Abstract:
A novel method and apparatus for computing the phase derivative and also the frequency of a received signal from digital baseband In-Phase (I) and Quadrature (Q) samples is derived and implemented. The resulting method computes the phase derivative and frequency of a received signal from I and Q data directly without the intermediate problem of phase unwrapping required for computing the derivative of modulo-mapped phase. The apparatus is intended for use both in single channel systems performing digital frequency demodulation and in direction-finding systems computing differential phase across two channels.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The invention relates to an improved method of extracting instantaneous frequency information from a received signal. More specifically, the invention relates to a method and system for computing the phase derivative, which is proportional to the signal instantaneous frequency, from the in-phase and quadrature components of an input signal without the need for the interim step of phase unwrapping. The invention can also be used to compute differential phase between two signals across two channels. 
         [0003]    2. Description of Related Art 
         [0004]    The process of extracting frequency information from a signal is well-documented. Methods exist for accomplishing the frequency extraction using analog or digital processing or a combination of both, and the different methods provide varying levels of fidelity in terms of resolution in time, frequency and spectral power. In the fields of communications and military signal processing, there is a need for high fidelity measurements of signal frequency. 
         [0005]    In the analog realm, an approach to deriving frequency information is with a superheterodyne receiver. In the superheterodyne receiver, a local oscillator (LO) is used to convert an incoming radiofrequency (RF) signal to a fixed intermediate frequency (IF) by the heterodyning (mixing) process. A single circuit tuned to the IF can then filter, amplify and otherwise process the signal. To sample frequency data, the LO is swept across the frequency range of interest, and the resulting amplitude at the output of the IF circuit can be sampled, for instance, to provide amplitude versus frequency. This process provides a spectral profile of the signal. 
         [0006]    Other heterodyne techniques may include additional processing of the analog IF signal in order to produce in-phase and quadrature (I and Q) signal components. The I and Q components make it convenient to derive the instantaneous signal envelope and phase. The derivative of phase with respect to time provides a measure of frequency. 
         [0007]    A typical implementation of an instantaneous frequency measurement receiver utilizes a crystal video receiver with the addition of a frequency sensing method. The frequency sensing may be accomplished by dividing the signal into two paths with different relative delays, then comparing the phase from each path. The phase difference is proportional to the carrier frequency. 
         [0008]    A typical implementation for digital processing is shown in  FIG. 1  and involves the following steps:
       1. Analog-to-digital conversion  20  of an analog input signal  10  at a sampling rate f s  that satisfies the Nyquist sample rate criterion,   2. Digital quadrature demodulation  30  to generate baseband in-phase (I)  40  and quadrature (Q)  50  signal components,   3. Computation of signal phase  80  and amplitude  70  from baseband  140  and Q  50  signal components, typically done using a coordinate rotation digital computer (CORDIC) routine  60 ,   4. Unwrapping  90  the phase to remove the modulo 2π discontinuities inherent in the arctangent function, and   5. Estimation of signal frequency  110  from the derivative  100  of adjacent samples of the unwrapped phase.       
 
         [0014]    The CORDIC method is a well documented and well utilized digital signal processing technique in the field of communications and RF signal processing. The use of the CORDIC routine for fast digital trigonometric computations is known from the article “The CORDIC Trigonometric Computing Technique,” published in the IRE Transactions on Electronic Computers, September 1959 by J. E. Voider. The computations are effected via simple signal processing operations such as binary shifts, additions, subtractions and by calling constants from look-up tables. The CORDIC thus has a very simple and efficient circuit structure which in an integrated form requires comparatively little processing resources. In one mode of operation, the CORDIC operates in the so-called rotation mode in which mode a Cartesian (rectangular) coordinate representation is converted into a polar coordinate signal representation. 
         [0015]    Examples of the utilization of the CORDIC routine are shown in literature. In Gerardus U.S. Pat. No. 5,230,011, the CORDIC is applied to achieve phase output. In Sullivan U.S. Pat. No. 7,020,190, the CORDIC is used as a means of accomplishing frequency translation, though direct computation of frequency is not shown. 
