Abstract:
A GMSK timing recovery loop in a receiver of a Gaussian Minimum Shift Keying (GMSK) link with a low channel Bit Signal-to-Noise Ratio (BSNR) and a small bandwidth-bit period BT product in a high bandwidth efficiency channel, includes a hard limiter for converting at baseband a GMSK demodulated received signal into a hard clocking signal clocking a conventional digital tracking transition loop generating the bit timing signal in closed loop control for stable time tracking performance for coherent demodulation of GMSK signals. The hard limiter provides the hard clocking signal at baseband having transitions at multiple bit periods adjusted by the bit timing error signal from the digital tracking transition loop for providing reduced jitter of the bit timing signal for accurate timing recovery and detection of communicated data.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention was made with Government support under contract No. F04701-93-C-0094 by the Department of the Air Force. The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to the field of communication systems. More particularly, the present invention relates to timing recovery loops used in Gaussian Minimum Shift Keying (GMSK) receivers for recovering transmitted data. 
     BACKGROUND OF THE INVENTION 
     Communication systems communicate signals using a variety of modulation methods. One such modulation method is Gaussian Minimum Shift Keying (GMSK). GMSK is a form of continuous phase modulation method exhibiting compact spectral occupancy and a constant envelope, thus making it compatible with a non-linear power amplifier operation without the concomitant spectral re-growth associated with non-constant envelope signals. As demands for channel capacity increase, the need for bandwidth-power efficiency with constant envelope modulation techniques is also increased. The GMSK modulation technique satisfies these two requirements. The GMSK modulation technique exhibits a constant envelope waveform with the occupied bandwidth determined by the BT product, where B denotes the 3 dB bandwidth of the baseband Gaussian filter, and T is the bit duration. These attributes render GMSK an attractive modulation scheme in communication systems where only a limited system bandwidth is available. 
     A formatted data signal, such as a non-return to zero (NRZ) data stream of a series of respective data pulses, is passed through a Gaussian filter and an integrator providing a continuous output for modulating the phase of the carrier signal. The output of the Gaussian filter is a series of Gaussian filter pulse responses that are passed through the integrator providing a continuous voltage signal to a phase modulator that phase modulates the carrier signal. Each of the predetermined number of prior data pulses contribute a signal component to the current output of the integrator at the current bit time. That is, the continuous output of the integrator at each bit time depends upon a predetermined number of prior data bits, that is, a predetermined number of prior data pulses that are inputted into the Gaussian filter and integrator, and hence the Gaussian filter and integrator have a memory represented by signal components from the prior data bits, or data pulses. This memory is known as intersymbol interference where a first data pulse is a symbol communicated as a signal having pulse filter response components lying within the time duration of the signal of a subsequent symbol of a subsequent data pulse. 
     In typical implementations, the NRZ data stream is a series of pulses having +/−1V voltage levels. Each +1V or −1V pulse contributes to a phase response that is accumulated over time. The Gaussian filter provides pulse responses to the +1V or −1V data pulses that are accumulated through the integrator. Each of the pulse responses is integrated to provide a respective phase shift of +/−π/2. The integrator provides a modulo 2π accumulated phase response of all of the +/−π/2 phase responses respectively for each Gaussian filter pulse response. The integrator output is hence an accumulated phase response from a predetermined number of prior data bits. The resulting modulo π/2 phase response is hence a continuous accumulated phase output that is a function of the prior predetermined number of data bits and resulting Gaussian filter pulse responses. The continuous accumulated phase integrator output is inputted into the phase modulator modulating the carrier signal for providing a transmitted GMSK phase modulated carrier signal where the modulated phase is the accumulated phase reduced modulo 2π representing all the previous data bits. 
     The GMSK phase modulated signal arrives at a receiver arbitrarily in time creating a carrier phase between the arrived carrier signal and a locally generated carrier signal used for coherent demodulation reception. Upon reception of the GMSK signal, the carrier phase must be firstly determined for demodulating the GMSK signal so that the resulting accumulated data phase can be determined to then enable reconstruction of the data stream at the receiver. Hence, determining the carrier phase is essential in coherent communications so that the carrier phase modulated by the data stream can be determined to recover the data. The current phase is the sum of a carrier phase and the accumulated data phase of the previous data channel bits. 
