Friday, April 13, 2012

How to Improve Forward Link Positioning for Cellular Networks? II. Fundamentals

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In general,  how to improve forward link positioning in a cellular network is a mix of dimension limitation issues and interference issues such as co-channel interferences.  It also relates to the well-known near-far issue.  In an actual development and deployment of a cellular network, both link budget and design target of the cellular network should be considered for improving forward link positioning.  Due to the complexity nature of this engineering issue, it is necessary to study it from various aspects and understand scalability of each involved engineering factor.  In the following, this topic is studied respectively from information theory, receiver design and engineering deployment perspectives.


A Information Theory Perspective

Information theory usually tells us how far we may go under a certain set of limitations.  More particularly, it may also help us understand how an optimal performance may scale with various combination of different inputs.  From an information theory perspective, a lower bound on the second order statistic of a signal parameter estimation is the well-known Cramer-Rao Lower Bound (CRLB), which in turned is decided by an inverse of Fisher information for unbiased cases.  Basically, this means that the achievable accuracy is dominated by the number of available uncorrelated samples and an achievable SNR value during a given signal estimation duration.  Appearantly when more uncorrelated signal samples and higher SNR are available, a more accurate positioning fix is possible. However, a CRLB may move up or down in different directions when the number of signal samples and/or a received SNR value change.  As shown in Figure 1, a root mean squared error (RMSE) in dB of positioning accuracy may have different linear relationships with SNR in dB and the number of samples. 

Figure 1. The scalability of CRLB

Asymptotically, this relationship may also be expressed as 

lg (  ΔRMSE  ) ~ O( SNRdB )  or  O( Nsample )

A Signal Processing Perspective

From a multiuser signal processing perspective, a near-far problem means a simple increase of forward link signal power may not help improve the SNR for forward link positioning.

A Link Budget Perspective

A standard representation of cellular networks can be sown in Figure 2, where the frequency reuse factor is K = 3. From a link budget perspective, the SINR and coverage of received reference signals are determined by both cochannel interference (CCI) and path loss. CCI is a function of both the distance to neighbor cells and frequency or time reuse factor K.  In general, the strength PCCI of CCI linearly decreases with the increasing of the reuse factor K. Its strength in dB is linear to the log of the average cell size of a cellular network. This can be shown as

PCCI  ~ O( K )  and  lg( PCCI ) ~ O( cell size in dB )


Figure 2. An illustration of cellular networks with a frequency reuse factor of 3.

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