corrections and I/Q imbalance corrections; and 
     a slicer unit, which is configured to extract the data bits from the corrected signal. 
     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 a communication system, in accordance with an embodiment of the present invention; 
         FIGS. 2 and 3  are block diagrams that schematically illustrate demodulators that compensate for I/Q imbalance and frequency offset impairments in the system of  FIG. 1 , in accordance with embodiments of the present invention; 
         FIG. 4  is a block diagram that schematically illustrates a transmitter, in accordance with an embodiment of the present invention; 
         FIG. 5  is a block diagram that schematically illustrates a demodulator that compensates for I/Q imbalance and frequency offset impairments in the transmitter of  FIG. 4 , in accordance with an embodiment of the present invention; 
         FIG. 6  is a block diagram that schematically illustrates a receiver, in accordance with an embodiment of the present invention; 
         FIG. 7  is a block diagram that schematically illustrates a demodulator that compensates for I/Q imbalance and frequency offset impairments in the receiver of  FIG. 6 , in accordance with an embodiment of the present invention; and 
         FIG. 8  is a flow chart that schematically illustrates a method for correcting I/Q imbalance and frequency offset impairments, in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Overview 
     In a typical Radio Frequency (RF) communication system, a transmitter produces a modulated signal that carries data, and transmits the signal to a receiver. The receiver processes the received signal so as to recover the data. Transmitters and receivers often represent the signal using two orthogonal signal components, referred to as In-phase (I) and Quadrature (Q) components. Various digital and analog transmitter and receiver components (e.g., digital-to-analog and analog-to-digital converters, quadrature modulators and demodulators, filters and mixers) process the signal by operating on the I and Q components. 
     Transmitter and receiver components may introduce imbalance between the I and Q signal components. Generally, I/Q imbalance may comprise gain imbalance (different gain applied to the I and Q components), phase imbalance (non-orthogonality between the I and Q components), delay or group delay mismatch between the I and Q components, and/or DC offset (a constant offset in the I and/or Q components). All of these impairments are collectively referred to herein as I/Q imbalance. In addition, the transmitter and receiver often introduce frequency offset into the signal, such as when the transmitter and receiver use different reference clocks. Excessive I/Q imbalance and frequency offset may distort the spectral shape of the transmitted signal and/or the signal received by the receiver, and therefore degrade the receiver performance. 
     In some communication systems, the signal is subjected to an alternating sequence of I/Q imbalance and frequency offset impairments as it is processed by the transmitter and/or receiver. For example, the signal may initially be up-converted in the transmitter by an I/Q modulator that introduces I/Q imbalance, then transmitted to the receiver and received with a certain frequency offset, and then down-converted by an I/Q demodulator that introduces additional I/Q imbalance. 
     Generally, I/Q imbalance impairments and frequency offset impairments are not commutative. In other words, two I/Q imbalance impairments cannot generally be modeled by a single time-invariant I/Q imbalance if there is an intervening frequency offset. Similarly, two frequency offset impairments cannot generally be modeled by a single time-invariant frequency offset if there is an intervening I/Q imbalance. Therefore, known compensation schemes that compensate for a single I/Q imbalance and/or a single frequency offset are usually ineffective for signals that are distorted by interleaved I/Q imbalance and frequency offset impairments. 