     The GMSK receiver includes a GMSK carrier tracking loop for tracking the carrier phase and frequency estimates for demodulating the GMSK carrier signal into the GMSK baseband signal. After carrier synchronization and demodulation, the GMSK carrier tracking loop provides a replica of the Gaussian filter response that is a time varying analog signal upon which the Gaussian time recovery loop operates to derive a timing signal for bit synchronization for reconstructing the data sequence. 
     Various forms of GMSK timing recovery loops using squaring loops have been described. GMSK Carrier and timing recovery techniques have used squaring or costas loops. GMSK modulators and demodulators operate at high bit signal to noise ratios (BSNR), that is, with BSNR greater than zero Db, and with Gaussian bandwidth-bit time duration products BT greater than 0.25. The GMSK demodulator has been used for carrier and bit timing synchronization under these conditions. For small values of BT and low BSNR, the carrier and bit synchronization for GMSK demodulators become extremely difficult. The loss due to squaring and self-noise due to intersymbol interference is unavoidable degrading system performance. Digital GMSK tracking loops do not perform very well in the presence of non-random data patterns where the discrete components for carrier and clock recovery may vanish. For data-derived timing recovery techniques which do not utilize squaring loops, the performance of the bit synchronizing tracking transition loops depends heavily on the BSNR and BT. For low BSNR and small BT, timing recovery becomes extremely difficult because of intersymbol interference and non-distinguishable bit transitions. For recovery of the carrier and bit timing information, the performance degradation, in terms of the carrier phase and timing jitter, associated with the existing schemes, are quite high at very low BSNR and small values of BT. 
     The GMSK carrier tracking loop has employed reverse modulation techniques for recovering the carrier phase coherently. Reverse modulation technique for tracking the GMSK signal with BT=0.3 use a phase locked loop with second order loop filter employed by the reverse modulator. The received signal R(t) is received by a reverse modulator in the GMSK carrier tracking loop to create the carrier tone fc that is acquired and tracked by the phase lock loop. The GMSK carrier tracking loop tracks the carrier tone fc to create a carrier reference that is generated by the phase lock loop for carrier demodulation of the received signal R(t), as is well known in the art. The reverse modulation techniques are used to avoid squaring loss associated with the costas or squaring loop. 
     For binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and M-ary phase shift keying, the communication signal is a square wave in nature and digital tracking transition loops (DTTL) are used for bit synchronization. That is, the DTTL is designed to track the baseband square waves of demodulated received signals. The DTTL performs optimally when the square wave signals are received in the presence of the additive white Gaussian noise. Digital transition tracking loops as part of a GMSK timing recover loop have been applied to demodulated GMSK received signals that are highly distorted square wave signals. The GMSK timing recovery loop operates upon the demodulated received GMSK signal using forms of a squaring loop or frequency doubler followed by a phase locked loop for bit timing recovery. The timing clock for timing recovery in the GMSK timing recovery loop is created by squaring the received demodulated signal, and the phase lock loop is tuned to the clock frequency for bit timing recovery. The demodulated GMSK received baseband signal containing data information, however, is severely distorted due to the Gaussian filtering at small BT products where the 3 dB cut-off frequency of the Gaussian filter is smaller than the data rate of the baseband signaling. Therefore, for small BT products of GMSK Gaussian filters, both prior GMSK timing recovery loops and DTTLs are not capable of recovering the timing information based on the received analog Gaussian filter response waveform. These and other disadvantages are solved or reduced using the invention. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to improve the bit error rate of Gaussian minimum shift keying (GMSK) demodulators. 
     Another object of the invention is to reduce data bit timing jitter of GMSK demodulators. 
     Another object of the invention is to provide a GMSK timing recovery loop including a digital tracking transition loop for bit synchronization of a received data sequence. 
     Another object of the invention is to hard limit a GMSK demodulated received signal for operating a digital tracking transition loop at baseband for the reduction of data bit timing jitter. 
     Another object of the invention is to provide GMSK timing recovery loop operating at baseband for timing synchronization of a received digital bit sequence. 
     The invention is directed to an improved GMSK timing recover loop in a GMSK receiver for providing a bit synchronization timing signal that is used for reconstructing a data sequence. The GMSK timing recovery loop includes a hard limited and a conventional digital tracking transition loop that has been used in binary phase shift keying (BPSK) and quadrature pulse shift keying (QPSK). The improved GMSK timing recovery loops operates at baseband and provides reduced bit timing synchronization jitter for reducing bit error rates. The improvement lies in the combination of a hard limiter and a digital transition tracking loop within the timing recovery loop where the synchronization performance is insensitive to the values of BT and low bit signal to noise ratios (BSNR). The improved GMSK timing recovery loop solves the GMSK bit synchronization problems for GMSK links with a low channel BSNR and small BT system using a conventional digital tracking transition loop coupled to a hard limiter for bit timing recovery. Additionally, the GMSK carrier tracking loop preferably is a reverse modulation carrier tracking loop for improved carrier tracking. 