         [0016]    The frequency computation process depicted in  FIG. 1  necessitates the unwrapping  90  of the phase  80  prior to differentiation  100 . The process of phase unwrapping is well documented, and it involves the detection and removal of discontinuities in the measured phase resulting from the modulo 2π characteristic of the arctangent function. An example of the phase-unwrapping problem is demonstrated in a recent US Patent Application by Puma, US2006/0115021. In Puma, a phase correction circuit (illustrated in  FIG. 4  of US2006/0115021) is utilized to correct the modulo 2π discontinuity in the typical CORDIC output. Discontinuities typically found in the unwrapped phase are shown in  FIG. 2  for a linear frequency modulated (LFM) signal  200  where the phase is constrained to modulo 2π and is centered at zero. 
         [0017]    As another example, the phase for a constant frequency signal is shown in  FIG. 3  in both wrapped  300  and unwrapped  310  forms. Note that the phase is linear for this constant frequency case. Here the impact of the modulus operator is more apparent where the limitation of a range of 2π  320  is shown for the wrapped phase  300 . In  FIG. 4  is shown the direct first-order difference of the wrapped phase  400  and the direct first-order difference of the unwrapped phase  410 . For the wrapped phase  300 , an approximate 2π discontinuity occurs in the derivative  400  where the phase wraps, which causes anomalous spikes  420  in the derivative. 
         [0018]    Phase unwrapping requires additional logic in a demodulator design and is fairly straightforward for signals that are highly over sampled (f s &gt;&gt;2*BW, sample frequency is much greater than two times the signal bandwidth) and with a high signal to noise ratio (SNR). However, for near critically sampled signals (f s ≈2*BW) with increased noise levels (lower SNR), the process can be prone to errors. 
       BRIEF SUMMARY OF THE INVENTION 
       [0019]    It is the object of this invention to provide a novel method and apparatus for computing the phase derivative and also the frequency of a signal from In-Phase (I) and Quadrature (Q) components of the signal. The resulting method computes frequency from I/Q data without the need for an interim step of phase unwrapping. The method is intended for use in either single channel systems performing digital frequency demodulation or in direction-finding systems computing differential phase across two channels. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]      FIG. 1  is an illustration of a typical digital frequency demodulation process. 
           [0021]      FIG. 2  is an illustration of the modulo 2π (wrapped) phase of a linear frequency modulated signal. 
           [0022]      FIG. 3  is an illustration of a linear phase signal, showing both the wrapped and unwrapped representation of phase. 
           [0023]      FIG. 4  is an illustration showing the discontinuities of the derivative of wrapped linear phase compared to the continuous derivative of unwrapped linear phase. 
           [0024]      FIG. 5  is an illustration of the complex vector representation of two signal samples. 
           [0025]      FIG. 6  is an illustration of a circuit to accomplish the phase derivative computation for a single channel. 
           [0026]      FIG. 7  is an illustration of a circuit to accomplish the two channel differential phase computation. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0027]    The present invention will now be described. The present invention provides a novel method for computing frequency directly from phase samples without the need for an interim step of phase unwrapping. 
         [0028]    Let two complex vectors Ŝ N    500  and Ŝ N-1    510  represent consecutive I/Q samples, as shown in  FIG. 5 . The complex vectors are given by 
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         [0029]    The product of the first vector with the conjugate of the second vector yields 
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         [0030]    The exponent argument θ N −θ N-1  is the phase difference Δθ between the consecutive samples. To compute it, the consecutive samples are expressed in rectangular form as 
         [0000]        Ŝ   N =( I   N   +j·Q   N )   E-4 
         [0000]      and 
         [0000]        Ŝ*   N-1 =( I   N-1   −j·Q   N-1 )   E-5 
         [0031]    and multiplied to yield 
         [0000]        Ŝ   N   ·Ŝ*   N-1 =( I   N   +j·Q   N )·( I   N-1   −j·Q   N-1 )   E-6 
         [0032]    Expanding Equation E-6 yields 
         [0000]        Ŝ   N   ·Ŝ*   N-1 =( I   N   ·I   N-1   +Q   N   ·Q   N-1 )+ j ( I   N-1   ·Q   N   −I   N   ·Q   N-1 )   E-7 
         [0033]    The corresponding differential phase between samples can be computed from Equation E-7 employing the arc tangent function: 
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         [0034]    The expression for differential phase given in Equation E-8 can be implemented using a CORDIC algorithm. The CORDIC algorithm is a commonly used digital signal processing technique used to implement several functions, including rectangular to polar conversion. The CORDIC therefore serves as a means of computing the phase angle of the equivalent polar coordinate representation of the rectangular coordinates given inputs that represent the abscissa  530  rectangular coordinate and the ordinate  520  rectangular coordinate. The present invention relates to modifying the inputs applied so that a means of computing the phase angle from rectangular coordinates yields the phase derivative rather than the phase. This modification of inputs when applied to, for example, a CORDIC routine results in the computation of the differential phase Δθ between adjacent samples. 
