The Role of Boolean Function in Fractal Formation and it s Application to CDMA Wireless Communication

The Role of Boolean Function in Fractal Formation and it’s Application to CDMA Wireless Communication Somnath Mukhe rjee Dr. B. C. Roy Engineering College Email: somnath.7.mukher jee@gmail.com Durgapur, West Bengal-713206, INDIA Pabitra Kumar Ghosh Dr. B. C. Roy Engineering College Email: pabitra061 14@gmail.com. Durgapur, West Bengal-713206, INDIA Abstract — In this paper, a new trans formation is generated from a three variable Boolean function 3, which is used to produce a self-similar frac tal pattern of dimension 1.58. Th is very fractal pattern is used to reconst r uct the whole structural position of resources in wireless CDMA network. This reconstruction minimizes the number of resources in the network and so naturally network consumption costs are getting reduced. Now - a -days resource controlling and cost minimization are still a severe problem in wireless CDMA network. To overcome this problem fr actal pattern produced in our research provides a complete solution of structural position of resources in this Wireless CDMA Network. Keywords- Boolean functions, Level of Boolean function, Fractal Pattern, Wireless CDMA Networks, BTS, Wireless Network Port . I. Introduction A three variable Boolean fun c tion is used to generate the fractal pattern for the implementation of Wireless CDMA Network. More precisely, one t rans formation is generated from the three variable Boolean function named as 3 (named according to the Wolfram naming conventions [2]) which can produce the self-similar fractal pattern in a significant manner of increasing the level of Boolean function. In papers [1], [2] we have explored an applicatio n in the formation of self- similar and chaotic fractal formations, using one transformation named as ‘Carry Value Transformation’ (CVT). In this paper, we have explored the alg e braic beauties of t he newly generated function and their application towards wireless communication problem basically on Wireless Code- Division-Multiple-Access (CDMA) network. It is to be noted that we have generated the fractals using a computational program written in C language and the compiler version is Borland C -3.0 by the newly defined transformation from the Boolean function 3. At first, we have generated one square matrix using the defined transform ation as obtained in [1], and then we got the fractal using the matrix entities. The Wireless CDMA Network is designed based on the above generated fractal pattern. The recourses of the wireless CDMA Network if placed in the fractal pattern then the efficiency and effectiveness would be enhanced on the basis of design and maintenance cost. Interestingly, the services into this des i gned network are uniformly dis tributed. II. Review of Earlier Wor ks and Fundamental Concepts In paper [3], resource allocation for the purpose of energy efficiency has been explored, but in t his paper with the he lp of fractal geometry we implement the des igning of the positional structure of resources in w ireless CDMA network. Let us first warm up ou rse lves with some fundamentals, which are related to the current pape r. A. Boolean Function: A Boolean function f (x 1 ,x 2 ,,x 3 ,x 4 ………x n )variables is defined as a mapping from {0,1} n into {0,1} . It is als o interpreted as the output column of its truth table f which is a binary str ing of length 2 n . For n -variables the nu mbe r of Boolean functions is 2 2n and each Boolean function is denot e d as f R n kn own as the function number R (als o interpreted as rule number R) , of n -variable. Her e R is the decimal equivalent of the binary sequence (starting from bottom to top, with top is the LSB) of the function in t he Truth Table, and nu mbe ring scheme is proposed by Wolf ram and popularly known as Wolframs naming convent ion. B. Fractal Pattern The pattern, which reserves a fractional real number, as its fractal di m ension is known as Fr actal patter n. Here we us e the similarity dimension as a fractal dimension. The sim ilarity dimension is defined as follows For a self-similar pattern, t he re is a relation between the scaling factor ‘S’ and the number of pieces ‘N’ into which the pattern can be divided and t hat relation is N = 1/S D this relation can be equi valently