Abstract:
A digital calibration circuit is used to provide joint-elimination of transmitter and receiver I/Q imbalances. Digital I and Q quadrature signals are received and converted to analog I and Q quadrature signals on I and Q for transmission on output channels. An output mixer is used to convert the quadrature signals to an unbalanced RF output. An unbalanced RF signal is received selectively either externally or from the RF output using a source follower, and the received signal is mixed to provide analog I and Q quadrature signals, using a local oscillator (LO). The LO adds an additional 90° phase shift between I and Q quadrature channels of the unbalanced RF input. Parameter estimating the transmitted digital I and Q quadrature signals and providing estimations of I and Q quadrature imbalance conditions.

Description:
BACKGROUND 
       [0001]    1. Field 
         [0002]    The present disclosure relates to digital calibration of transmitters and receivers of quadrature modulated signals, implemented using an internally switched signal path. Keywords include algorithm, CORDIC, calibration, I/Q imbalance, local oscillator (LO), transceiver, transmitter (TX) and receiver (RX). 
         [0003]    2. Background 
         [0004]    Quadrature modulation is fundamental in nearly all wireless transceivers for its high spectral efficiency, but mismatches of components and physical layout generally leads to gain and phase mismatches between the I and Q quadrature signals. The resultant image effect can significantly degrade the error vector magnitude (EVM), especially for very dense signal constellations such as 16-QAM and 64-QAM. Since I/Q imbalances can happen in the receiver (RX), transmitter (TX) and local oscillator (LO), the desired calibration algorithm should be able to correct the I/Q imbalances with minimum add-on hardware for better cost and area efficiencies. 
         [0005]    A number of techniques have been reported to deal with the I/Q imbalance problem. Examples are the loop-back detector with a recursive algorithm, two-dimensional iterative search algorithm, and blind estimation algorithm. The first two are demanding in hardware and computation, inducing a long calibration time and are power and area hungry in their implementation. For the third, although no training sequence is entailed, the estimation process still involves heavy computation (e.g., inverse matrix) and can suffer from the instability issue in the recursive loop. 
       SUMMARY 
       [0006]    Digital calibration circuit for joint-elimination of transmitter and receiver I/Q imbalances is performed by using a feedback circuit and a joint estimation circuit to provide I/Q parameters estimation. I and Q quadrature signals are received and analog I and Q quadrature signals are transmitted on I and Q output channels. Output mixing is performed to convert the quadrature signals to an unbalanced RF output. An unbalanced RF input is received and mixed to provide analog I and Q quadrature signals, and analog to digital conversion is performed on the I and Q quadrature signals. A source follower amplifier is selectively connected between the unbalanced RF output with the unbalanced RF input, establishing a feedback loop from the unbalanced RF output through the source follower amplifier to the unbalanced RF input. A local oscillator (LO) is used to provide an LO signal to the output and input mixer circuit, and the LO adds an additional 90° phase shift between I and Q quadrature channels of the unbalanced RF input. Parameter estimation is performed on the received digital I and Q quadrature signals and is used for providing estimations of I and Q quadrature imbalance conditions. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  is a schematic block diagram of a system configured to provide non-recursive digital calibration, in which the calibration provides joint elimination of transmitter and receiver I/Q imbalances of quadrature signals. 
           [0008]      FIG. 2  is a graphical diagram showing signal response in terms of image attenuation vs. frequency to provide image rejection over a broad spectrum. 
           [0009]      FIGS. 3A and 3B  are schematic diagrams showing I/Q imbalance at 0 phase shift ( FIG. 3A ) and 90° phase shift ( FIG. 3B ). 
           [0010]      FIG. 4  is a graphical diagram showing calibrated transmission image-rejection ratio (IRR) as a function of LO IRR. 
           [0011]      FIG. 5  is a topography layout diagram superimposed over a chip micrograph, showing approximations of the layout locations of circuit components according to the disclosure. 
           [0012]      FIG. 6  is a schematic block diagram showing an experimental setup for testing the disclosed circuitry. 
           [0013]      FIG. 7  is a time diagram of the data picking process. 
           [0014]      FIGS. 8A and 8B  are graphical diagrams showing the TX output spectrums for a single tone test before and after calibration, respectively. 
