Conclusions

The purpose of this thesis, as stated in Chapter 1, was to i. identify issues with joint data/pilot tracking; ii. analyse the impact of those issues;

iii. propose methods to overcome the identified issues;

iv. analyse the performance of the proposed methods against pilot-channel- only tracking.

In order to establish a reliable metric to analyse the performance of the tracking algorithms, the problem of reliable C/N0 estimation was also addressed.

7.1.1 Reliable C/N0 Estimation

A comprehensive theoretical analysis of C/N0 estimation was provided, with

emphasis on using both the data and the pilot channels. The CRLB derived for C/N0

estimation helped in understanding the following aspects:

i. the noise variance reduction achievable in using both the data and the pilot channels for C/N0 estimation gradually diminishes for signals weaker than

ii. the CRLB for C/N0 estimation using correlator outputs accumulated over

shorter predetection intervals (𝑇𝑇_{𝑐𝑐𝑐𝑐ℎ}) is shown to be lower than the one using observations with longer 𝑇𝑇_{𝑐𝑐𝑐𝑐ℎ}; a choice of 𝑇𝑇_{𝑐𝑐𝑐𝑐ℎ} = 1 ms with the knowledge of 20 observations per data bit was shown to avoid information loss as compared to the use of 𝑇𝑇_{𝑐𝑐𝑐𝑐ℎ} = 20 ms where the data bit sign reverses with every observation.

The bounds presented in this thesis can be used as a reference in the performance analysis of any joint data/pilot C/N0 estimator. Further, a maximum-likelihood (ML)

estimator that uses both data and pilot channels was derived. The approximation used in deriving the ML estimators was shown to degrade in performance for signals weaker than 25 dB-Hz, and the degradation being manifested as a bias in the estimates. Hence, the joint data/pilot estimator with approximation is unreliable for weak signals. An iterative solution was proposed to overcome this issue and a detailed analysis was presented. The proposed joint data/pilot iterative ML estimator has been demonstrated to be reliable for estimating C/N0 down to 17 dB-Hz. For lower C/N0 values, standard tracking loops (with

constant noise bandwidth) lose lock, and the C/N0 cannot be estimated. However, as is

evident from the numerical simulation results, the estimator is less biased even for C/N0

lower than 17 dB-Hz.

7.1.2 Joint Data/Pilot Carrier Frequency Tracking

The purpose of Chapter 4 was to outline issues related to joint data/pilot carrier frequency tracking, to provide a detailed performance analysis of said tracking, and to use the knowledge gained to design methods for joint data/pilot carrier phase tracking.

One of the issues in joint data/pilot frequency tracking is the increase in noise variance of the frequency error estimates under weak C/N0 conditions, due to the non-

linear nature of the discriminators used. An application of on-the-fly variance estimators (Moir 2001) to compute the weights was demonstrated to overcome this issue. Finally, a performance analysis was presented for two differently-weighted discriminator combinations, with emphasis on performance under weak C/N0 conditions. The Costas

discriminator combination, which uses cross product discriminators with decision feedback (𝐷𝐷_{𝑑𝑑𝐸𝐸}) on both the data and pilot channels, was shown to suffer from significant degradation in tracking threshold. The only advantage of the Costas discriminator combination is in operation under moderate-to-strong signal conditions. Further, using identical discriminators on both data and pilot channels allows one to assign equal weights in the combination eliminating extra computational burden from the weight computation algorithm. The discriminators used by the standard discriminator combination on the data and pilot channels are different. The analysis provided in this thesis used a cross product (𝐷𝐷_{𝑐𝑐𝑃𝑃𝑐𝑐𝐿𝐿𝐿𝐿}) discriminator on the pilot channel and a cross product with decision feedback (𝐷𝐷_{𝑑𝑑𝐸𝐸}) discriminator on the data channel. With proper weighting, the standard discriminator combination was shown to acquire and maintain frequency lock over the same levels of attenuation as an FLL running solely on the pilot channel. However, under weak C/N0 conditions, some degradation in frequency jitter was

observed by using a standard discriminator combination as compared to pilot-channel- only tracking. This was explained as the effect of the change in discriminator gain due to data bit decision errors in 𝐷𝐷_{𝑑𝑑𝐸𝐸}, which were unaccounted for in the design.

The results obtained in this chapter demonstrated the importance of the discriminator linearity region and appropriate weighting in joint data/pilot tracking, which is utilized in the design of methods in the subsequent chapters.

7.1.3 Joint Data/Pilot Carrier Phase Tracking

Chapter 5 discusses problems specific to joint data/pilot carrier phase tracking. Two different methods were proposed to overcome problems arising in joint data/pilot phase tracking. One method is an extension of the weighted discriminator combination available in the literature for standard tracking architecture, whereas the other utilizes a Kalman filter-based architecture.

For joint data/pilot tracking with a weighted discriminator combination, utilizing ATAN2 discriminators on both data and pilot channels was shown to help in reducing the bias in the estimates under weak C/N0 conditions, mitigating the impact of the reduced

phase pull-in range of Costas discriminators. In order to use an ATAN2 discriminator on the data channel, a data bit decision process as explained in Chapter 5 has been used. This process introduces noise due to an increase in data bit decision errors under weak C/N0

conditions. This has been accounted for in the computation of weights in the combination (using on-the-fly weight computation), as well as in the cost function of the noise bandwidth adaptation algorithm. Further, the design of the PLL in the digital domain helped in accurately predicting the effect of thermal noise and dynamic stress for a given scenario. These design considerations led to a more stable design of joint data/pilot tracking with adaptive noise bandwidth. From the results presented in Chapter 6, it is evident that the proposed method suffers no significant loss (less than 1 dB) in tracking sensitivity as compared to pilot-channel-only tracking.

A second approach for joint data/pilot tracking is provided using a Kalman filter (KF). The tracking sensitivity performance of KF-based joint data/pilot tracking in a static environment has been demonstrated to be similar to that of the previous method. In summary, both proposed methods demonstrated the ability to maintain lock over the same level of attenuation as a pure PLL on the pilot channel. Through comparison of the two proposed methods, it became apparent that the method based on the standard architecture is able to provide performance similar to a KF-based architecture for a static receiver, with less computational burden.

Chapter 6 also highlights the advantage of using a joint data/pilot over a single channel tracking for scenarios with user dynamics in severely attenuated conditions and increasing acceleration stress under open sky conditions. Since joint data/pilot tracking methods can make use of the power from both data and pilot channels, the effect of tracking jitter due to thermal noise is reduced as compared to single channel tracking. Thus, joint data/pilot tracking methods can use a larger noise bandwidth in the presence of dynamics. The results obtained in Chapter 6 under dynamic scenarios with a user taking several turns demonstrate the advantages of joint data/pilot tracking in reducing the bias in Doppler estimates, the time taken to regain phase lock, and, most importantly, to maintain phase lock under these conditions.

In summary, the proposed joint data/pilot phase tracking algorithms can help in utilizing both data and pilot channel information, without significantly losing the inherent advantages of a pure PLL.