     The improved GMSK timing recovery loop enables recovery of the bit timing signal τb(t) with high accuracy at low BSNR and small BT product, and has the advantage of negligible loss due to non-random data patterns. Another advantage associated with GMSK timing recovery loop is that it adopts the well-known digital transition tracking loop (DTTL) used in M-ary PSK systems with a modification of adding the hard limiter. The GMSK system includes the modulator and the demodulator between which is transmitted the GMSK signal. The demodulator includes a carrier tracking loop for providing a GMSK demodulated received signal Ro(t) and a bit timing recovery loop for providing the bit timing signal τb(t). The carrier tracking loop preferably employs the reverse modulation. The GMSK timing recovery loop performance employs the hard limiter adjusted by a bit timing error signal τe(t) for improved insensitivity to the values of BT while operating at low BSNR. The GMSK timing recovery loop take advantage of the observation that the cosine of the baseband GMSK signal has zero-crossings at multiples of the bit duration. The hard-limiter is used to create the NRZ data stream clocking signal that has the zero-crossings at multiples of the bit duration. The digital transition tracking loop is then used to track the zero-crossings of the NRZ data stream clocking signal from the received demodulated GMSK signal, and the bit timing signal is then generated by the DTTL with less jitter for improved data detection. In the GMSK timing recovery loop, the hard limiter is adjusted by the bit timing error signal τe(t) to reduce jitter in tracking the NRZ data stream. Hence, the digital transition tracking loop tracks the adjusted zero-crossings of the NRZ data stream, and the reduced jitter bit timing signal τb(t) is then generated for accurate data detection. 
     During data detection, the bit timing error signal τe(t), provided by the DTTL, pre-adjusts the zero crossing of the hard clock signal from the hard limiter for driving the DTTL at precise bit periods. The bit timing error signal τb(t) provided by the DTTL is used by the hard limiter to adjust the zero-crossings of the received demodulated signal Ro(t) to produce accurate timing transitions for the DTTL as part of a feedback approach. The bit timing error signal adjusts the zero-crossings of the received demodulated signal Ro(t) to produce accurate transitions for the hard limiter as tone tracking within a feedback loop. 
     Initially, the hard limiter provides the NRZ square wave transition clocking signal corresponding to the zero crossings of the received demodulated signal having time durations equaling to multiples of the bit period with the DTTL functioning to divide each square wave into an integer number of square waves corresponding to the number of bit periods without the hard limiter clocking signal in the feedback loop and without the transitions being adjusted. This open loop operation of the hard limiter is initially used to drive the DTTL in open loop with no adjustment of the zero-crossings of the demodulated received signal Ro(t) to firstly reduce the bit timing error signal τe(t) of a low predetermined value so that the bit timing error is less than ½ of a bit period. After this initialization, when the bit timing error signal τe(t) is reduced, the reduced bit timing error signal then secondly adjusts the received demodulated signal zero crossing transition for further reducing the jitter of the bit timing signal τb(t). For bit timing recovery at low BSNR and small BT, the feedback connection of the bit timing error signal τe(t) reduces the amount of jitter of the bit timing signal τb(t), while the initial non-feedback configuration is advantageous for initial acquisition. These and other advantages will become more apparent from the following detailed description of the preferred embodiment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a GMSK communication system having a GMSK timing recovery loop including a digital tracking transition loop and a hard limiter. 
     FIG. 2 is a block diagram of the GMSK timing recovery loop including the digital tracking transition loop and the hard limiter. 