           [0015]      FIGS. 9A and 9B  are graphical displays of received output (RX) as a function of frequency before ( FIG. 9A ) and after ( FIG. 9B ) post-compensation, respectively. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    Overview 
         [0017]    A non-recursive digital calibration technique, namely local oscillator (LO) switching, is provided for jointly eliminating the transmitter (TX) and receiver (RX) I/Q imbalances of quadrature signals, in one combined process. The digital calibration technique provides joint correction of RX and TX I/Q imbalances under a reference LO, using add-on analog parts limited to a set of source followers and MOS switches. The latter is to employ the 90° phase shift property of the LO available in most quadrature transceivers, generating adequate conditions to estimate the I/Q imbalance parameters non-recursively. An experimental verification is described, as a non-limiting example, based on a 65 nm CMOS transceiver chip co-designed with a CORDIC algorithm implemented in the FPGA. 
         [0018]    The add-on analog parts are limited to a set of source followers (0.00228 mm 2 ), and MOS switches (0.00017 mm 2 ) for reusing the 90° phase shift property of the reference LO, avoiding the sinusoidal test tone, loop-back detector, high-speed analog-to-digital converter and 2-dimensional iterative search algorithm, mostly required in the prior art. A 65 nm CMOS transceiver, co-designed with a FPGA-based CORDIC algorithm, measures a 10 dB improvement of image rejection ratio (IRR) for both TX (27.8→37.2 dB) and RX (31.2→42 dB). The required digital circuitry for the algorithm is also assessed and simulated. 
         [0019]    Transceiver-FPGA System Co-Design 
         [0020]      FIG. 1  is a schematic block diagram of a system configured to provide non-recursive digital calibration, in which the calibration provides joint-elimination of transmitter and receiver I/Q imbalances of quadrature signals. In the calibration mode, the RF output from the TX mixers is looped back to the RX via the TX-RX switch, such that the calibration process can be moved to the digital domain, reusing the existing hardware, while, more importantly, linking up together the I/Q imbalances of both RX and TX for joint calibration. The integrated TX includes two first-order passive RC lowpass filters (LPFs) for reconstructing the I and Q quadrature inputs generated by the off-chip digital-to-analog converters (DACs). After I/Q up-conversion by the passive mixers, a single-ended class B driver amplifier (DA) with an inductive load delivers the RF output for 50 n measurements. 
         [0021]    By focusing on the calibration mode, the on-chip RX path is able to provide a simplified approach to rapid prototyping. In the baseband, only first-order active RC LPFs are employed to suppress the image at 2×LO frequency generated by the TX, which is already adequate to minimize the calibration error due to aliasing in the analog-to-digital converters (ADCs). 
         [0022]    Typical direct-conversion transmitters using sub-sampling for imbalance calibration require a high-speed sub-sampling ADC, for example 200 MHz, to serve as the loop-back RX. In contrast, the disclosed technology simply reuses the existing RX mixers, LPFs, and ADCs that are much more relaxed in terms of speed. By way of non-limiting example, the sub-sampling ADC speed is 80 MHz. The source follower provides isolation between the passive mixers on the TX and RX sides. The low-noise amplifier (LNA) was not integrated the focus is on the I/Q imbalance calibration. 
         [0023]      FIG. 2  is a graphical diagram showing signal response in terms of image attenuation vs. frequency to provide image rejection over a broad spectrum. The disclosed I/Q imbalance calibration employs the LO as the reference such that joint calibration of RX and TX can be achieved. Thus, the I/Q accuracy of the LO is crucial and must be robust over process variations. Here, the LO path is led by an active balun implemented with a cascaded differential amplifier, and followed by a RC-CR network as the polyphase filter (PPF) for 4-phase (0°, 90°, 180°, 270°) sine LO generation at ˜1.4 GHz (a frequency convenient for this design). As shown in  FIG. 2  from simulations, for an image-rejection ratio (IRR) of 60 dB, a 3-stage RC-CR network with properly positioned poles is adequate to cover a broad spectrum (1.27 to 1.94 GHz), such that the worst RC variations can still be tolerated. 
         [0024]    At the circuit level, before driving the 4-phase LO to the I/Q passive mixers, logic operation is applied to transform them from sine LO into a set of 25% duty-cycle square LO with guard intervals, avoiding I/Q crosstalk, while saturating the LO amplitude to improve the gain balancing. 
         [0025]    Field Programmable Gate Array (FPGA) 
         [0026]    The left side of  FIG. 1  shows a field programmable gate array (FPGA) used to implement pre-compensation and post-compensation. For the TX digital baseband, the imbalanced baseband output can be modeled as x tx,imb (t)=I tx,imb +JQ tx,imb , such that 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             I 
                             
