In this dissertation work, an improved digital tanlock loop (DTL) called the multi-sampling DTL (MSDTL) is proposed, its performances in various noisy environments are analyzed, and practical applications for tracking and detecting various digital modulation signals are studied. The proposed MSDTL is based on the multi-sampling scheme in which the two quadrature input signals are sampled more than once in one period of input sinusoidal signal. It has several important advantages over other digital phase locked loops (DPLL's) and the conventional DTL. These include linear characteristics, wider locking range, faster acquisition behavior. and less steady state phase error mean in the absence of noise.
In the presence of Gaussian noise, assuming that the loop phase noise disturbances due to Gaussian noise are mutually independent, we calculate the steady-state phase error probability density functions (pdf's) of the first- and second-order MSDTL's with various parameter values by solving numerically the Chapman-Kolmogorov equations. With the pdf's obtained, we determine the steady-state phase error means and variances of the first-and second-order MSDTL's by solving their respective system difference equations without approximating the sinusoidal nonlinearity or having numerical computation as is usually done in the case of the sinusoidal DPLL. The results show that as the number of samples in one period of the input sinusoidal signal increases, the steady-state phase error mean of the first-order MSDTL becomes close to zero, and that as the loop gain parameter increases, the steady-state phase error variances of the first- and second-order MSDTL's are reduced drastically.
In the case of fading communication channels, we first find the mathematical models of fading communication channels having characteristics such as log-normal, Rician, or Rayleigh distribution function. We then obtain the pdf's, means and variances of steady-state phase error of the first- and second-order MSDTL's in the three fading channels by using the same analysis method as was used in the Gaussian noisy case. As a result, it has been found that as the variance of the fading phase error process increases, the performances of the first- and second-order MSDTL's are degraded, and as the number of samples taken in one period of the input sinusoidal signal increases, the variance of phase noise disturbance due to the fading channel decreases, thereby reducing the steady-state phase error variances of the first- and second-order MSDTL's.
And, we model the loop behavior as a first passage time problem of the reduced modulo-2π phase error process with the phase-lock state and the absorption state, and derive the mean cycle-slip time and mean acquisition time from the appropriate Chapman-Kolmogorov equation describing the transition of the phase error sequence in the presence of Gaussian noise and in the fading channels. It has been observed that as the number of samples taken in one period of input sinusoidal signal increases, the normalized mean acquition times of the first-and second-order MSDTL's decreases sharply, and that as the loop gain parameter $G_c$ increases, their performances are improved slightly.
In addition, we implemented the first-order MSDTL, measured its performance for various parameter values, and compared the experimental result with the theoretical result. According to the results, the performance of the implemented MSDTL appears to be in general inferior to the theoretical prediction, possibly because of internal self-noise, quantization noise, and processing time delay of the implemented system.
As applications of the MSDTL, we newly propose two tracking and an demodulator loops, that is, the N-phase MSDTL, data-aided MSDTL, and the MSK demodulator. We analyze their performance in the absence and presence of Gaussian noise and in the fading channel. The N-phase MSDTL is a loop for tracking and detecting suppressed-carrier N-ary PSK signals. Comparing with the N-phase DTL and the digital N-phase IQ loop, the locking region of the N-phase MSDTL is considerably wider, and its steady-state phase error mean and variance are much smaller.
The data-aided MSDTL may be regarded as an improved version of the N-phase MSDTL, which utilizes a data phase detector instead of the N-times multiplication function for elimination of modulated data phase from the received suppressed carrier N-ary PSK signal. It yields the same locking range as that of the MSDTL but has better performance (e.g., bit error probability, steady state mean and variance of phase error) than the N-phase MSDTL. Finally, the MSK demodulator is essentially a two-phase first-order DTL with a fixed loop gain parameter for tracking and detecting the binary MSK signal.
For data phase estimation of the three proposed loops, we introduce two data extraction techniques based on the majority- and average-rule decision schemes, and obtain their bit and symbol error probabilities for the cases of perfect and imperfect symbol time synchronization in the presence of Gaussian noise and in the fading channel. The results shown that, as the number of samples in one symbol time increases, the bit and symbol error probabilities are reduced sharply. It has been found that the performance of the data extractor using the average-rule decision method is superior to that using the majority-rule decision method for the case of perfect symbol time synchronization, but the opposite is true for the case of imperfect symbol time synchronization when the number of the samples taken in the non-synchronized symbol time duration is larger than half of the number of samples sampled in one symbol time duration. Also, it has been found that, unlike the conventional demodulator using an analog PLL, the error rate performances of the data extractors of the three proposed loops are not dependent on the symbol time duration but on the number of samples taken in a symbol time duration.