         [0035]    An apparatus devised with logic circuitry to compute the differential phase between adjacent I/Q samples is shown in  FIG. 6 . The typical implementation of the CORDIC  665  utilizing the quadrature inputs of the I  600  and Q  605  signals is shown, where the CORDIC  665  outputs are signal amplitude  670  and phase  675 . The delay registers  630  and  631  are used for time alignment of the outputs of CORDIC  660  and CORDIC  665 . In order to obtain the phase derivative and signal frequency, the phase output  675  of the CORDIC  665  must first be unwrapped to remove any modulo 2π discontinuities. 
         [0036]    An apparatus for computing the signal frequency directly without the interim step of phase unwrapping is also shown in  FIG. 6  and is implemented using a separate CORDIC  660 . The apparatus consists of one inverter  640 , four multipliers  620 ,  621 ,  622  and  623 , two adders  650  and  655 , and eight delay registers  610 ,  615 ,  632 ,  633 ,  634  and  635 , provides the instantaneous differential phase  690 , which is proportional to frequency, per clock cycle without the need for phase unwrapping. The other output  680  of the CORDIC  660  is not used. 
         [0037]    The device shown in  FIG. 6  utilizes the sampled I  600  and Q  605  signal components as input. Delay registers  610  and  615  are used to generate a one sample delay in each the I  600  and Q  605  data. Multiplier  620  multiplies the I  600  data with the one sample delayed I data and passes the result to delay register  632 . Multiplier  621  multiplies the Q  605  data with the one sample delayed Q data and passes the result to delay register  633 . Multiplier  622  multiplies the Q  605  data with the one sample delayed I data and passes the result to delay register  634 . Multiplier  623  multiplies the I  600  data with the one sample delayed Q data and passes the result to delay register  635 . 
         [0038]    The output of delay registers  632  and  633  are combined by adder  655 . The output of delay register  635  is inverted by inverter  640  and combined with the output of delay register  634  by adder  650 . The combined outputs of adders  650  and  655  are the modified inputs to the CORDIC  660 . These modified inputs are what produce the instantaneous phase derivative  690  at the phase output of the CORDIC  660 . Frequency is easily computed from the phase derivative by scaling the phase derivative by a scale factor proportional to the sample rate of the input signal. 
         [0039]    While the CORDIC has been shown here as a preferred implementation for computing the phase angle of the equivalent polar coordinate representation of the rectangular coordinates given inputs that represent the abscissa  530  rectangular coordinate and the ordinate  520  rectangular coordinate, it should be apparent to those skilled in the art that a number of means could be applied to compute this phase angle, including the use of a look-up table or some other form of arctangent calculation. 
         [0040]    In  FIG. 7 , a circuit similar to that described in  FIG. 6  is used to compute the differential phase between two channels. The input in-phase  600  and quadrature  605  signals and the delay registers  610  and  615  are replaced by channel two in-phase  601  and quadrature  606  sampled signals and channel one in-phase  602  and quadrature  607  sampled signals. 
         [0041]    Multiplier  620  multiplies the channel one I  602  data with the channel two I data  601  and passes the result to delay register  632 . Multiplier  621  multiplies the channel one Q  607  data with the channel two Q  606  data and passes the result to delay register  633 . Multiplier  622  multiplies the channel one I  602  data with the channel two Q  606  data and passes the result to delay register  634 . Multiplier  623  multiplies the channel two I  601  data with the channel one Q  607  data and passes the result to delay register  635 . 
         [0042]    The output of delay registers  632  and  633  are combined by adder  655 . The output of delay register  635  is inverted by inverter  640  and combined with the output of delay register  634  by adder  650 . The combined outputs of adders  650  and  655  are the modified inputs to the CORDIC  660 . These modified inputs are what produce the differential phase  690  between the two channels at the phase output of the CORDIC  660 . 
         [0043]    It should be understood that the description of the present invention is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention. The details may be varied substantially without departing from the spirit of the invention, and the exclusive use of all modifications which are within the scope of the appended claims is reserved.