                               tx 
                               , 
                               imb 
                             
                           
                         
                       
                       
                         
                           
                             Q 
                             
                               tx 
                               , 
                               imb 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               α 
                                
                               
                                   
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               θ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               α 
                                
                               
                                   
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               θ 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               I 
                               tx 
                             
                           
                         
                         
                           
                             
                               Q 
                               tx 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the gain and phase imbalances are represented by α and θ, respectively. Similarly, for the RX, the imbalanced baseband output is given by, 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             I 
                             
                               rx 
                               , 
                               imb 
                             
                           
                         
                       
                       
                         
                           
                             Q 
                             
                               rx 
                               , 
                               imb 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               β 
                                
                               
                                   
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               ξ 
                             
                           
                           
                             
                               β 
                                
                               
                                   
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               ξ 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               I 
                               
                                 rx 
                                 , 
                                 ideal 
                               
                             
                           
                         
                         
                           
                             
                               Q 
                               
                                 rx 
                                 , 
                                 ideal 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the gain and phase imbalances are represented by β and ξ, respectively. I rx,ideal  and Q rx,ideal  refer to the down-converted output with an ideal RF input with no I/Q imbalance. 
         [0027]    Such an RF model is used as the basis for the following estimation process. With a reference LO mixed with the digital baseband signals, we obtain the RF signal as, 
         [0000]        s   RF =( I   tx +α sin θ Q   tx )cos ω t +α cos θ Q   tx )sin ω t   (3)
 
         [0028]    The pre-compensation of TX and the post-compensation of RX are operated by inversing directly the baseband system model between the TX and RX, in which both matrixes can be represented as, 
       Compensation for TX: 
       [0029]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             I 
                             
                               tx 
                               , 
                               pre 
                             
                           
                         
                       
                       
                         
                           
                             Q 
                             
                               tx 
                               , 
                               pre 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               
                                 - 
                                 tan 
                               
                                
                               
                                   
                               
                                
                               θ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sec 
                                
                               
                                   
                               
                                
                               θ 
                                
                               
                                 / 
                               
                                
                               α 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               I 
                               tx 
                             
                           
                         
                         
                           
                             
                               Q 
                               tx 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
       Compensation for RX: 
       [0030]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             I 
                             
                               rx 
                               , 
                               post 
                             
                           
                         
                       
                       
                         
                           
                             Q 
                             
                               rx 
                               , 
                               post 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 - 
                                 tan 
                               
                                
                               
                                   
                               
                                
                               ξ 
                             
                           
                           
                             
                               sec 
                                
                               
                                   
                               
                                
                               ξ 
                                
                               
                                 / 
                               
                                
                               β 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               I 
                               rx 
                             
                           
                         
                         
                           