written D = log N/log (1/S). This ‘D’ is called fractional dimension or fractal dimension (self-similarity dimens ion). . C . BTS (Base Transceiver St ation) A base transceiver st ation or cell site (BTS) is a piece of equipment that facilitates wireless communication between user equipment ( UE) and a network. UEs are devices like mobile phones (handsets), WLL phones, computers with wireless internet connectivity, WiFi and WiMAX gadgets etc. The network c an be that of a ny of the wireless co mmunication technologies like GS M, CDMA, WLL, WAN, WiFi, WiMAX etc. BTS is also referr ed to as the radio base station (RBS) , node B (in 3G Networks) or, simply, the base station (BS). D. Wireless Network Port Wireless Network ports ar e the points that contains the device to emit web to provide users uninterrupted network, it may be compared with the BTS(Base Transceive r Station ) of the mobile communication E . Why. Wireless CDMA Network There are several wireless networks like TDMA(Time Division Multiple Access), FDMA(Frequency Division Multiple Access),CDMA(Code Division Multiple Access). In FDMA t he available bandwidth is divided into frequency bands, that means each station i s allocated to send its data. In TDMA each s tation share the bandwidth of the channel in time , each station is allocated a t im e slot during which it can send data. In both (FDMA & TDMA) case a switching technique is r equired to pro vide the network service to the station. CD MA(Code Divisi on multiple Access) Network is a third-generation (3G) wireless communications and it is a form of multiplexing, which allows numerous signals to occupy a single transmission channel, optim izing the use of available bandwidth. The technology is used in ultra -hi gh- frequency (UHF) cellular telephone systems in the range from 800-MHz to 1.9 -GH z. In CDMA one channel carries all transmissions simultaneously where channel means a common path between sender and receiver [4]. CDMA simply m eans communications with different codes. Let us assume we have three stations namely station-1, station-2 and station-3 are connected with the same channel The data from station -1 is d1, from stati on-2 is d2 and so on are allocated for each station. Each station have to be assigned also a particular code e.g. c1,c2 and so on. The data carried out by the channel is the sum of the terms(d1.c1,d2.c2,d3.c3…), that means the data in the channel at any instant time is the sum of the values of d1.c1,d2.c2,d3.c3 and so. Any station wants to receive the data that is sent from the other station ,have to multiply the data on the channel by the code of the sender. That means here is no time delay for transmission of data like any others wireless communication. In case of CDMA there i s no such switching technique is requir ed to provide the network service. So the implementation of CDMA wireless netw ork by the model of fractal pattern is possible in practically to provide the network services am ong the stations. F. Carry Value transform ation (CVT ) In [1] we have defined a new transformation named as CVT and shown its use in the f ormation of fractals. If 1 1 ( , , . . ., ) nn a a a a and 1 1 ( , , . . ., ) nn b b b b are two n-bit strings then 1 1 1 1 ( , ) ( , , . . . , , 0 ) n n n n CV T a b a b a b a b is an (n+1) bit string, belongin g to the set of non-negative integers, and can be computed bit wise by logical AND operation followed by a 0. Conceptually, CVT in binary number system is same as performing the bit wise XOR operation of the operands (ignoring the carry-in of each stage from t he previous stage) and s imultaneously the bit wise AND ing of the operan ds to get a string of carry- bit s, the latter string is padded with a ‘0’ on the right to signify that there i s no carry -in to the LSB (the overflow bit of th is ANDing being always ‘0’ is simply ignored). Example: Consider the CVT of the numbers (13) 10 ≡ (1101) 2 and (14) 10 ≡ (1110) 2 . Both are 4-bit nu m bers. The carry value is computed as follows: Carry: 1 1 0 0 0 Augend: 1 1 0 1 Addend: 1 1 1 0 XOR: 0 0 1 1 Carry genereted in ith column saved in (i -1)th column In the above example, bit wise XOR gives (0011) 2 ≡ (3) 10 and bit wise ANDing followed by zero-padding gives (11000) 2 ≡ (24) 10 . Thus ( 110 1 ,1 110 ) 1 1 0 0 0 CV T and equivalently in decimal