Friday, April 27, 2012

How to Improve Forward Link Positioning for Cellular Networks? III. Hearability and Accuracy

How to Improve Forward Link Positioning ... ? I. Introduction
1x HDP Enhancements
Enhanced Location Based Services Support in cdma2000
Enhance Downlink Positioning in WiMAX/16m
How Wide A Widband Channel Should Be?
IEEE ICC 2008 Tutorial, Location Based Services for Mobiles
Location Based Services for Mobiles: I. Introduction

Hearability Issue

Hearability of a forward-link positioning system usually is quantified by how many reference signals a terminal may utilize to make a positioning fix in a pre-defined positioning duration.  In theory, a terminal need measure parameters of only 4 different reference signals for a precise three-dimension fix.  However, more reference signals a terminal can use, more diversity benefits a terminal may use for a more accurate positioning fix.

A hearability issue of a cellular positioning network generally is a dimension limitation issue.  It mostly is due to limitations of network geometry and network deployment.  In other words, it is a network issue.  For example, for a given cellular network, say a CDMA2000 1x RTT network or a WCDMA network, its hearability mainly depends on a network topology of the cellular network and a frequency reuse factor of the cellular network.  The network topology including network sectorization may affect achievable DoP values for positioning.  The frequency reuse factor may have a significant impact on co-channel interference to a terminal, which in turn relates to the positioning accuracy achievable by the terminal.  Hearability of an exemplary CDMA2000 1x RTT network is shown in Figure 1.

Figure 1. The hearability of CDMA2000 1x Pilots for AFLT, IEEE ICC 2008 "cdma2000 Highly Detectable Pilot" 
On the other hand, since major considerations for an actual deployment of cellular network base stations are voice and data service capacity, environmental impact and financial limitations, etc.,  a mobile phone network usually is not optimized for mobile positioning in nature.

Accuracy Issue

Positioning accuracy of cellular network forward link positioning is a dimension limitation issue.  Mainly the accuracy is limited by a frequency reuse factor and available bandwidth.  In general, given a certain positioning duration, wider bandwidth received reference signals have, more uncorrelated signal samples a terminal can obtain.  On the other hand, it is known that an achievable SNR highly depends on the frequency reuse factor of a cellular network.  More particularly, a CRLB of the achievable positioning accuracy is asymptotically linear to the number of uncorrelated signal samples and SNR value in dB.

In addition, from a signal processing or a receiver design perspective, a correlation between received signal samples largely depends on a sampling frequency on the received signals and achievable multipath resolution.  Multipath resolution is a function of both a channel delay profile and a bandwidth of received signals.  For example, a statistic delay profile of an exemplary cellular network is shown in Figure 2.  Additional discussions on the statistic delay profile can be found in another blog, "How Wider A Wideband Channel Should be?".   In general, wider the bandwidth of a transmit signal is and  higher the multipath resolution of a channel is achievable.

Figure 2. A statistic model of delay spread. 

Additional Reference

[1] E. Sousa, V. Jovanovic, C. Daigneault, “Delay spread measurements for the digital cellular channel in Toronto”, IEEE Trans. on Vehicular Technology, Nov 1994
[2] J. Ling, D. Chizhik, D. Samardzija, R. Valenzuela, “Wideband and MIMO measurements in wooded and open areas”, Lucent Bell Laboratories,
[3] K. Baum, “Frequency-Domain-Oriented Approaches for MBWA: Overview and Field Experiments”, Motorola Labs, IEEE C802.20-03/19, March 2003
[4] L. Greenstein, V. Erceg, Y. S. Yeh, M. V. Clark, “A New Path-Gain/Delay-Spread Propagation Model for Digital Cellular Channels,” IEEE Transactions on Vehicular Technology, VOL. 46, NO.2, May 1997, pp.477-485.
[5] A. Algans, K. I. Pedersen, P. Mogensen, “Experimental Analysis of the Joint Statistical Properties of Azimuth Spread, Delay Spread, and Shadow Fading,” IEEE Journal on Selected Areas in Communications, Vol. 20, No. 3, April 2002, pp. 523-531.
[6] Spatial Channel Model AHG (Combined ad-hoc from 3GPP & 3GPP2), “Spatial Channel Model Text Description ”, 3GPP, 2003

Friday, April 13, 2012

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

How to Improve Forward Link Positioning ... ? I. Introduction
1x HDP Enhancements
Enhanced Location Based Services Support in cdma2000
Enhance Downlink Positioning in WiMAX/16m
How Wide A Widband Channel Should Be?
IEEE ICC 2008 Tutorial, Location Based Services for Mobiles
Location Based Services for Mobiles: I. Introduction

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.

Monday, April 2, 2012

How to Improve Forward Link Positioning for Cellular Networks? I. Introduction

How to Improve Forward Link Positioning ... ? III. Hearability and Accuracy
1x HDP Enhancements
Enhanced Location Based Services Support in cdma2000
Enhance Downlink Positioning in WiMAX/16m
How Wide A Widband Channel Should Be?
IEEE ICC 2008 Tutorial, Location Based Services for Mobiles
Location Based Services for Mobiles: I. Introduction

There are many ways locating a mobile in a cellular network. The basic methods include dead reckon, proximity sensing, signal signature tracking, trilateration, multilateration, triangulation, etc. Some major approaches for cellular networks can be illustrated in Figure 1.

Figure 1. Mobile Positioning Techniques, IEEE ICC 2008 "Location Based Services for Mobiles"

Positioning performance is understood through quantifying the two parameters, hearability and accuracy. Hearability indicates how many hearable good references a terminal can track in a single snapshot. A typical number should be not less than 4. Accuracy is a well-known parameter for understanding the stability of each fix.  Usually it is quantified through the 2nd order statistics of fixes. A comparison of several mobile positioning schemes is shown in Figure 2.

Figure 2. A comparison of mobile positioning schemes
For cellular network forward link positioning, its performance is determined by 1) reference signal bandwidth, 2) channel delay spread profile, 3) co-channel interference  and 4) dilution of precision ( DoP ) or network topology.