                             
                               Q 
                               rx 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0031]    LO Switching I/O Imbalance Calibration 
         [0032]      FIGS. 3A and 3B  are schematic diagrams showing how the I/Q imbalance parameters can be extracted. With the I/Q imbalance model is shown in  FIG. 3A , the overall gains of the TX and RX are denoted as A and B, respectively, and the overall phase shift passing through them is denoted as φ. The outputs for the TX baseband are I tx  and Q tx  and the inputs for the RX baseband are I rx  and Q rx . As shown in  FIG. 3A , if a DC training signal is sent from I tx  and Q tx  separately into the system, only four equations are available to estimate the wanted I/Q imbalance parameters. Consequently, only the conventional Least Mean Square (LMS) method can be applied, which is slow and has a limited accuracy. The LO switching technique presented here has the objective of finding more independent equations. The procedure is two-fold: 1) transmit a DC training signal from I tx  and Q tx  to the system, and 2) switch the LO can generate an extra 90° phase shift between the two input channels, offering more equations to solve the desired I/Q imbalance parameters. Specifically, if a DC training signal with amplitude c at I tx  and Q tx  is separately injected into the I/Q imbalance model, the output signals can be represented as, 
       The Output Signal Through Path 1, 
       [0033]    
       
         
           
             
               
                 
                   
                     I 
                     
                       rs 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           cA 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         cAB 
                         2 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       φ 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
       The Output Signal Through Path 2, 
       [0034]    
       
         
           
             
               
                 
                   
                     Q 
                     
                       rs 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           cA 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           β 
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                                 + 
                                 ξ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         cAB 
                         2 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             φ 
                             + 
                             ξ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
       The Output Signal Through Path 3, 
       [0035]    
       
         
           
             
               
                 
                   
                     I 
                     
                       rx 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           c 
                            
                           
                               
                           
                            
                           α 
                            
                           
                               
                           
                            
                           A 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 θ 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         
                           c 
                            
                           
                               
                           
                            
                           α 
                            
                           
                               
                           
                            
                           AB 
                         
                         2 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             θ 
                             - 
                             
                                 
                             
                              
                             φ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0036]    Then, considering  FIG. 3B , the phase of the LO is switched for a phase shift of 90°. In this case, if we transmit a DC training signal at I tx  and Q tx , the output signals can be represented as, 
       The Output Signal Through Path 4, 
       [0037]    
       
         
           
             
               
                 
                   
                     I 
                     
                       rx 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         4 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           cA 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         cAB 
                         2 
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       φ 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
       The Output Signal Through Path 5, 
       [0038]    
       
         
           
             
               
                 
                   
                     Q 
                     
                       rx 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         5 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           cA 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           β 
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                                 + 
                                 ξ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         
                           c 
                            
                           
                               
                           
                            
                           β 
                            
                           
                               
                           
                            
                           AB 
                         
                         2 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             φ 
                             + 
                             ξ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   0 
                   ) 
                 
               
             
           
         
       
     
       The Output Signal Through Path 6, 
       [0039]    
       
         
           
             
               
                 
                   
                     I 
                     
                       rx 
                       , 
                       
                         Path 
                          
                         
                             
                         
                          
                         6 
                       
                     
                   
                   = 
                   
                     
                       LPF 
                        
                       
                         { 
                         
                           c 
                            
                           
                               
                           
                            
                           α 
                            
                           
                               
                           
                            
                           A 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 θ 
                               
                               ) 
                             
                           
                            
                           
                               
                           
                            
                           B 
                            
                           
                               
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 + 
                                 φ 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         
                           c 
                            
                           
                               
                           
                            
                           α 
                            
                           
                               
                           
                            
                           AB 
                         
                         2 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           θ 
                           - 
                           φ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0040]    Thus, the overall gain G=AB/2, and the overall phase shift φ can be computed as, 
         [0000]        G =√{square root over (( I   rx,Path3   /c ) 2 +( I   rx,Path4   /c ) 2 )}{square root over (( I   rx,Path3   /c ) 2 +( I   rx,Path4   /c ) 2 )},  (12)
 
         [0000]      φ=tan −1 ( I   rx,Path4   /I   rx,Path1 )  (13)
 
         [0041]    Finally, the gain and phase mismatches of the TX and RX are solved, leading to, 
         [0000]      α= G   −1 √{square root over (( I   rx,Path6   /c ) 2 +( I   rx,Path3   /c ) 2 )}{square root over (( I   rx,Path6   /c ) 2 +( I   rx,Path3   /c ) 2 )},  (14)
 
         [0000]      θ=tan −1 ( I   rx,Path3   /I   rx,Path6 )+φ  (15)
 