notation one can write ( 13 ,14) 2 4 CVT . In the next section, a new notion of CVT named as Level Sensitive Carry Value Transformation is discusse d. III Level Sensitive Carry V alue Transformation The Level Sen sitive Carry Value Transform ation is defined on the domain ( ZxZxN) and it maps to Z . e. In ot her words, LSCVT is a mapping from ZxZxN- >Z where Z is set of non- negative integers and N is the set of all natural num ber . Here we have considered Boolean function 3 and firstly the the decimal number ‘3’ is converted to it’s binary form then the corresponding binary values are assigned according to the functional values of the truth table of a three variable Boolean func tion. For Boolean function 3 the functional values of the truth table are assigned to the corresponding binary values of 3. Function -------------- Value f(0,0,0) ------ 1. f(0,0,1) ------ 1. f (0,1,0) ------ 0. f(0,1,1) ------ 0. f (1,0,0) ------ 0. f(1,0,1) ------ 0. f(1,1,0) ------ 0. f(1,1,1) ------ 0. Now the binary values of the corresponding any number in a matrix are Z1 ----- the binary form of Z1 Z2 ----- the binary form of Z2 N ----- the binary form of N ------------------------------- ----------- The corresponding functional value from the above truth table. Example:- Z1=4, Z2=5, N=4 Then the corresponding binar y values are 4 ----- 1 0 0 5 ----- 1 0 1 4 ----- 1 0 0 --------------------- 0 1 0 So the decimal value of t he corresponding binary value is 2. Thus LSCVT(100,101,100) = 010 and equivalently in decimal notation it can be w ritten LSCVT(4,5,4) = 2. IV. Generation of Self-Simila r Fractal Pattern Using LS CVT A matrix is constructed tha t contains only the carry values (or even terms) defined above between all possible integers a’s , b’s and c’s are arranged in an ascending order of x, y and z-axis respectively. We observe so m e i nter esting patterns in the matrix. We would like to make it clear how the matrix is constructed Step 1 : Arrange all integers 0,1,2,3,4 …(as long as we want) in ascending order and place it in three axis(x,y,z) in the matrix. Step 2: Com pute LSCVT (a,b,c) for c =1,2,3…using Boolean function 3 of three variab le and store it in deci m al form at (a,b,c) position. Step 3: Then we notice on the pattern of value ‘0’ and we have m ade it a specific c olor (green) and the other values except ‘0’ a lso made a specific color (red) in the matrix. The pattern made by ‘0’ in the matrix shown as a fractal (describe in figure -1below). . Z= 4 to 7 0 1 2 3 4 5 6 7 X 0 7 6 5 4 3 2 1 0 1 6 6 4 4 2 2 0 0 2 5 4 5 4 1 0 1 0 3 4 4 4 4 0 0 0 0 4 3 2 1 0 3 2 1 0 5 2 2 0 0 2 2 0 0 6 1 0 1 0 1 0 1 0 7 0 0 0 0 0 0 0 0 Y Figure-1 Fractal formation in a matrix Here Y represents the row of the matrix, X represents the Column and Z represe nts the level of the matrix. For an example, the positional decimal value of the matrix in the position (6,4 , 4) is 1. For Boolean function 3 the functional values of the truth table ar e assigned to the corr esponding binary values of 3. Function -------------- Value f(0,0,0) ------ 1. f(0,0,1) ------ 1. f (0,1,0) ------ 0. f(0,1,1) ------ 0. f (1,0,0) ------ 0. f(1,0,1) ------ 0. f(1,1,0) ------ 0. f(1,1,1) ------ 0. Now the binary values of the corresponding positional number in the matrix ar e 6 ----- 1 1 0 4 ----- 1 0 0 4 ----- 1 0 0 --------------- 0 0 1 So the decimal value of 001 is 1. In this way the total posional values are calculated in the matrix A. Observation We have observed the matrix and also found some interesting fractal pa ttern in specific level wise(level 0,1,2…,) . We also consider the level of the Boolean function upto 255 from 0.and consider the level in a signifant of manner ,e.g. from level 0 to 1, from level 2 to 3,from level 4 to 7,from level 8 to 15 , from level 16 to 31 , from level 32 to 63, from level 64 to 127, from level 128 to 255. 