The present invention generally relates to a system and method for producing baseband analog modulation signals in response to serial bits of digital data. The present invention more particularly relates to such a system and method for use in producing in-phase (I) and quadrature (Q) baseband analog modulation signals for use in Gaussian Minimum Shift Keying (GMSK).
GMSK modulation is well known in the art. It is a special case of Frequency Shift Keying (FSK) modulation. It has the advantage of having a narrower spectrum, which makes it useful in radio communication.
In FSK modulation, the output frequency f(t) is the carrier frequency, f.sub.c, shifted up or down the spectrum by a value f.sub.m, the modulating frequency. Such FSK modulation is produced in digital systems in the following manner.
Given a digital binary data stream b(n), a series of rectangular pulses p(t) with duration T and values of +1 or -1 can be created. The pulses p(t) may be represented by the equation below. EQU p(t)=.SIGMA.b'(n)P(t-nT), n=0, . . .
Wherein:
P(t) is the unit pulse of amplitude 1 and width T, centered at t=0;
b'(n) is +1 if b(n) equals 1; and
b'(n) is equal to -1 if b(n) is equal to 0.
The waveform p(t) is used to modulate the instantaneous frequency of a sinusoidal carrier of frequency f.sub.c. The instantaneous angular frequency is the time derivative of the phase, so the phase of the carrier is made equal to .PHI.(t)=(2.pi.f.sub.c) t+2.pi.f.sub.m .intg.p(t)dt. Its p(t)dt. Its time derivative is seen to be w(t)=d.PHI.(t)/dt=2.pi.f(t)=2.pi.f.sub.c +2x.pi.f.sub.m p(t).
The instantaneous frequency f(t) can thus be seen to vary by an amount + or -f.sub.m around a center frequency f.sub.c. The generated waveform will be phase-continuous if the integral of p(t) is continuous. The slope of the waveform at the bit boundaries is, however, not continuous and causes the spectrum to be poorly confined. In radio communication this means the energy outside the main spectral lobe will interfere with adjacent channels, which is generally undesirable.
To reduce the width of the spectrum of Frequency Shift Keying, Minimum Shift Keying (MSK) has been developed. Here, the two frequencies f.sub.c +f.sub.m and f.sub.c -f.sub.m are chosen to be as close as possible while still providing waveforms that are orthogonal over the one bit interval T. This requires the interval T to contain N cycles of the waveform of frequency f.sub.c -f.sub.m and N+1/2 cycles of the waveform of frequency f.sub.c +f.sub.m. The frequency difference is given below. EQU .DELTA.f=f2-f1=2f.sub.m =(N+1/2)/T-N/T=1/(2T)
The above relationship holds for any center frequency f.sub.c and depends only upon the value of T. For example, if T corresponds to a signaling rate of 72,000 bits per second, this results in the modulating frequency equalling 18 kilohertz. In this case, the phase change during a bit interval of duration T is + or -.pi./2 for p(t)=+ or -1 respectively.
For certain radio communication applications, such as cordless telephony, the channel width in the frequency domain is 100 kilohertz. Unfortunately, Minimum Shift Keying, even with the minimum frequency difference, produces a spectrum which still contains unacceptably high energy in the adjacent channel regions in the ranges above f.sub.c +50 kilohertz and below f.sub.c -50 kilohertz. To further reduce this effect, Tamed Frequency Modulation (TMF) has been developed wherein the binary digital serial data p(t) is low-pass filtered. Gaussian Minimum Shift Keying is a form of Tamed Frequency Modulation and uses a Gaussian filter for the low-pass filter. Such filters have a Gaussian impulse response and also a Gaussian spectrum which minimize the product of the RMS duration of the impulse response and the RMS spectral width. This permits faster signaling in the time domain while producing the narrowest spectrum. As is well known in the art, Gaussian filters may be approximated by linear phase (Bessel) filters, with a typical order of 8, and typically have cutoff frequencies anywhere between 0.4 and 1.0 times the bit rate of 1/T.
In Gaussian Minimum Shift Keying, the phase of the carrier is made equal to .PHI.(t) as represented in the equation below. EQU .PHI.(t)=2.pi.f.sub.c t+2.pi.f.sub.m .intg.g(t)dt
Wherein: g(t) is the low-pass filtered version of p(t).
In Gaussian Minimum Shift Keying, the phase change during a bit interval T depends on the shape of g(t) during that interval and will be + or -.pi./2 only if g(t) is equal to 1 or -1 during all the interval.
For practicing Gaussian Minimum Shift Keying, the modulated signal may be represented by the equation below. EQU y(t)=cos[.PHI.(t)]=cos [2.pi.f.sub.c t+2.pi.f.sub.m .intg.g(t)dt]
The modulated signal can be generated directly by producing the value of .PHI.(t) and using that value in a look up table such as a read only memory (ROM) table containing corresponding cosine values. This requires integrating a constant phase increment corresponding to 2.pi.f.sub.c which is modified in time by an amount representing 2.pi.f.sub.m g(t). This approach has been practiced in the prior art and has exhibited a significant problem when the sampling rate, which must exceed two times f.sub.c +f.sub.m, is too high. Another problem with this implementation has been the required large size of the ROM.
To overcome the problems of sampling rate and ROM size referred to above, the equivalent baseband signal (I-Q) method was developed. Here, the carrier and the modulating frequencies are separated using a trigonometric identity on y(t) as shown below. EQU y(t)=cos [2.pi.f.sub.c t]cos[2.pi.f.sub.m .intg.g(t)dt]-sin [2.pi.f.sub.c t]sin[2.pi.f.sub.m .intg.g(t)dt] EQU y(t)=-Q(t) sin[2.pi.f.sub.c t]+I(t) cos[2.pi.f.sub.c t]
As can be seen from the above, the carrier and the modulating frequencies have been separated. The I component and the Q component can be expressed as shown below. EQU I(t)=cos [2.pi.f.sub.m .intg.g(t)dt] EQU Q(t)=sin [2.pi.f.sub.m .intg.g(t)dt]
I(t) is referred to in the art as the in-phase component and Q(t) is referred to in the art as the quadrature component of the modulating signals and are known as equivalent baseband signals. The mixing, as well known in the art, can now be done in the analog domain to obtain y(t). I and Q have been generated by integrating and scaling the modulating signal to obtain the phase and then finding the cosine and sine of the phase by using a look up table in ROM, for example. This is substantially more convenient than the previously referred to method from the point of view of digital synthesis since the phase waveform has a relatively low frequency. As will be explained in greater detail hereinafter, ROM size continues to pose a problem. If a smaller ROM is utilized, truncation of the phase is required which produces errors that manifest themselves as spurs in the output spectrum. Techniques to correct this effect are known but involve multiplication operations which are not always practical to implement in some applications. Another problem with this method is that the binary waveform p(t) must still be filtered using a low-pass filter implemented either as a real digital filter or as a filtered waveform synthesizer using ROMs. However, utilizing ROMs to simulate the filter characteristics may require toleration of some time and amplitude quantization.
As will be seen hereinafter, the present invention circumvents the errors caused by prior art methods in producing I and Q analog baseband modulating signals which separate the filtering from the integration and the sine and cosine computations. As will be described hereinafter, and in accordance with the present invention, data representing the waveform amplitudes of the I and Q modulation baseband analog signals are stored in a ROM and accessed for direct synthesis of the I and Q signals in hardware. The ROM may be of very economical size including on the order of 256 addressable memory locations with each location storing a 6-bit sample word. In addition, the control logic is rendered extremely less complicated.
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