     Embodiments of the present invention that are described hereinbelow provide improved receiver configurations, which compensate for alternating sequences of I/Q imbalance and frequency offset impairments. In some embodiments, a demodulator at the receiver comprises a cascade of I/Q correction and frequency correction modules, which is arranged in reverse order to the order of the impairments that distort the signal. The demodulator thus applies a sequence of alternating I/Q imbalance and frequency offset corrections. 
     Consider, for example, a signal that is first subjected to a frequency offset denoted ΔF 1 , then to an I/Q imbalance denoted ΔIQ, and then to another frequency offset denoted ΔF 2 . A demodulator that compensates for this distortion may comprise a frequency correction module for correcting ΔF 2 , followed by an I/Q correction module that corrects ΔIQ, and followed by another frequency correction module that corrects ΔF 1 . In some embodiments, a sequence of two frequency offsets with an intervening I/Q imbalance is compensated for by a single frequency correction module, followed by an I/Q correction module whose correction varies over time as a function of the first frequency offset. 
     Typically, the corrections applied by the different I/Q correction and frequency correction modules are decision-directed, i.e., depend on the data that is extracted from the signal by the receiver. Alternatively, however, some corrections may be computed using blind adaptation. In some embodiments, the corrections are computed in an adaptive process, such as using Least Mean Squares (LMS) adaptation. 
     The compensation schemes described herein are applicable to any suitable communication system in which the signal is subjected to an alternating sequence of I/Q imbalance and frequency offset impairments. Several example system configurations and corresponding compensation schemes are described herein. By using the disclosed techniques, the receiver is able to compensate for complex combinations of I/Q imbalance and frequency offset with high accuracy, and therefore demodulate the data with high reliability. 
     Example System Configuration 
       FIG. 1  is a block diagram that schematically illustrates a communication system  20 , in accordance with an embodiment of the present invention. System  20  comprises a transmitter  24 , which transmits to a receiver  28 . A system of this sort can be used in a variety of applications, such as in microwave or millimeter-wave links. In the configuration of  FIG. 1  (as well as in subsequent figures), only transmitter and receiver elements that are necessary for demonstrating the disclosed techniques are shown. Many transmitter and receiver elements, which are not mandatory for understanding the principles of the disclosed techniques, are not shown in the figures for the sake of clarity. 
     Transmitter  24  accepts data for transmission from a host system or other source. The transmitter comprises a mapper  32 , which maps the bits of the incoming data onto symbols in accordance with a certain modulation scheme. Any suitable modulation scheme can be used, such as, for example, Binary Phase Shift Keying (BPSK), Quaternary Phase Shift Keying (QPSK) or Quadrature Amplitude Modulation (QAM). Typically, mapper  32  selects the symbols from a predefined symbol constellation, which is defined in the two-dimensional In-phase/Quadrature (I/Q) plane. Mapper  32  thus outputs a sequence of complex (I/Q) symbols that represent the data for transmission. 
     A transmitter frequency correction module  36  applies a certain frequency offset to the sequence of symbols produced by mapper  32 . This frequency offset is used, for example, when subsequent frequency conversion operations in the transmitter are performed at a finite frequency granularity. For example, a Local Oscillator (LO) signal used for up-conversion in the transmitter may be produced at a finite frequency granularity. Module  36  can be used to compensate for the resulting frequency inaccuracy. The frequency offset applied by module  36  is denoted ΔF 1 . Module  36  typically comprises digital circuitry. Any suitable circuitry that is capable of applying frequency offset to a digital signal, such as a Numerically-Controlled Oscillator (NCO), can be used for this purpose. 
