CA2093975C - Apparatus and method for non-regular channel assignment in wireless communication networks - Google Patents

Abstract

A channel assignment system assigns channels to various cells by the optimal partitioning of the available radio frequencies into non-overlapping sets, the optimal grouping of co-user cells, and the best assignment of the former to the latter.
The objective is the maximization of traffic handling capacity which, given the multitude of cells, is expressed as the maximization of a bottleneck capacity ratio.
The capacity ratio for a cell is defined as the ratio of the number of radio frequencies assigned to the cell over the number of radio frequencies needed to meet blocking probability requirements. The solution to attain an optimal non-regular channel assignment is decomposed into two mathematical programs designated a Master Program and a Subprogram. These are solved iteratively with assistance from a channel set augmentation technique impelmented between solutions of the Master and Subprogram.

Description

APPARATUS AND METHOD FOR NON-REGULAR
CHANNEL AS!;IGNMENT IN WTRF1.F.~S
COMMUNICATION NETVVORKS
Field of the In~ ' This invention relates to wireless/cellular radiotelephone systems and an a~ alu~ and method for the ~ciignm~nt of radio L~ucncy (RF) 't~C~,IIUlll channels to the different cells within a cellular system for optimi_ing l1ti1i7slti~n of the available overall radio spectrum.
Back~round of the Il-~. t ~-The service area of a wireless co~ tions system is partitioned into co~ c t .d service domains known as cells, where radio telephone users co.n.,.~..ir~t~., via radio links, with the base station serving the cell. The base station (BS) is coupled to the land network. F.ffiriPnt use of the available radio frequency ~l~e~ ulll iS achieved through the reuse of the same radio Lbquellcies in design~ted 15 co-user cells that are s--ffici.-nt1y separated by distance so that the combined int~,lr~,lbnce g~ner~t~d by all co-user cells is below tolerable levels. The acsignm~nt of radio L~ue/lcies to cells has been based on regularity as:,ullJp~ions (i.e., equal-sized regularly-spaced cells with uniformly distributed traffic loads), which enable the adoption of simple rules for identifying co-user cells, and for partitioning the RF
20 :~;IIUIII into channel sets. When the regularity assumpdons do not hold -- as is L~uenîly the case in real world situations -- the rules of regular channel :lccignml nt do not lead ncce,~- ;ly to the efficient lltili7~tion of the RF ~t~[~,a~UIll, if they can be applied at all. To optimally utili_e the RF ~.,IIUlll one must solve the non-regular channel assignment problem.
25 Summary of the Invention Therefore a channel assignment system, embodying the principles of the in~.e.~tion, assigns channels to various cells by the optimal partitioning of the available radio L~lue.-~ :GS into non-overlapping sets, the optimal grouping of co-user cells, and the best ~ccignm~nt of the forrner to the latter. The objective is the 30 "~-~C;"~ tion of traffic h~n-lling capacity which, given the m-1l~itnde of cells, is bA~lb;tsed as the ...-~;...;,..lion of a bottleneck capacity ratio, known as the capaciry factor. A capacity ratio for a cell is defined as the ratio of the number of radio frequencies assigned to the cell over the number of radio frequencies needed to mee~
blocking probability requirements. Given a channel ~Ccignmpnt> the latter is fixed 35 once the traffic loads and desired blocking are specified.