1. From level (Z) 0 to 1 :- In this two level if we consider a 2x2 square matrix the follow ing result is obtained:- At level 0 a squar e matrix is found which is form ed by only 0 entities and at level 1 a s quare matrix is also found formed by 0 and 1 entities. The basic structure of the pattern of the square matrix at level 0 is below:- Z=0 0 1 X 0 0 0 1 0 0 Y Figure-2 Formation of Euclidean geometry by the element 0 In this square matrix all combination is formed by 0 The basic structure of the pa ttern of the square matrix in le vel (Z) 1 as bellow — Z= 1 0 1 X 0 1 0 1 0 0 Y Figure-3 Formation of Fractal by the element 0 This is also a square matrix fo rm ed by 1 and 0. The pattern which is formed by 0 is symmetric t o a right angle triangle In this level(z=1) if we calculate a 4x4 matrix ,then we can not get fractal pattern formed by matrix entities .of 0. The patt er n is given below in the m atrix:- Z =1 0 1 2 3 X 0 1 0 1 0 1 0 0 0 0 2 1 0 1 0 3 0 0 0 0 Y Figure-3 Formation of Euclidean geometry by the element 0 2. From level (Z) 2 to 3 :- In this two l ev els if we consider 4x4 square matrix, the same pattern which is formed by the 0 entities of the square matrix of 2x2 order at level 1 is repeated and regenerated .The basic pattern is here also fixed. The pattern is generated below:- Z =2 to 3 0 1 2 3 0 3 2 1 0 X 1 2 2 0 0 2 1 0 1 0 3 0 0 0 0 Y Figure-4 Formation of Fractal by the element 0 In t his level if we also calculate 8x8 m atrix, then we can not get t he fractal patter n formed by 0 of the matrix . The pattern is given below:- Z= 2 to 3 0 1 2 3 4 5 6 7 X 0 3 2 1 0 3 2 1 0 2 2 2 0 0 2 2 0 0 2 1 0 1 0 1 0 1 0 3 0 0 0 0 0 0 0 0 4 3 2 1 0 3 2 1 0 5 2 2 0 0 2 2 0 0 6 1 0 1 0 1 0 1 0 7 0 0 0 0 0 0 0 0 Y Figure-5 Formation of Euclidean geometry by the element 0 3. From level 4 to 7 :- In this four levels if we consider a 8x8 square matrix ,then at all levels (e.g. 4,5,6,7 )the same basic fractal pattern formed by the 0 entities of the square matrix of level 2 to 3 is repeated and also regenerated ,The pattern is g iven below:- Z=4 to 7 0 1 2 3 4 5 6 7 X 0 7 6 5 4 3 2 1 0 1 6 6 4 4 2 2 0 0 2 5 4 5 4 1 0 1 0 3 4 4 4 4 0 0 0 0 4 3 2 1 0 3 2 1 0 5 2 2 0 0 2 2 0 0 6 1 0 1 0 1 0 1 0 7 0 0 0 0 0 0 0 0 Y Figure -6 Formation of Fractal by the element 0 4.From level 8 to 15 :- In this levels if we consider 16x16 square matrix, at all levels ( e.g. 8,9,….15 levels) the sam e basic pattern formed by 0 entities of the square matrix of level 4 to 7 is repeated and regenerated upto level 15 Z=8 to 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 14 14 12 12 10 10 8 8 6 6 4 4 2 2 0 0 2 13 12 13 12 9 8 9 8 5 4 5 4 1 0 1 0 3 12 12 12 12 8 8 8 8 4 4 4 4 0 0 0 0 4 11 10 9 8 11 10 9 8 3 2 1 0 3 2 1 0 5 10 10 8 8 10 10 8 8 2 2 0 0 2 2 0 0 6 9 8 9 8 9 8 9 8 1 0 1 0 1 0 1 0 7 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 8 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 9 6 6 4 4 2 2 0 0 6 6 4 4 2 2 0 0 10 5 4 5 4 1 0 1 0 5 4 5 4 1 0 1 0 11 4 4 4 4 0 0 0 0 4 4 4 4 0 0 0 0 12 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 13 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 14 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Y Figure-7 Formation of Fractal by the element 0 5 From level 16 to 31 :- In this levels if we consider 32x32 square matrix, at all levels (e. g. 16 , 17,18…….31 levels) the same basic pattern formed by 0 entities of the square matrix of level 8 to 15 is repeated and also regenerated upto level 31. The same case is repeated and regenerated in also from level 32 to 63 if we consider 64x64 square matrix, and from 64 to 127 consider 128x128 square matrix ,and from 128 to 255 level cons ider 255x255 square matrix . B.. Dimension of the pattern There are some level(Z) where we have got an Euclidean geometric figure(Figure-1,Figure-3,Figure- 5…),so we can not calculate the dimens ion of that particular pattern. From level 1 to 255 if we calculate a particular square matrix, then the dimension of the pattern formed only by the entities 0 is fixed and it is D= log3/log2, That is 1.5849 which is a Fractal. C. Analysis of the matrix We have ana lyzed the m atrix and construc ted a rule to get the corresponding level in which the fr actal pattern belongs .. 1. From level 1 if we consider 2x2 matrix then we get the expected pattern of F ractals. 2. From l evel 2 to 3 if we consider 4x4 matrix then we get the expected patter n of Fractals. 3. Level 4 to 7 if we consider 8x8 matrix then also get the expected pattern of F ractals. 