     The digital signal produced by module  36  is typically converted into a pair of analog baseband I and Q signal components using a pair of digital-to-analog converters (not shown). An analog I/Q modulator  40  converts the baseband signals into a single I/Q Intermediate Frequency (IF) signal. I/Q modulator  40  introduces a certain I/Q imbalance into the IF signal. This I/Q imbalance is denoted ΔIQ, and it may comprise gain imbalance, phase imbalance and/or DC offset. 
     An up-converter  44  up-converts the IF signal to a suitable Radio Frequency (RF). Up-converter  44  typically comprises one or more mixers, which up-convert the IF signal by mixing it with one or more LO signals (denoted TX LO). As noted above, the circuitry that produces the LO signals (e.g., a frequency synthesizer) may have a finite frequency granularity, which is compensated for by the frequency offset ΔF 1  applied by module  36 . The RF signal produced by up-converter  44  is filtered, amplified and transmitted toward receiver  28  via a transmitter antenna  48 . 
     In receiver  28 , the signal is received by a receiver antenna  52  and down-converted by a down-converter  56 . Down-converter  56  typically comprises one or more mixers, which down-convert the RF signal to baseband by mixing it with one or more LO signals (denoted RX LO). In many practical scenarios, the up-conversion by up-converter  44  and the down-conversion by down-converter  56  introduce some frequency offset into the baseband signal at the down-converter output. This frequency offset (denoted ΔF 2 ) may be caused, for example, by a frequency difference between the reference clocks that are used for generating the LO signals in the transmitter and the receiver, or for any other reason. The signal produced by down-converter  56  is digitized by one or more analog-to-digital converters (not shown). The digital signal is then demodulated by a demodulator  60 , which extracts the data from the signal. The extracted data is provided as output of receiver  28 . 
     As can be seen in the example system of  FIG. 1 , the signal at the input of demodulator  60  is distorted by three impairments applied in sequence. The signal is first distorted by the frequency offset of module  36  (ΔF 1 ), then by the I/Q imbalance of I/Q modulator  40  (ΔIQ), and finally by the frequency offset between the transmitter and the receiver (ΔF 2 ). Generally, frequency offsets and I/Q imbalance impairments are not commutative. In the specific example of  FIG. 1 , ΔF 1  and ΔF 2  cannot be modeled (and corrected) by a single time-invariant frequency offset and a single time-invariant I/Q correction, since ΔIQ is applied between them. 
     In some embodiments, demodulator  60  comprises circuitry that compensates for the interleaved sequence of impairments ΔF 1 →ΔIQ→ΔF 2 , and produces a corrected signal having little or no frequency offset or I/Q imbalance. 
       FIG. 2  is a block diagram that schematically illustrates some of the internal structure of demodulator  60 , in accordance with an embodiment of the present invention. Demodulator  60  comprises a cascade of frequency correction and I/Q correction modules, which are arranged in reverse order to the order of the impairments that distort the signal. In the present example, demodulator  60  comprises a frequency correction module  64  that compensates for ΔF 2  (i.e., applies a frequency offset of −ΔF 2 ), followed by an I/Q correction module  68  that compensates for ΔIQ, followed by a frequency correction module  72  that compensates for ΔF 1 . 
     Frequency correction module  64  can be implemented using any suitable circuitry that applies frequency offset, such as a NCO. I/Q correction module  68  is also usually implemented using digital circuitry. Module  68  typically multiplies the incoming digital signal (which is an I/Q signal, i.e., a sequence of I samples and a respective sequence of Q samples) by one or more 2-by-2 matrix that represents the desired I/Q correction. For example, module  68  can apply a gain imbalance correction β by multiplying the signal by a matrix of the form: 
     