     FIG. 3 is a normalized timing jitter plot depicting an improvement in bit synchronization time jitter. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     An embodiment of the invention is described with reference to the figures using reference designations as shown in the figures. Referring to FIG. 1, a Gaussian minimum shift keying (GMSK) communication system includes a transmitter  10  and a receiver  12  communicating GMSK signals S(t) from a transmitting antenna  14  to a receiving antenna  16 . The transmitter  10  includes a data source  18 , a formatter  20  and a modulator  22 . The formatter  20 , such as an NRZ formatter, communicates a sequence of data pulses d(t) to the modulator  22  that in turn includes a Gaussian filter  24  receiving the data pulses d(t) and providing pulse responses, an integrator  26  receiving the pulse responses and providing phase responses, and a phase modulator having a modulation index of π/2 for modulating a carrier reference  30  by the phase response to generate the GMSK signals S(t) transmitted from antenna  14 . The transmitter  10  is of conventional design. The signal S(t) arrives at the receiving antenna  16  arbitrarily in time as a received signal R(t) having a carrier phase difference between the arrived signal R(t) and a locally generated carrier reference, not shown. The receiver  12  includes a demodulator  32  for demodulating the receive signal R(t) into a demodulated received signal Ro(t) and for generating a bit synchronization timing signal τb(t). The receiver  12  also includes a GMSK carrier phase acquisition loop  34  for estimating the carrier phase θc and a GMSK carrier frequency acquisition loop  36  for estimating the carrier reference fc. This is required due to the difference in frequency caused by Doppler shifts and Doppler shift rates. The receiver  12  further includes a GMSK timing acquisition loop  38  for providing a bit synchronization estimate signal τo, and includes a data detector  40  for receiving and detecting the demodulated receive signal Ro(t) and the bit synchronization signal τb(t) for reconstructing and estimating the data sequence {circumflex over (d)}(t) communicated to a data sink  42 . The demodulator  32  includes a GMSK carrier tracking loop  44  for receiving the received signal R(t), the carrier phase estimate θc and the carrier frequency estimate fc for generating the demodulated receive signal Ro(t). The demodulator  32  further includes a GMSK timing recovery loop  46  for receiving the initial timing synchronization estimate signal τo and the demodulated received signal Ro(t) and for generating the bit synchronization timing signal τb(t). The receiver  12  is of conventional design with an improvement in the GMSK timing recovery loop  46  including a conventional digital tracking transition loop  48  and a hard limiter  50  that provides a hard clocking signal C H (t) for improved bit synchronization and bit period tracking. 
     Referring to FIGS. 1 and 2, and more particularly to FIG. 2, the GMSK timing recovery loop includes the new hard limiter  50  and the conventional digital tracking loop  48  including an in-phase integrator  52 , a hard limiter  54 , a transition detector  56 , a mixer  58 , a mid-phase integrator  60 , a delay  62 , a sampling rate down converter  64 , loop filter  66 , a numerically controlled oscillator (NCO)  68 , and a timing logic generator  69 . An error variant estimator  70  and an error comparator  71  are used for initial bit timing synchronization. 
     The hard clocking signal C H (t) is fed into the integrators  52  and  60 . The in-phase integrator  52  and mid-phase integrator  60  are used to generate an error bit timing signal τe(t) in a close loop operation. The in-phase integrator  52  provides an in-phase continuous signal with zero crossings. The in-phase continuous signal is hard limited between plus or minus values by limiter  54  providing an in-phase square wave signal to the transition detector  56  detecting positive to negative and negative to positive transitions of the in-phase square wave signal. The mid-phase integrator  60  integrates from −T/2 to +T/2, where T is the bit period, to provide an error output communicated to the delay  62  that is mixed with the output of the transition detector  56 . The mid-phase output is delayed by delay  62  to match in time for synchronization with the output of the transition detector  56 . The mixer  58  provides a positive or negative error signal to the converter  64  that is respectively used to advance or retard the bit timing signal τ(t) by an amount corresponding to the error output of the mid-phase integrator  60 . The sampling rate converter  58  provides a down sampled error signal to the loop filter  66  that averages and converts the timing tracking errors into a numerical value that is communicated to the numerically controlled oscillator  68  that then adjusts the digital value of the initial frequency estimate τo to the current bit timing error signal τe(t) communicated to the timing logic generator  69  for adjusting the bit timing signal τb(t). The timing logic generator  69  provides signal synchronization between the bit timing signal error τe(t) and the bit timing signal τb(t) clocking the integrators  52  and  60  to maintain the digital tracking loop  48  in synchronization in reference to the demodulated signal Ro(t). 