- 2 -Given a group of cells of arbitrauy shape, size, and/or location, the available RF ~ ,LlUllJ iS partitioned into opt;mal channel sets, and these channel sets are ~c5ignP~ to cells in an o~ llulll way. Sitlce traffic loads may vary from cell to cell, the ~i~ignmf nt objective is the maximizadon of the cells' combined traffic-S h~nrlling capacity. This objective is e~ ,SSfd as the Illa4illli~tion of the bottleneckcapacity ratio that can be susts~inf d at a s Iticf,~ctory blocking rate and interference level, which is the lowest capacity ratio across all cells.
The solution of the optimal non-regular channel ~ignm~nt is decomposed, according to the invention, into two ~ I,f."~tir~l programs designated 10 as a Master Program and a Subprogram. These are solved iteratively with assistance from a channel set augmentation technique impelm~nted between solutions of the Master and Subplu~lalll.
Brief Dc~ 1 of the Drawin~
In the Drawing:
FIG. 1 is a schf ";~ir of a regular cell area layout of a wireless/cellular radiotelephonc system;
FIG. 2 is a block schematic of a wireless/cellular radiotelephone system;
FIG. 3 is a block schPmotir of a data ~lucf~ ng system for assigning radio ch~nnP1c to various cells of a wireless/cellular r~liot~ honc system;
FIG. 4 is a flow process diagram of a method for assigning channels to various cells of a wireless/cellular radiotelephone system;
FIG. S is a flow process diagram of a method for making initial feasible channel ~i~ip.."..~
FIG. 6 is a flow process diagram of a method for providing an integer 25 solution for the Master F~u~a~
FlG. 7 is a flow process diagram of a method for channel set augmPnt~tion; and FIG. 8 is a flow process diagram of a method for solution of the Subprograrn.
30 Detailed D~.;l~ti~l~
A conventional regular hexagonal cell layout, of a cellular r~Aint~' rhone system, is shown in schematic form in FIG. 1. Depicting the geographical service area in terms of a hexagonal grid sets a geometric pattern that allows frequencies to be assigned in a patterned disposition that allows the reuse of 35 these frequencies in a controlled repeatable regular ~signment model. The cell areas each have specific channel sets assigned to them. Each channel set comprises a S~397~

-3 -plurality of individual transmit and receive radio channels for use within the cell area. In this model, shown in FIG. 1, cells rnarked "A" are co-user cells and all use the same channel set. The same is true for co-user cells marked "B", "C", etc., each of which have their own assigned channel set.
Each cell is radiated by an antenna system associated with a base stalion (BS), that includes the radio transceivers and which are in turn connected to the public switched tclel)hone network (PSTN) via trunk lines or suitable equivalent.
Antennas 101 are either omi-directional or di.~ional. Directional antennas 102 are used to sect--nY~. cells into smaller angular wedge type serving areas.
A typical cellular system is shown in the block diagram of FIG. 2. A
plurality of rnobile switching centers (MSC), 202 and 203, are shown conn~cting the mobile radiotelephone system to the public switched tclephonc network 201 (PSTN).
The switching of the MSCs int~,l.,-olmccts a plurality of base stations (BS) 210 each providing service to a cell coverage area. Each coverage area is shown as having15 irregular boundaries typical of an actual system. Each BS has radio transmit/receive e~uip~ nl and radiating antennas to serve mobile radiotelephones 250 within its cell co.elage area.
An operations and mA-~gem.ont center (OMC) 220 is coupled to the MSCs 202 and 203 to control their system operation and their ~csor~ d BSs 210.
20 OMC 220 is a central control station which includes data ~luc~ g equipment and input for accepting data input from data storage and real time control. This data L~occssillg Arrang~mPn~ may be utilized in h,ll,lel.~nting channel :~signml~n~ in colllbinalion with remotely tunable radio transceiver~s located at the BSs.
An illu~llali~, embodiment of data pluccssillg equipment included in 25 the OMC for controlling the Ac5i~nm~n~ and tuning of radio transceivers at the BSs is shown in block schf..,.Al;r form in the FIG. 3. A general purpose CcJIlllJut~,. 310 has a stored program included in its memory 311. This program includes instructions for pe~rc,l,l~i-lg the non-regular assignment of radio ch~nn~1~ to a cellular system as disclosed in further detail below. Initial input data is supplied through the input 30 circuit 312 to the c(jln~ut~,l 310. Inputs include the available cells. The available radio frequencies are also input into the COIlllJUlUr 310. Further inputs include hlle.~l~,ncc inrulllldtion usually in the form of a cell-to-cell interference matrix, which defines the h~ ce to each cell from every other cell. The inputs also include system consll~~ nccessal~ for the desired channel a~cignm~ nr Traffic 35 usage patterns are supplied as an input. Traffic may be measured in real time.