       
         
           
             
               [ 
               
                 
                   
                     1 
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     β 
                   
                 
               
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     Additionally or alternatively, module  68  can apply a phase imbalance correction α by multiplying the signal by a matrix of the form: 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       cos 
                       ⁢ 
                       
                         α 
                         2 
                       
                     
                   
                   
                     
                       sin 
                       ⁢ 
                       
                         α 
                         2 
                       
                     
                   
                 
                 
                   
                     
                       sin 
                       ⁢ 
                       
                         α 
                         2 
                       
                     
                   
                   
                     
                       cos 
                       ⁢ 
                       
                         α 
                         2 
                       
                     
                   
                 
               
               ] 
             
               
           
         
       
     
     By applying frequency corrections and I/Q corrections in reverse order, modules  64 ,  68  and  72  in demodulator  60  compensate for the impairment sequence ΔF 1 →ΔIQ→ΔF 2  with high accuracy. As a result, the corrected signal at the output of the cascade (at the output of module  72 ) has little or no frequency offset or I/Q imbalance. In other words, the corrected signal comprises a sequence of stable constellation symbols, which are located at the appropriate positions in the I/Q plane. 
     A slicer circuit  76  extracts the data bits from the corrected signal. Typically, the slicer examines each symbol in the corrected signal, and decides which of the constellation symbols has the shortest distance (in the I/Q plane) to this received symbol. The data bits represented by the selected constellation symbols are provided as output. 
     In some embodiments, one or more of the frequency corrections and/or I/Q corrections applied by demodulator  60  are set adaptively, based on the data bits that are produced by slicer  76 . This process is sometimes referred to as decision-directed adaptation. In the example of  FIG. 2 , the frequency corrections applied by modules  64  and  72 , as well as the I/Q correction applied by module  68 , are set adaptively based on the output of slicer  76 . In a typical implementation, the demodulator produces one or more decision-directed error signals based on the slicer output, and calculates the I/Q imbalance and frequency offset corrections based on these error signals. 
     In the present example, demodulator  60  comprises a de-rotation module  80 , which de-rotates the decision-directed error signal (which is based on the symbols produced by slicer  76 ). Module  80  applies a frequency offset of ΔF 1 , i.e., reverses or compensates for the operation of frequency correction module  72 . The de-rotation operation causes the slicer output to have the same frequency offset (i.e., phase rotation rate) as the signal processed by I/Q correction module  68 . As such, the de-rotated error signal can be used for setting the I/Q imbalance correction applied by module  68 . An I/Q adaptation module  84  computes the appropriate I/Q imbalance correction (e.g., phase imbalance correction a and gain imbalance correction ( 3 , as described above) based on the de-rotated slicer output. 
     Additionally, demodulator  60  comprises a correction reversal module  86 , which applies de-rotation and reverse I/Q imbalance correction to the error signal produced by slicer  76 . Module  86  reverses the corrections carried out by modules  68  and  72 . As a result, the error signal at the output of module  86  and the signal processed by module  64  are matched with regard to their frequency and I/Q coordinate system. The error signal at the output of module  86  is then used for setting the frequency correction applied by module  64 . 
     In alternative embodiments, any of the frequency corrections and/or I/Q imbalance corrections applied by demodulator  60  may be constant (e.g., hardwired or pre-programmed), or they may be adapted using any other suitable method. For example, a Least Mean Squares (LMS) adaptation process, as is known in the art, can be used. 
