C Seoul, Korea Lucent Technologies Inc. grants a free, irrevocable license to 3GPP2 and its Organizational Partners to incorporate text or other copyrightable material contained in the contribution and any modifications thereof in the creation of 3GPP2 publications; to copyright and sell in Organizational Partner's name any Organizational Partner's standards publication even though it may include all or portions of this contribution; and at the Organizational Partner's sole discretion to permit others to reproduce in whole or in part such contribution or the resulting Organizational Partner's standards publication. Lucent Technologies Inc. is also willing to grant licenses under such contributor copyrights to third parties on reasonable, non-discriminatory terms and conditions for purpose of practicing an Organizational Partner’s standard which incorporates this contribution. This document has been prepared by Lucent Technologies Inc. to assist the development of specifications by 3GPP2. It is proposed to the Committee as a basis for discussion and is not to be construed as a binding proposal on Lucent Technologies. Lucent Technologies Inc. specifically reserves the right to amend or modify the material contained herein and to any intellectual property of Lucent Technologies Inc. other than provided in the copyright statement above. Title:Handling varying longitude spacing away from the equator ___________________________________________________________ Source:Sarvar Patel, Lucent Technologies __________________________________________________________ Date:August 18, 2003 ___________________________________________________________ Recommendation: Review and adopt.

C Seoul, Korea Problem Distance between longitudes decrease as you move away from the equator. There are 360 degrees of longitudes at the equator and at all other latitudes. However, the radius/circumference of the circle at different latitudes is smaller than at the equator. Samsung’s lat/long proposal assumes 314 miles reusable distance ( where PLCM won’t repeat) this is only true at the equator, at different latitudes the reusable distance shrinks. Uses long >> 5 mod 2 11 Even though the longitude resolution in degrees stays the same, it shrinks in terms of miles away from the equator.

C Seoul, Korea shrinking factor r r x lat x = r * cos|lat| equator at latitude “lat”

C Seoul, Korea shrinking resuable distance At different latitudes PLCM reusable distance may be smaller than 314 miles - the proposal as is may require special checks and PLCM repeat avoidance procedures (e.g. partitioning) But there is a simpler better solution...

C Seoul, Korea Solution The radius of the circle at a given latitude is equal to R  cos |lat| R is the radius of the circle at the equator. thus there is a shrinking by factor cos|lat|. long >> 5 is equivalent to  long/2 5  this brings the precision of longitude to.153 miles at the equator. Its less, away from the equator as discussed. instead of dividing by 2 5 we can divide by other numbers for a different precision.  long/ (2 5 /cos|lat|)  will bring the resolution to.153 miles even away from the equator. For e.g. at lat 60 degrees, cos60 =.5; hence  long/ 2 6 

C Seoul, Korea Summary For latitude there is no change. For longitude the 11 bits are created by:  long/ (2 5 /cos|lat|)  mod 2 11 The resuable distance remains around 314 miles independent of the latitude.