         [0000]      β= G   −1 √{square root over (( Q   rx,Path2   /c ) 2 +( Q   rx,Path5   /c ) 2 )}{square root over (( Q   rx,Path2   /c ) 2 +( Q   rx,Path5   /c ) 2 )},  (16)
 
         [0000]      ξ=tan −1 ( Q   rx,Path2   /Q   rx,Path5 )−φ  (17)
 
         [0042]    The feasibility of the above algorithm can be limited by 1) the numerical estimation accuracy, and 2) the LO&#39;s gain and phase errors. For the former, Verilog simulations show a maximum gain error of 8×10 −4  and phase error of ±0.1° in number estimation under 105 time runs, which correspond to an IRR of 65 dB. Thus, the former should not be the limiting factor for most transceivers. 
         [0043]      FIG. 4  is a graphical diagram showing calibrated transmission image-rejection ratio (IRR) as a function of LO IRR. For the LO&#39;s gain and phase errors, we can consider a non-ideal LO as, LO=γe (jωt+η) , where γ(η) denotes the LO gain error, mostly appearing as phase error. The achievable IRR in the TX with respect to that of the LO is plotted in  FIG. 4 . They are linearly related. Thus, for an IRR of 60 dB in the LO ( FIG. 2 ), the IRR of the TX and RX should only be limited by themselves. 
         [0044]    Measurement Results 
         [0045]    A transceiver chip and test setup is shown in  FIG. 5 .  FIG. 5  is a topography layout diagram superimposed over a chip micrograph, showing approximations of the layout locations of circuit components according to the disclosure. The transceiver was fabricated in a 65 nm CMOS process. The active die area is 0.82×0 mm 2 , of which only 0.00245 mm 2  is due to the LO switches and source followers added to assist the calibration. 
         [0046]      FIG. 6  is a schematic block diagram showing an experimental setup for testing the disclosed circuitry. The baseband I/Q signals are generated by the ALTERA DE4 FPGA. It interfaces with the RX and TX through the Texas Instrument DACs (5662) and ADCs (ADS62P23). Both have a 12-bit resolution and a 80 MHz conversion rate. The master clock is generated by the FPGA for synchronization. All RF and LO switches are driven by the FPGA through digital level shifters downscaling the control signal from 3.3 to 1.2 V befitting the employed 65 nm CMOS devices. The output signal from the DA is measured by the R&amp;S FSU-8 spectrum analyzer for the single tone test. The digital outputs from the FPGA are captured by the Agilent  16902 B logic analyzer for the RX post-compensation test. 
         [0047]    Algorithm Implemented in the FPGA and Simulated in ASIC 
         [0048]      FIG. 7  is a time diagram of the data picking process. The pre-read phase learns the DC offsets. A DC signal with an amplitude c (˜0.2 V, to uphold the linearity) is then transmitted at I tx  to obtain I rx  and Q rx . Afterwards, the transmit data is exchanged, i.e., I tx =0 and Q tx =c to obtain I rx , where Q rx  is ignored. The process is repeated once after creating the 90° phase shift via LO switching. After the data collection, the I/Q imbalance parameters can be computed in the FPGA. 
         [0049]    The computation employs a CORDIC algorithm. CORDIC (for COordinate Rotation DIgital Computer), also known as the digit-by-digit method and Volder&#39;s algorithm, is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. The CORDIC algorithm can be used when no hardware multiplier is available. The CORDIC algorithm is able to be implemented through simple microcontrollers and FPGAs because the only operations it requires are addition, subtraction, bit shift and table lookup. By way of non-limiting example, only shift bits and adders in the entire computation, rendering it very power and area efficient. For example, after picking I rx,Path1  and I rx,Path4 , Equations. (12) and (13) can be solved by the CORDIC after 25 clock cycles under a 100 MHz clock rate. Since there are 3 sets of equations, 75 clock cycles are entailed totally. There is 1 more clock cycle for the computation of the parameters in Equations. (4) and (5). 
         [0050]    The algorithm is also converted into a 65 nm CMOS ASIC under the Cadence Encounter™, the required power, area and calibration time are estimated, as summarized in Table I. The simulated digital power during compensation is 366.55 μW and the entire calibration process takes 760 ns and consumes 206 pJ of energy to complete at a 100 MHz clock rate. The entailed digital area is ˜0.02 mm 2 . 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 Power Consumption and Area simulated with Standard 65 nm CMOS 
               
               
                 Process at 1.1 V and 25° C. 
               