       FIG. 3  is a block diagram that schematically illustrates an alternative demodulator  90 , which may also be used for correcting the I/Q imbalance and frequency offset impairments in system  20  of  FIG. 1  above, in accordance with an embodiment of the present invention. Unlike demodulator  60  of  FIG. 2  above, demodulator  90  comprises a single frequency correction module  94 , which compensates for both ΔF 1  and ΔF 2 . The output of module  98  is processed by an I/Q correction module  98 , which compensates for ΔIQ. 
     Demodulator  90  comprises a slicer  102  and an I/Q adaptation module  106 , similar to slicer  76  and module  84  of  FIG. 2  above, respectively. The extracted bits at the output of slicer  102  are used for producing a decision-directed error signal, which is used for setting the frequency correction of module  94  and the I/Q imbalance correction of module  98 . 
     Note, however, that in demodulator  90  there is only one frequency correction, and that corrections are not applied in reverse order to the order of the impairments that distort the signal. As a result, the I/Q corrections to be applied by module  98  are now time-varying, at a rate that depends on ΔF 1 . Demodulator  90  comprises an I/Q coefficient rotation module  110 , which computes these time-varying I/Q corrections. In some embodiments, module  110  accepts as input the phase imbalance correction α and gain imbalance correction β from adaptation module  106 . In addition, module  110  accepts a time-varying rotation matrix denoted φ(t), which represents the rotation of the signal in the I/Q plane at a rate of ΔF 1 . Module  110  rotates the coefficients α and β using φ(t), to produce time-varying coefficients α′(t) and β′(t). The time-varying coefficients are provided to module  98 , which applies the time-varying I/Q imbalance correction accordingly. 
     Demodulator  90  further comprises a correction reversal module  112 , which reverses the I/Q imbalance correction applied by module  98 . The error signal at the output of module  112  is used for setting the frequency correction applied by module  94 . 
     In comparison to demodulator  60  of  FIG. 2  above, demodulator  90  applies only a single frequency correction. On the other hand, the adaptation of the I/Q imbalance correction is considerably more complex because of the continuously time-varying nature of the I/Q corrections. Nevertheless, both demodulator configurations can provide highly-accurate compensation for the interleaved impairment sequence ΔF 1 →ΔIQ→ΔF 2 . 
     Split-Mount Transmitters with Re-Modulation 
     In some system applications, the transmitter functions are split between two separate units that are connected by RF cable. For example, the transmitter may comprise an Indoor Unit (IDU) that is connected by coaxial cable to an Outdoor Unit (ODU). The IDU typically comprises the digital processing section of the transmitter (e.g., transmit modem) and some IF circuitry. The ODU typically comprises up-conversion and RF circuitry, and is usually mounted near the antenna. Such a configuration is referred to as a split-mount configuration. In other transmitter configurations (referred to as “single-mount” configurations), the entire transmitter is mounted in an ODU. 
     Some split-mount transmitters apply re-modulation to the transmitted signal. In these schemes, the signal is up-converted in the IDU to IF and transferred to the ODU over a cable. In the ODU, the IF signal is down-converted to baseband again, and then up-converted again to RF. The down-conversion to baseband is sometimes advantageous, for example in order to use a common baseband-to-RF up-converter for both split-mount and single-mount transmitters. Some aspects of re-modulation in transmitters are addressed in U.S. Pat. No. 6,844,787, whose disclosure is incorporated herein by reference. Some aspects of split-mount transmitters are addressed in PCT International Publications WO 2009/063447 and 2009/083949, whose disclosures are incorporated herein by reference. 
       FIG. 4  is a block diagram that schematically illustrates a transmitter  120  that uses re-modulation, in accordance with an embodiment of the present invention. Transmitter  120  comprises an Indoor Unit (IDU)  124  and an Outdoor Unit (ODU)  128 , which are connected by a cable  140 . Data for transmission is modulated in IDU  124  onto a baseband signal, and the signal is up-converted to IF by an I/Q modulator  132 . The I/Q modulator up-converts the signal by mixing it with an LO signal that is synchronized to a reference clock source  136 . The IF signal is sent over cable  140  to ODU  128 . In the ODU, an I/Q demodulator  144  down-converts the IF signal to baseband again. An I/Q modulator  148  up-converts the baseband signal to RF, and the RF signal is transmitted to a receiver via a transmitter antenna  156 . ODU  128  comprises a reference clock source  152 , which produces a reference clock signal for producing the LO signals used by I/Q demodulator  144  and I/Q modulator  148 . In alternative embodiments, I/Q demodulator  144  and I/Q modulator  148  can be driven by LO signals that are based on separate reference clock sources. 