4. Level 8 to 15 and 16 to 31 and so on upto level 255 we get the expected pattern of fractals if we consider the order of matrix nXn, Where n= the highes t no. of level +1. Illustratati Level 1 if we consider the 1+1 =2 order matrix ,that is 2x2 ma trix then we get the expected self symmetric patter n of Fractals. Level 2 to 3 If we consider the 2+2=4 order matrix ,that is 4x4 matrix then we get the same result. In the same iteration process all levels satisfy the condition as below:- Level 2 0 to (2 (0+1) – 1) ----calcula te 2 (0+1) X2 (0+1) order matrix. Level 2 1 to (2 (1+1) – 1) - ---- calculate 2 (1+1) X2 (1+1) order matrix. Level 2 2 to (2 (2+1) - 1) ----- calculate 2 (2+1) X2 (2+1) order matrix Level 2 3 to (2 (3+1) - 1) ------calculate 2 (3+1) X2 (3+1) order matrix. Level 2 4 to (2 (4+1) -1) ------calculate 2 (4+1) X2 (4+1) order matrix. ………………………………………… ……………………… …….. ………………………………………… ……………………… ……... ………………………………………… ……………………… ……… ………………………………………… ……………………… ………… By method of Induction We can get Level (Z variable in the square matrix) 2 n to (2 (n+1) – 1) ------- calculate 2 (n+1) X2 (n+1) order matrix to get the expected original pattern of fractals. All levels L Є ( 2 n to (2 (n+1) -- 1). Where n Є Z+ ( set of all pos itive integer.) V. Application The a pplication of these fractal patterns at different m atrix dimension is towar ds the efficient as well as cost effective design of Wireless CD MA Networks.. Our aim of the im plementation is to share small resour ces among the vast wireless CDM A network . Let us take a small example; our basic pattern comes like :- Z=1 0 1 X 0 1 0 1 0 0 Y Figure-8 Basic Fractal pattern by the element 0 in 2x2 square matrix. Suppose in this 2 x 2 matrix 4 blocks represent 4 resources and they access the wireless network. N ow to provide the web service we need to have 4 active wireless web ports, now in our technique 4 ports are needed but we have to make active on ly 3 ports at an instant time and there is a certain switching devices which virtually rotates the apparent position of active wireless port of a certain clock speed i n a specific direction. So, according to these concepts the signal that i s sent to each user is same in respect of signal measurement and the clock speed is so high that it is seemed that the signal is continuous to the users . Now the quantities measure in respec t of resour ce saving comes out in a very significant way. This process is like that w hether we need to active 4 po rts all times in a normal network structure, here just we need to active only 3 ports at all times and one port should stand by in its position. By some mathematical calculation we can say that our plan is {(1/4)*100} % = 25% efficient to save the resource for this basic pattern of Fractal. A typical diagram shows below to represent the Fractals in Wireless CDMA Network :- Figure -9 If we consider our general formula that is Level 2 n to (2 (n+1) – 1) -------calculate 2 (n+1) X 2 (n+1) order matrix to get the expecte d original pattern of fractals. Z=2 to 3 0 1 2 3 0 3 2 1 0 X 1 2 2 0 0 2 1 0 1 0 3 0 0 0 0 Y Figure-10 Formation of Fractal by the entities 0 in 4x4 Squar e matrix . As the rule i f we consider 4x4 matrix fo r l eve l 3 the same pattern of the fractals is r epeated and regenerated. In this case we also apply the previous concept, if the total pattern rotates in a certai n clock speed x in a cer tain direction; then the elementary pattern that is depicted below Z=1 0 1 X 0 1 0 1 0 0 Y Figure -11 Elementary Fractal pattern by the element 0 in 2x2 Square matrix. have to rotate in 4x speed at the same direction. Here the prefix 4 is to be added because after changing the initial position again returning to t he initial position one pattern has to change position 4 times.By the help of simple arithmetic as the previous one we are able to ca lculate the % of efficient shave of the recourse; {(7/16)*100}%=43.75% It seems that our efficie ncy has grown up. Then if we calcula te as ou r proposed formula 8x8 matrix at level 7 then the pattern is repeated as well as re generated . Z=4 to 7 0 1 2 3 4 5 6 7 X 0 7 6 5 4 3 2 1 0 1 6 6 4 4 2 2 0 0 2 5 4 5 4 1 0 1 0 3 4 4 4 4 0 0 0 0 4 3 2 1 0 3 2 1 0 5 2 2 0 0 2 2 0 0 6 1 0 1 0 1 0 1 0 7 0 0 0 0 0 0 0 0 Y Figure-12 Fractal pattern by the element 0 in 8x8 Square matrix Apply and approach same as the previous one. Now in this case if the total pattern rotates in certain clo c k s peed x in certain direction then the corresponding elementary p a ttern level 1 Z=2 to3 0 1 2 3 0 3 2 1 0 X 1 2 2 0 0 2 1 0 1 0 3 0 0 0 0 Y Figure-13 Fractal pattern by the element 0 have to