             
          
           
               
                   
                 Number 
                   
                   
                   
               
               
                   
                 of 
                 Power 
                   
                 No. of 
               
             
          
           
               
                 FPGA 
                   
                 Operators 
                 Leakage 
                 Switching 
                 No. of 
                 Area 
                 Clock 
               
               
                 Operation 
                 Algorithm 
                 Used 
                 (nW) 
                 (nW) 
                 Gate 
                 (μm 2 ) 
                 Cycle 
               
               
                   
               
             
          
           
               
                 Parameter 
                 CORDIC 
                 1 
                 55282.87 
                 214631.06 
                 2104 
                 8107.32 
                 25 × 3 
               
               
                 Estimator 
               
               
                 Compensator 
                 Secant 
                 2 
                 12209.07 
                 62558.95 
                 241 
                 1055.6 
                 1 
               
               
                   
                 Division 
                 2 
                 19533.42 
                 73553.22 
                 421 
                 1597.44 
                 9 
               
               
                   
                 Multiplication 
                 4 
                 22362.89 
                 68595.1 
                 371 
                 1714.44 
                 1 
               
               
                   
                 Addition 
                 2 
                 1814.31 
                 9544.43 
                 36 
                 149.76 
                 1 
               
               
                   
               
             
          
         
       
     
         [0051]    IRR Before and after Calibration 
         [0052]      FIGS. 8A and 8B  are graphical diagrams showing the TX output spectrums for a single tone test before and after calibration, respectively. The IRR is improved from 27.8 to 37.5 dB. The calculated I/Q imbalance parameters are shown in Table II: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 Calculated I/Q Imbalance Parameters. 
               
             
          
           
               
                 G 
                 φ 
                 α 
                 θ 
                 β 
                 ξ 
               
               
                   
               
               
                 0.3055 
                 44.7003° 
                 1.0281 
                 −3.2828° 
                 1.0823 
                 1.9306° 
               
               
                   
               
             
          
         
       
     
         [0053]      FIGS. 9A and 9B  are graphical displays of received output (RX) as a function of frequency before ( FIG. 9A ) and after ( FIG. 9B ) post-compensation, respectively. While the results depicted in  FIGS. 9A and 9B  are similar, it is noted that on negative (left) side, there are differences in the peaks, for example the Img peak as compared to the 0-offset peak (center). The IRR is improved from 31.2 to 42 dB. For a 64-QAM OFDM signal, these results correspond to 4% improvement of EVM from 6% to 2% for the TX, and 2.86% improvement of EVM from 3.84% to 0.98% for the RX. 
         [0054]    For wideband applications, the disclosed method can be extended using different sets of I/Q imbalance parameters trained under a number of selected frequencies in the baseband bandwidth. A preliminary study shows that it was desirable to add a digital baseband detector, and that it was desirable to use a Finite Impulse Response (FIR) filter as the compensator. 
         [0055]    D. Architectural Comparison 
         [0056]    The measurement summary is given in Table III. The add-on analog area is extremely small (0.00245 mm 2 ) as most circuitry are reused between the TX and RX: 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 Chip Summary. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Technology 
                 65 nm CMOS 
               
               
                   
                 Transceiver Chip Area 
                 0.41 mm 2   
               
               
                   
                 Analog Area for Calibration 
                 0.00245 mm 2   
               
               
                   
                 Operation Frequency 
                 1.4 GHz 
               
             
          
           
               
                   
                 Power Consumption 
                 RX Path 
                 18 mW 
               
               
                   
                   
                 LO Generator 
                 22 mW 
               
               
                   
                   
                 DA 
                 20 mW 
               
             
          
           
               
                   
                 TX IRR Before and after Calibration 
                 27.8 dB → 37.2 dB 
               
               
                   
                 RX IRR Before and after Calibration 
                 31.2 dB → 42 dB 
               
               
                   
                   
               
             
          
         
       
     
         [0057]    As the hardware between the presently disclosed technology and prior art techniques can be very different, they should not be directly compared. Nevertheless, a summary of their features is shown in Table IV: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE IV 
               
             
             
               
                   
               
               
                 Comparison with the State-of-the-Art. 
               