     The processing applied to the signal by IDU  124  and ODU  128  demonstrates another example, in which the signal is subjected to an alternating sequence of I/Q imbalance impairments and frequency offsets. First, I/Q modulator  132  causes an I/Q imbalance denoted ΔIQ 1 . Then, up-conversion by I/Q modulator  132  and down-conversion by I/Q demodulator  144  cause a frequency offset denoted ΔF 1 , since the IDU and ODU use different reference clock sources. Then, I/Q demodulator  144  and I/Q modulator  148  cause an I/Q imbalance denoted ΔIQ 2 . (The I/Q imbalance of both components can be modeled as a single imbalance, regardless of whether they are based on the same reference clock or on separate reference clocks.) Finally, a frequency offset between the ODU and the receiver at the other end of the link (not shown) is denoted ΔF 2 . In summary, the signal is subjected to the alternating sequence of impairments ΔIQ 1 →ΔF 1 →ΔIQ 2 →ΔF 2 . 
       FIG. 5  is a block diagram that schematically illustrates a demodulator  160  that compensates for the I/Q imbalance and frequency offset impairments in transmitter  120  of  FIG. 4  above, in accordance with an embodiment of the present invention. Demodulator  160  can be used in a receiver that receives the signal transmitted from transmitter  120 . Demodulator  160  comprises two frequency correction modules and two I/Q correction modules, which are cascaded in reverse order to the order in which the impairments distort the signal. 
     The cascade comprises a frequency correction module  164  that compensates for ΔF 2 , followed by an I/Q correction module  168  that compensates for ΔIQ 2 , then a frequency correction module  172  that compensates for ΔF 1 , and finally an I/Q correction module  176  that compensates for ΔIQ 1 . A slicer  180  produces symbol decision, as explained above. The symbols produced by the slicer are processed by an adaptation module  184  in a decision-directed adaptation process. In other words, module  184  computes the frequency and I/Q imbalance corrections to be applied by modules  164 ,  168 ,  172  and  176 , based on the output of slicer  180 . 
     In the present example, all the frequency and I/Q imbalance corrections are computed in a decision-directed manner. Alternatively, however, any of these corrections may be constant, or it may be adapted using any other suitable method. Typically, a given error signal produced by adaptation module  184  is de-rotated and/or de-I/Q-corrected, in order to match the signal processed by the I/Q correction or frequency correction module it controls. In other words, the error signal that controls a given module in the processing chain is processed so as to reverse the corrections applied by all subsequent modules in the cascade. For example, the signal that, controls module  172  is typically de-rotated to reverse the operation of module  176 . The signal that controls module  168  is typically processed so as to reverse the operation of modules  172  and  176 . 
     Note that the alternating sequence of I/Q imbalance and frequency offsets in transmitter  120  is caused, at least partly, by the fact that IDU  124  and ODU  128  use separate reference clock sources ( 136  and  152 , respectively). If the IDU and ODU were to use the same reference clock source (e.g., by transferring a reference clock signal over cable  140 ), then ΔF 1  would be zero. As a result, ΔIQ 1  and ΔIQ 2  could be represented by a single equivalent I/Q imbalance, and the problem would be simplified considerably. Transferring a reference clock signal over the cable, however, causes design complications and adds to the size, cost and complexity of the system. When using the compensation scheme of  FIG. 5 , on the other hand, the receiver is able to compensate for the different impairments without having to transfer clock signals over the cable and without compromising receiver performance. 
     In some implementations of transmitter  120 , the baseband sections of the transmitter may introduce I/Q delay mismatch, i.e., delay mismatch between the I and Q signal components. In  FIG. 4 , for example, I/Q delay mismatch may occur at the input of I/Q modulator  132  in the IDU, and/or between I/Q demodulator  144  and I/Q modulator  148  in the ODU. In some embodiments, demodulator  160  of  FIG. 5  may comprise circuitry that compensates for this delay mismatch. 
     For example, an I/Q delay mismatch at the input of I/Q modulator  132  may be corrected by inserting a delay element (not shown) between I/Q correction module  176  and slicer  180 . When a delay mismatch exists between I/Q demodulator  144  and I/Q modulator  148 , ΔIQ 2  can be modeled by two I/Q imbalances having an intervening delay mismatch. Therefore, the delay mismatch between I/Q demodulator  144  and I/Q modulator  148  may be corrected by inserting a delay element followed by an additional I/Q imbalance correction module (both not shown) between I/Q correction module  168  and frequency correction module  172 . In embodiments in which IDU  124  and ODU  128  share the same reference clock source (e.g., by transferring a reference clock signal over cable  140 ), demodulator  160  can be simplified to include a frequency correction module, followed by an I/Q imbalance correction module, followed by a delay element, followed by another I/Q imbalance correction module, followed by another delay element. 
