Conclusions and perspectives

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Chapter 6

Conclusions and perspectives

In this thesis, we have explored the fundamental limits of time-delay estimation (TDE) accuracy of spread spectrum (SS) signals making use of estimation theory and signal synchronization tools.

In particular, we have focused on positioning systems, such as the Global Navigation Satellite Systems (GNSS) and we have derived some criteria to improve positioning accuracy in the additive white Gaussian noise (multipath-free) scenario, focusing on the (satellite) transmitter side of a SS system. Positioning accuracy in satellite navigation systems depends on TDE between satellite transmitted codes and local receiver replicas. Since the CRB poses the ultimate limit on the accuracy of an estimator, we have derived methods of signal design and analysis by means of studies on the Cram´er-Rao (CRB) bound for TDE. As a matter of fact, a simple criterion to determine the ultimate accuracy of a GNSS system at transmitter side, is to pose the limits with signals that can minimize such bound.

Nevertheless, GNSS systems are complex systems for which the totalitarian mini- mization of accuracy doesn’t reflect into an optimization of the entire system. For these reasons, our analysis has also explored the effects of other constraints derived from the system, such as the effect of bandlimiting and non-linearities introduced on-board the satellite, maintenance of the same levels of multiple access interference and acquisition of actual systems, and effects on system performance due to channel affected by multipath.

Let us outline the main conclusions from the development above:

• The CRB for TDE is determined by the spectral shape of the observed signal in AWGN irrespective of the specific time-domain signal format;

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146 Conclusions and perspectives

• Analysis of the optimization of linearly modulated DS-SS signal have been performed. Design criteria for both a pulse shape and spreading waveform have been introduced. A numerical algorithm able to compute a set of optimal waveforms that can achieve high accuracy while maintaining good multiple access interference and acquisition properties have been defined by means of sequential quadratic programming.

• SS-CPM modulation have been analyzed as a response to the stringent require- ments on spectral occupancy and out of band emissions typical for future GNSS.

Thanks to a proper signal parameters design, this type of signals revealed easily adaptable to the requirements on emissions while still maintaining good tracking performance. Some estimators have also been designed and analyzed, showing performance close to the correspondent CRB.

• The center frequency of the signal PSD has a strong influence on the CRB for TDE. Sideband demodulation of a bandpass signal can add a lot in terms of es- timation accuracy at the expense of widening the needed processing bandwidth of the receiver, and increasing estimation ambiguity;

• A multicarrier signal can automatically take advantage of the effect described in the previous item by playing with the subcarrier amplitudes and switching on/off come subcarriers (or subbands altogether) to yield better TDE accuracy;

• A good candidate for an MC ranging signal is Filtered Multi-Tone (Filter-Bank Multicarrier Modulation) with variable-amplitude subcarriers;

• In the presence of strong interference on the FBMCM subbands, that we can model as an ACGN channel, it is easy to find the optimum power allocation of the FBMCM radio signal on the different sub-bands to experience the minimum CRB.

For the classes of linearly modulated DS-SS signals and SS-CPM signals, the fun- damental issues investigated in this thesis in terms of estimation error bounds can be reapplied without any loss to real systems. In fact, the proposed estimators reach the CRB. For multicarrier signals, the fundamental issues investigated here in terms of estimation error bounds are the basis for future design of estimators that may hopefully reach such bounds. Previous work have shown that non-data aided timing

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estimators [48] for data communications perform not so closely to the MCRB. Design and performance assessment of code-tracking algorithms for MC ranging signals is ongoing.

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