본 논문에서는 기존의 digital tanlock loop (DTL)를 개선한 multi-sampling DTL (MSDTL)이 제안되었고, 이 새로운 MSDTL을 이용한 다양한 디지탈 변조 신호의 동기 및 복조를 위한 시스템들이 연구되었다. 또한 기존의 여러 시스템들과의 성능 비교를 위해 다양한 잡음 환경에서의 성능분석이 행해졌다. 제안된 MSDTL은 입력 정현 신호 (sinusoidal signal)의 한 주기에 두 quadrature 입력 신호들을 한 번이상 여러번 sampling하는 multi-sampling 방법을 사용하고 있어서, 기존의 DTL을 포함한 다른 디지탈 phase locked loop (PLL)들에 비해 몇가지 중요한 장점들 즉, 선형특성, 확장된 locking 영역, 초기 동기 시간 (acquisition time) 및 정적 위상 오차 평균 (steady-state phase error mean)의 감소등을 지니고 있다.
Gaussian 잡음이 있을때와 log-normal, Rician, Rayleigh 확률밀도함수를 가지는 여러 fading channel들에서의 제안된 MSDTL의 성능 분석을 위해 먼저 시스템 특성식을 구한후 Chapman-Kolmogorov 적분식을 이용하였다. 그래서, 정적 위상 오차에 대한 확률밀도함수, cycle-slipping time, acquisition time등을 다양한 loop parameter 및 입력 신호대 잡음전력비 (SNR)에 대해 구하였으며, 컴퓨터 simulation을 사용하여 구해진 결과들과 비교함으로써 이론적인 분석법이 정확함을 확인하였다. 얻어진 결과들로 부터, 여러가지의 잡음들이 있는 상황에서도, 제안된 MSDTL에서 multi-sampling횟수가 증가함에 따라, 그 성능이 급격히 향상되어, 기존의 디지탈 PLL들에 비해 훨씬 우수함을 보였다.
또한 실지로 제안된 MSDTL을 디지탈 부품들을 사용하여 제작하였고, 그 성능을 여러 변수에 대해 측정하였다. 그리고 그 실험적인 결과들을 앞에서 구한 이론적인 결과들과 비교분석한 결과, 일반적으로 제작된 MSDTL의 성능은 제작된 시스템 내의 자체잡음, 양자화 잡음, 처리시간 지연등의 이유로 이론적인 예측치보다 약간 떨어졌다.
그리고, 제안된 MSDTL을 응용하여, 디지탈 변조 신호의 동기추적 (tracking) 및 복조 (demodulation)을 위해 다양한 시스템들을 제안하였다. 먼저 N-ary phase shift keying (PSK) 신호의 동기추적 및 복조를 위해 N-phase MSDTL을 연구하였다. N-phase MSDTL은 입력신호인 N-ary PSK 신호로 부터 동기추적을 위해 변조된 데이타 위상을 제거하려는 목적으로 N배 체배하는 방법을 사용하였기에 잡음에 대한 위상오차가 증가하게 되는데, 이것으로 인한 성능저하는 N-phase MSDTL의 sampling 횟수 증가로 개선할 수 있어서, 성능분석 결과, 기존의 N-phase DTL을 포함한 다른 디지탈 PLL들 보다 좋은 성능을 가졌다. 이러한 N-phase MSDTL의 N체배 방법으로 인한 성능저하를 방지하기 위해, 본 논문에서는 데이타 위상 검출기를 사용한 data-aided MSDTL에 대해 연구하였다. Data-aided MSDTL의 성능은 데이타 위상 검출기의 정확도에 따라 크게 좌우되는데, 데이타 위상 검출기에 오차가 없을 경우에는 앞에 언급한 MSDTL과 같은 좋은 성능을 가진다. 그리고 binary minimum shift keying (MSK)의 복조를 위해 기존의 DTL을 개조한 새로운 형태의 MSK 복조기를 개발하였다. 그 결과 symbol time 동안에 sampling 하는 횟수가 증가 할수록 그 성능이 급격히 증가하여 기존의 analog PLL을 사용한 optimum correlator receiver의 성능 보다도 우수함을 보였다. 또한 MSDTL을 응용한 N-phase MSDTL, data-aided MSDTL, MSK demodulator의 성능을 fading channel에서도 분석해 본 결과 sampling 횟수를 증가 시킬 때 Gaussian 잡음이 있을 때 보다 더욱 급격히 성능 향상이 됨을 보였다.