     The delay elements in the above-described configurations typically delay one of the I and Q signal components with respect to the other signal component, so as to cancel the corresponding delay mismatch impairment. The delay of a given delay element may be fractional and not necessarily an integer number of samples. 
     Split-Mount Receivers with Re-Demodulation 
     In some system applications, the receiver functions are split between two separate units that are connected by RF cable. For example, in some split-mount applications, the receiver functions are split between the ODU and IDU. Some split-mount receivers use a re-demodulation scheme, in which the received RF signal is down-converted to baseband in the ODU and then up-converted to IF in order to send it over the cable. In the IDU, the IF signal is down-converted to baseband again for demodulation. Re-demodulation schemes are sometimes advantageous, for example in order to use a common RF-to-baseband down-converter in both split-mount and single-mount receivers. Certain aspects of receivers that use re-demodulation are addressed in U.S. patent application Ser. No. 12/553,101, which is assigned to the assignee of the present patent application and whose disclosure is incorporated herein by reference. 
       FIG. 6  is a block diagram that schematically illustrates a receiver  190  that uses re-demodulation, in accordance with an embodiment of the present invention. Receiver  190  comprises an ODU  194  and an IDU  198 , which are connected by a cable  202 . An RF signal sent from a transmitter (not shown) is received by a receiver antenna  206 . An I/Q demodulator  210  down-converts the signal to baseband. An I/Q modulator  214  up-converts the baseband signal to IF. Both I/Q demodulator  210  and I/Q modulator  214  perform frequency conversion by mixing the signal with one or more LO signals. The LO signals in the ODU are synchronized to a reference clock source  218 . In IDU  198 , an I/Q demodulator  222  down-converts the IF signal to baseband for demodulation. Down-conversion in the IDU is performed using one or more LO signals, which are synchronized to a reference clock source  226 . Thus, the ODU and IDU use separate reference clock sources for generating LO signals. 
     The processing applied to the signal by ODU  194  and IDU  198  show yet another example, in which the signal is subjected to an alternating sequence of I/Q imbalance impairments and frequency offsets. First, the frequency offset between the transmitter (not shown) and ODU  194  is denoted ΔF 1 . Then, I/Q demodulator  210  and I/Q modulator  214  cause an I/Q imbalance denoted ΔIQ 1 . (The I/Q imbalance of both components can be modeled as a single imbalance because no frequency offset is applied between them.) Then, up-conversion by I/Q modulator  214  and down-conversion by I/Q demodulator  222  cause a frequency offset denoted ΔF 2 , since the ODU and IDU use separate reference clock sources. Finally, I/Q demodulator  222  causes an I/Q imbalance denoted ΔIQ 2 . In summary, the signal is subjected to the alternating sequence of impairments ΔF 1 →ΔIQ 1 →ΔF 2 →ΔIQ 2 . 
       FIG. 7  is a block diagram that schematically illustrates a demodulator  230 , which compensates for the I/Q imbalance and frequency offset impairments in receiver  190  of  FIG. 6  above, in accordance with an embodiment of the present invention. Demodulator  230  can be used to demodulate the signal produced by I/Q demodulator  222 . 
     Demodulator  230  comprises two I/Q correction modules and two frequency correction modules, which are cascaded in reverse order to the order in which the impairments distort the signal. The cascade comprises an I/Q correction module  234  that compensates for ΔIQ 2 , followed by a frequency correction module  238  that compensates for ΔF 2 , then an I/Q correction module  242  that compensates for ΔIQ 1 , and finally a frequency correction module  246  that compensates for ΔF 1 . 
     An adaptation module  250  computes the frequency and I/Q imbalance corrections to be applied by modules  234 ,  238 ,  242  and  246 . The adaptation unit may receive inputs from one or more points in the cascade, and calculate the frequency and I/Q imbalance corrections based on these inputs. As noted above with respect to module  184  of FIG.  5 , adaptation module  250  typically applies de-rotation and/or reverse I/Q imbalance corrections to its outputs, so that each of modules  234 ,  238 ,  242  and  246  is controlled by an error signal that matches the signal processed by that module with regard to frequency and I/Q coordinate system. 
