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Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 1 Optimal Planning of Digital Cordless a T elecomm unication Systems � T. Fr uhwir th Ludwig-Maximilians-Univ ersit� at M � unc hen, German y � P . Brisset Ecole Nationale de l'Aviation Civile, F rance a W ork w as done at ecr c , Munic h, German y � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 2 Using a Mobile Phone in a Building BS BS � p a ct97 T. Fr uhwir th & P. Brisset BS PABX PSTN

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 3 The popular protot yp e Data : � A blue-prin t of the building � Information ab out the materials used for w alls and ceilings The problem : � Placing senders to co v er all the ro oms in the building � Computing the minim um n um b er of senders needed The solution : � Using constrain t tec hnology � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 4 Propagation mo del: loss/distance 110 107 dB 100 90 92 dB 80 path loss / dB 70 � p a ct97 T. Fr uhwir th & P. Brisset 60 50 40 38 dB 30 1 2 3 4 5 6 7 8 9 10 15 20 25 30 distance / m

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 5 Propagation mo del (con t.) X X L = L + 10 n log d + k F + p W 1 m i i j j 10 i j L T otal path loss in dB L path loss in 1 m distance from the sender 1 m n propagation factor d distance b et w een transmitter and receiv er k n um b er of �o ors of kind i in the propagation path i F atten uation factor of one �o or of kind i i p n um b er of w alls of kind j in the propagation path j W atten uation factor of one w all of kind j j � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 6 Direct Enco ding A naiv e solution w ould b e to � Discretize the space in grid p oin ts P i � Express the relation (constrain t) b et w een senders S p ositions and j signal lev el at eac h p oin t P : i S ig nal ( P ) = max ( S ig nal ( S ) � Loss ( S ; P )) i j j j i � Express that the signal m ust b e ab o v e a threshold at eac h p oin t : S ig nal ( P ) � T hr eshol d i It do es not w ork b ecause the relations are to o complex to constrain senders p ositions. � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 7 Dual Problem Since the propagation of a signal is not directional, sender and receiv er can b e exc hanged. Therefore the t w o follo wing prop erties are equiv ale n t : Eac h grid p oin t is reac hed b y the signal of one sender : 8 P 9 S P 2 C ov er ed ( S ) i j i j There is a sender in the neigh b ourho o d of eac h grid p oin t : 8 P 9 S S 2 C ov er ed ( P ) i j j i The dual problem is easier to solv e b ecause the C ov er ed ( P ) zones can b e i staticall y computed. � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 8 Grid of test p oin ts test point step/x step step/x � p a ct97 T. Fr uhwir th & P. Brisset H2 H2 H1 H1 1,7m

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 9 Represen tation of Co v ered Surfaces In order to express the constrain t S 2 C ov er ed ( P ), the C ov er ed ( P ) m ust j i i b e simple enough. It can b e appro ximated b y � A rectangle � A list of rectangles Algorithm 1. Compute the C ov er ed ( P ) zone b y ra y tracing for eac h P i i 2. Appro ximate C ov er ed ( P ) i 3. Set the constrain ts S 2 C ov er ed ( P ) j i 4. Do clev er lab eli ng � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 10 Ra y T racing path wall wall (xw,yw,zw) f loor2 � p a ct97 T. Fr uhwir th & P. Brisset (xf,yf,zf) sender f loor1 (xs,ys,zs)

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 11 Appro ximation b y a Union of Rectangles � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 12 Constrain t Handling Rules What? : A declarativ e language designed for writing user-de�ned constrain ts : a commited-c hoice language with m ulti-headed rules for rewriting the constrain ts in to simple ones. i e Ho w ? : A library for the Prolog ECL PS system including � a translator from constrain t handling rules to Prolog co de, � a run time for handling the constrain t store. � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 13 CHR inside constrain t Rules for the inside constrain t stating that a p oin t is inside a rectangle % inside((X0, Y0), (XLeftLow, YLeftLow)-(X Rig htU p, YRightUp)) inside(_, (Xm, Ym)-(XM, YM)) ==> Xm < XM, Ym < YM. inside((X, Y), (Xm, Ym)-(XM, YM)) ==> Xm < X, X < XM, Ym < Y, Y < YM. inside(XY, (Xm1,Ym1)-(X M1, YM1 )), inside(XY, (Xm2,Ym2)- (XM 2,Y M2) ) <=> Xm is max(Xm1,Xm2) , Ym is max(Ym1,Ym 2), XM is min(XM1,XM2) , YM is min(YM1,YM 2), inside(XY, (Xm,Ym)-(X M,Y M)) . � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 14 Extension to Union of Rectangles Rules for the inside constrain t stating that a p oin t is within a list of rectangles (a GEOMetrical ob ject) inside(S, L1), inside(S, L2) <=> intersect_geoms(L1 , L2, L3), inside(S, L3). intersect_geoms(L1, L2, L3) <=> setof(Rect, intersect_geom(L 1, L2, Rect), L3). intersect_geom(L1, L2, Rect) <=> member(Rect1, L1), member(Rect2, L2), intersect_rectangl es(Re ct1, Rect2, Rect). � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 15 Lab eling The constrain t phase asso ciates a sender to eac h C ov er ed ( P ) zone. The i lab eling phase has to c ho ose the n um b er and the p ositions of the senders. It is expressed b y stating that as man y senders as p ossible are equal. equate_senders([]) <=> true. equate_senders([S|L] ) <=> ( member(S, L) or true ), % Try to equate a sender with others equate_senders(L). � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 16 A T rue Example � p a ct97 T. Fr uhwir th & P. Brisset

Optimal Planning of Digital Cor d less T ele c ommunic ation Systems 17 Conclusion On this application, constrain t tec hnology (CHR) pro v es to � ha v e big expression p o w er: the whole program for solving the problem is only a couple of h undred lines and required few man-mon ths to b e implemen ted. � b e �exible: the �rst protot yp e w as easily extended from rectangles to union of rectangles, from 2-D to 3-D, ... � b e extensible: for example, restricting allo w ed senders lo cations to w alls needs only one more inside constrain t. � b e e�cien t: for a t ypical o�ce building, an optimal placemen t is found within a few min utes (up to 25 base stations). � p a ct97 T. Fr uhwir th & P. Brisset