     In operation, the NCO  68  provides the bit timing error signal τe(t) that is fed into the hard limiter  50  that in turn provides the hard clocking signal C H (t) as part of a control feed back loop in which the hard limiter  50  functions to adjust the zero crossings transition of the received signal Ro(t) by an amount indicated by the bit timing signal error τe(t). Initially, the initial bit timing estimate signal τo is received by the NCO  68  for setting the initial bit time signal error τe(t), and hence the bit timing signal τb(t). The error variance estimator  70  provides an error signal indicating the first moment and second moment of the bit timing signal τb(t). The error variant signal is then communicated to the error comparator  71  that compares error variant signal to a predetermined value to determine if multiples of the zero crossings of the received signal Ro(t), indicating the bit period is within at least ½ of the bit period of the bit timing signal τb(t). The comparator  71  communicates an initialization signal to the hard limiter indicating when the DTTL bit timing signal τb(t) is within at least ½ of the bit period of the demodulated receive signal Ro(t). If that is not true, the hard limiter does not adjust the hard limiter signal C H (t) by the bit timing error signal τe(t) from the DTTL  48  and the clock signal C H (t) is triggered only by zero crossing of the received signal Ro(t). The unadjusted clock signal C H (t) is communicated to the DTTL for updating the bit timing signal τb(t) to be within at least ½ of the bit periods of the received signal Ro(t). Once the bit timing signal τb(t) is initially updated, the hard limiter  50  then adjusts the transitions of hard clocking signal C H (t) corresponding to the zero crossings of the received signal Ro(t) to be in synchronism with transitions of the bit timing signal τb(t). By way of example, the carrier frequency fc may be 1 MHz with a bit period of one microsecond in a channel having a BSNR of 6 db. During initialization, the error variance estimator  70  may provide an error variance of between 2.0 to 0.6 percent. The comparator  71  may have a predetermined error variance value of 0.5 percent. After initialization, the error variance may drop to 0.4 percent, indicating reduced jitter, as the hard limiter  50  adjusts the hard clock signal C H (t), by an amount indicated by the bit timing error signal τe(t), at which time, the DTTL stabilizes the bit timing signal τb(t) with reduced jitter for improved data recovery. 
     Bit synchronization timing improvement is perfected by the use of the hard limiter  50  within the feed back loop of the digital tracking loop  48  in which the limiter  50  receives the bit timing error signal τe(t) adjusted into the hard clock signal C H (t) using the demodulated receive signal Ro(t). The demodulated receive signal Ro(t) is a continuous signal that has zero crossings at multiples of the bit period. However, the zero crossing waveforms do not have sharp transitions and have superimposed noise, and consequently, the bit timing from the zero crossings of the received signal Ro(t) will jitter from zero crossing to zero crossing thereby producing poor triggering transitions. However, the hard limiter  50 , after the initial adjustment, adjusts these poor triggering transitions of the received signal Ro(t) to be in synchronism with the transitions of the bit timing signal τb(t) having consistent bit periods referenced to sharp transitions for stable DTTL clocking through reduced jittering of the hard clocking signal C H (t) to thereby reduce the jitter in the bit timing signal τb(t), for improved data detection. 
     The digital tracking transition loop  48  of conventional design optimally operates upon square waveforms having sharp transition at the zero crossings having a predetermined consistent bit period between zero crossings, but not upon analog type GMSK demodulated signals Ro(t) that would otherwise result in poor bit time synchronization and excessive jitter, due to noise and Gaussian filtering. Hence, the hard limiter  50  is used to square demodulated waveform Ro(t) so as to provide the DTTL  48  with sharp zero crossing transitions for improved synchronization. The time duration between the zero crossings of the GMSK demodulated receive signal Ro(t) is a multiple of the bit period. The hard limiter  50  functions as a comparator in respect to the demodulated receive signal Ro(t) to generate a square wave having multiple bit period duration then adjusted by the bit timing signal τb(t) so that the hard limiter  50  provides the square wave hard clocking signal C H (t) square wave each having the same bit period with slight timing errors upon which the DTTL operates to adjust the bit timing signal τb(t) under close loop control. 
     Referring to all of the Figures, and more particularly to FIG. 3, conventional BPSK or QPSK timing jitter performance  72  is improved by the GMSK jitter performance  74  and  76 , for GMSK timing recovery loops responsive to a GMSK filter having BT equal to 0.125 and a truncation length L of eight, or to a GMSK filter having a BT equal to 0.143 and a truncation length of seven, respectively. The GMSK jitter performances  74  and  76  is improved over GMSK systems using conventional squaring loops. Those skilled in the art can make enhancements, improvements and modifications to the invention, and these enhancements, improvements and modifications may nonetheless fall within the spirit and scope of the following claims.