     In the present example, the frequency and I/Q imbalance corrections are computed in a blind adaptation process, i.e., irrespective of the slicer output. Alternatively, however, any of these corrections may be constant, or it may be adapted using any other suitable method. 
     In some embodiments, demodulator  230  may also compensate for I/Q delay mismatch introduced by baseband sections of transmitter  190 . For this purpose, delay elements, and possibly additional I/Q correction modules, may be inserted at the appropriate points in the processing cascade of demodulator  230 . The delay mismatch correction can be implemented using similar principles to the delay mismatch correction in demodulator  160  of  FIG. 5 , as described above. In order to compensate for these I/Q delay mismatches, the processing cascade of demodulator  230  can be modified so as to apply an I/Q delay mismatch correction, followed by an I/Q imbalance correction, followed by a frequency correction, then a second I/Q imbalance correction, then a second I/Q delay mismatch correction, followed by a third I/Q imbalance correction, and finally a second frequency correction. With reference to  FIG. 7 , demodulator  230  can be modified by adding a delay element before I/Q correction module  234  (at the input of the processing cascade), splitting I/Q imbalance correction module  242  into two separate I/Q imbalance correction modules, and inserting a second delay element between these two I/Q imbalance correction modules. 
     In this example too, the alternating sequence of I/Q imbalance and frequency offsets is caused, at least partly, by the fact that the ODU and IDU use separate reference clock sources. If the IDU and ODU were to use the same reference clock source (e.g., by transferring a reference clock signal over cable  202 ), then ΔF 2  would be zero, and ΔIQ 1  and ΔIQ 2  could be represented by a single equivalent I/Q imbalance. Thus, the compensation scheme of  FIG. 7  enables the receiver to compensate for the different impairments accurately without having to transfer clock signals over cable  202 . 
     As explained above, the frequency correction modules used in the different demodulator configurations described herein may comprise any suitable circuitry that shifts the frequency of a digital signal, such as a NCO. The I/Q correction modules used in the demodulator configurations described herein may comprise any suitable digital circuitry, such as logic that performs 2-by-2 matrix multiplication. The adaptation units used in the different demodulator configurations described herein can be implemented in hardware, in software, or using a combination of hardware and software elements. 
     The different demodulator elements may be implemented, for example, in one or more Application-Specific Integrated Circuits (ASIC) or Field-Programmable Gate Arrays (FPGA), and/or using discrete components. The analog transmitter and receiver elements may be implemented using discrete components and/or in one or more RF Integrated Circuits (RFIC) or Monolithic Microwave Integrated Circuits (MMIC). 
     Compensation Method Description 
       FIG. 8  is a flow chart that schematically illustrates a method for correcting I/Q imbalance and frequency offset impairments, in accordance with an embodiment of the present invention. The method begins with a demodulator receiving a signal, which is distorted by an alternating sequence of frequency offset and I/Q imbalance impairments, at an input step  260 . The impairment sequence comprises at least (1) two frequency offset impairments with an intervening I/Q imbalance impairment, or (2) two I/Q imbalance impairments with an intervening frequency offset impairment. 
     The demodulator applies an alternating sequence of frequency corrections and I/Q imbalance corrections, at a correction step  264 . Typically, the corrections are performed in reverse order to the order in which the impairments distort the signal. The output of this process is a corrected signal having little or no I/Q imbalance and frequency offset. The demodulator then extracts the data from the corrected signal, an a data extraction step  268 . The extracted data is provided as output. 
     The transmitter and receiver configurations described herein are chosen by way of example. In alternative embodiments, the disclosed techniques can be used in any other suitable system or application in which a signal is distorted by an alternating sequence of frequency offset and I/Q imbalance impairments. Although the embodiments described herein mainly address wireless communication transmitters and receivers, the methods and systems described herein can also be used in wire-line applications that involve RF transmission, such as in cable communication systems. 
     It will thus 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 sub-combinations 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.