switch in 4x speed in same di r ection and the corresponding elementary patter n level 2 Z=1 0 1 X 0 1 0 1 0 0 Y Figure- 14 Elementary Fractal pattern by the element 0 have t o rotate in 4 2 x speed. Same simple clock logic as the previous one. From the calculation as the previous one we are able to calculate the % of efficiency to optimizes the resources. {(37/64)*100}% = 57.8125% It shows that our efficiency has grown up gradually. Then the same occurrence repeated of the matrix arrangement at level 7 as the pattern is generated in case of 16 x 16 matrix and also the % of efficiency for sav ing the resources increases; {(172/256)*100}%=67.18% Same pattern is regenerated for consideration of 32 x 32 matrix at level 16, the % of efficiency here is also save of the recourse and becomes ; {(781/1024)*100}%=76.26% As the process goes on we can see that the efficiency of ou r implementation increases ; So we can say that our proposed concept is more efficient for the large coverage ar ea of a wireless CDMA networ k. In all above case we have to increase the speed elementary pattern level va lue ,( the level value may vary from 1 ,2,3,4,,5, ,n; where n is any natural positive number.) at the order of 4 level value . So according to this if the t ota l pattern rotates at certain clock sp ee d x ; then the speed of the then the elementary pattern at different level rota tes according to the multiple of their corresponding level value . So, from the above discussion we can conclude that the speed of the particular elementary pattern at the particular level de pends on the level value and that can be expressed as [ 4 level value * x ]. VI. Comparison of our CDMA system with existing CDMA system A. Advantages There are mainly three advantages of our propo se d CDMA system over the existing CDMA system. Fi r st of all n umber of resources are getting reduced at any instant time without affecting the network service to the station . Secondly as the number of resources getting reduced, so the cost of network service is also getting reduced. Lastly at any instant time the number of resources will remain standby in our CDMA system, so the energy w ill also save. B. Limitations There is a limitation to construct this CDMA network on the basis of fractal pattern, To get the fractal pattern the number of resources shoul d be in our proposed manner, that means if we imagine th e resources of the network as in the position of a matrix entities, then all the resources will be reconstructe d according to the position of the entities of a square matrix. If the above conditions will satisfy then, it i s possible to construct such network m odel on the basis of frac tal pattern. VII. Conclusion and F urther Research In this paper we have used three variable Boolean function 3 in formation of fractal pattern and also completing the analysis we can say at level 2 n to (2 (n+1) – 1) of a level of a square matrix if we consider the 2 (n+1) x2 (n+1) square matrix the fractal pattern of the dimension same as the dimension of sierpinski trian gle that m eans the dimension will be 1.5849 is produced. From this pattern model we can designing a new area of Wireless CDMA Network that can be used for a efficient and effective resources saving Wireless CDMA Communication . . In further case if we try to implem ent the a new Wireless LAN technology ,it is possible to construct from our research . VIII. References [1]. P. P. Choudhur y, S. Sahoo, B. K Nayak, and Sk. S. Hassan, Carry Value Transformation: It s Applicati on in Fractal Formation 2009 IEEE International Advanced Computing Conference (IACC 2009), Patiala, I ndia, 6-7 March, pp 2613-2618, 2009. [2]. P. P. Choudhur y, S. Sahoo, B. K Nayak, and Sk. S. Hassan, Act of CVT and EVT in Formation of Number- Theoretic Fractals (Com municated to World Scientific journa l FRACTALS. Wolfram, Cellular Automata and Complexity Collected Papers, Addison-Wesley Publis hing [3]. S tefano Buzzi, S enior Member, IEEE, and H. V incent Poor, Fellow, IEEE on Joint R ece iver and Transmitter Op timization for Energy-Efficient CD MA Communications. [4]. ISBN 0- 201 -62664-0, 1994. Data Communications and N etworking by BEHROUZ A FOROUZA N forth edition published from Tata McGr aw-Hill Publishing Com pany Limited, New Delhi. Special Indian Edit ion 2006, ISBN 0- 07 -063414-9