             
          
           
               
                   
                   
                 Sine 
                   
                 High 
                   
                   
               
               
                   
                 2-D 
                 Test 
                 Dedicated 
                 Speed 
                 TX IRR 
                 RX IRR 
               
               
                   
                 Search 
                 Tone 
                 Detector 
                 ADC 
                 Improved 
                 Improved 
               
               
                   
                   
               
             
          
           
               
                 present disclosure 
                 x 
                 x 
                 x 
                 x 
                 10 dB 
                 10 dB 
               
               
                 auto-I/Q calibrated 
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 12 dB 
                 12 dB 
               
               
                 CMOS transceiver [1]   
               
               
                 direct-conversion 
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 15.6 dB   
                 No 
               
               
                 transmit mixer with lo 
               
               
                 feedthrough and I/Q 
               
               
                 imbalance cancellation [2]   
               
               
                 wideband direct- 
                 ✓ 
                 ✓ 
                 x 
                 ✓ 
                 24 dB 
                 No 
               
               
                 conversion transmitter 
               
               
                 with sub-sampling- 
               
               
                 based output power [3]   
               
               
                   
               
               
                 Descriptions of the transceivers used in the comparison are: 
               
               
                   [1] Y. H. Hsieh, W. Y. Hu, S. -M. Lin, et al., “An Auto-I/Q Calibrated CMOS Transceiver for 802.11g,” IEEE J. Solid-State Circuits, vol. 40, no. 11, pp. 2187-2192, November 2005. 
               
               
                   [2] C. P. Lee, A. Behzad, D. Ojo, et al., “A Highly Linear Direct-Conversion Transmit Mixer Transconductance Stage with Local Oscillation Feedthrough and I/Q Imbalance Cancellation Scheme,” in IEEE ISSCC Dig. Tech. Papers, pp. 368-369, February 2006. 
               
               
                   [3] E. Lopelli, S. Spiridon, J. van der Tang, “A 40 nm Wideband Direct-Conversion Transmitter with Sub-Sampling-Based Output Power, LO Feedthrough and I/Q Imbalance Calibration,” in IEEE ISSCC Dig. Tech. Papers, pp. 424-426, February 2011. 
               
             
          
         
       
     
         [0058]    One advantage of the present technique is the ability to jointly calibrate the TX and RX. Although the achieved 37.2 to 42 dB IRR are suboptimal, this work exhibits attractive advantages such as non-recursive operation, joint-calibration capability of TX and RX in one combined process, and low requirement on the analog and digital parts. Indeed, the achieved IRR is fairly adequate for many wireless applications, but should be improvable when implementing in a monolithic ASIC. 
       CONCLUSION 
       [0059]    A non-recursive digital calibration technique for joint elimination of TX-RX I/Q imbalances has been described. The only add-on analog hardware are a set of source followers and MOS switches for generating an extra 90° phase shift in the reference LO which is shared among the TX and RX. The I/Q accuracy of the LO is optimized at the circuit level via employing a 3-stage RC-CR network to achieve adequate I/Q accuracy over process variations. This work avoids the sinusoidal test tone, loop-back detector, high-speed ADC and 2-dimensional recursive search algorithm that were commonly required in the prior art. A 65 nm CMOS transceiver prototype co-designed with a FPGA-implemented algorithm shows a 10 dB improvement of IRR for both TX and RX in one combined process. 
         [0060]    It will be understood that many additional changes in the details, materials, steps and arrangement of parts, which have been herein described and illustrated to explain the nature of the subject matter, may be made by those skilled in the art within the principle and scope of the invention as expressed in the appended claims.