- 4 -In this illustrative embodiment of the invention, the ~Csignmp-nt process is p~,lro~ ed in the CO~ ut~,l 310 according to the instructions con~ined in memory 311. The resulting non-regular ascignm~ont is output via the output 313 to the MSC
315 and is in turn forwarded to the BSs 321. The individual tunable radios 322 S in-~hl(led in the BSs are tuned to the proper frequencies in accord with the aCcignm~n~ of radio channels determin~d by the aCcignm~n~ process. Added output leads permit graphical and data printr lltC at the OMC.
To state the above ~ccignmPnt problem algebraically, the following notation is utilized. Let 10 j = 1, ..., J index of different logical cells (A logical cell is the portion of the coverage area of a cell served by a logical face.) i = 1, , J... same as j (the combination (i, j) ~3esi$n ltPs a pair of logical cells) yj number of channels needed in logical cell j to meet blocking I~ U~i~ S
N number of available ch~nnP!c Iij co-channel hlt~rGI~nce contribution by logical face i to logical cell j S j signal strength of logical face j T threshold level of the signal-to-in~lÇ~I~,nce ratio 20 The unknown quantities of the problem are:
g capacity factor (bottleneck capacity ratio) K number of channel sets N~c size of channel set k Jl if logical cell j is covered by channel set k xki ~0 otherwise The channel ~ccignm~nt can be expressed as a .~.;ul.f pro~ l.... l.hlg problem of the form:
Maximize g Subject to: ~ Xk; Nk 2 yj g for j = 1, .. , J (I) k ~; N k C N (2) - s -.

Prob ~ xki < T + M (1 - Xkj) .~ 1 - oc for j = 1, ..., J and k = 1, ..., K

Xkj = 1, 0

5 N" > 0, integer where M is a large positive number.
The constraints in (1) allocate channels to logical cells in proportion to the cells' l~uh~ ,. In coll~,tldint (2) the total number of assigned channels islimited to the number of channels available. ConsL-dil-l (3) ensures that the ratio of 10 signal strengtn to co-channel inlclrblbilce is above the desired threshold value with cc-nfi~1~nce level 1 - a. The above formulation of the channel ~ccignm.ont problem can P''CO~ t~ iti()n~l COnslldilltS that would reflect a user's special needs.
Exarnples of such COIi5~ , are ~iiccucsed herein below in a tlicc-lccir,n of thesolution IJlUC~lUlb for the basic formulation.
The above problem is a large scale nonlinear mixed-integer stoch~cti~
n~ "~ l program. If, for example, a cellular grid has 210 logical cells (70 cellsites, with 3 logical faces per cell site), and 200 channel sets are considered, there would be 42,211 coll~ dint~, and 42,200 integer variables (exch~ling slack variables), of which 42,000 would be binary.
In accord with the principles of the invention this problem is ~lf co" ,l~se~l into two computationally tractable parts using generalized linear ".."",;n~ The original problem is decomposed into two smaller problems which are solved one after the other in an iterative se~luellce, eYrh~nging their Ib;~ solntinnc until the optimal solution is reached. Following established 25 convention, the two ~)lubl~ s are called the Master Program and the Subprogram.
The Master Program consists of all but the stochastic constraints in (3), which make up the Subprogram constraints.
The algebraic formulation of the Master Program and Subprograrn are expressed as follows. The following expressions define the Master Prograrn of block 30 420 subsequently (liscllcsed with respect to FIG. 4:

- 6 -Maxirnize g Subject to:~, Xk; Nk 2 yj g for j = 1, .. , J
all available k S all availnble k (S) Nk 2 0, integer where Xk; are con~ satisfying the co-channel il"t;lr~l~,ncc conditions. These values are supplied by the Subprogram described below.
The Subplu~,-alll contains the constraints assuring that the ratio of signal 10 strength to co-channel hlt.,.r~ ,ncc is above a desired threshold value. Its objective coeffiri~-ntc are the simplex multipliers coll~ x)nding to constraints (4) of the Master Program.

The Subprogram has the following form:

Maximize v = ~ x;
J

15 Subject to:

Prob ~ j xi ~ T + M (1 - Xj) 2 1 - a for j = 1, ~ J (6) xj = 1,0 where ~j is the simplex mlllfirli~r corresponding to the jth constraint in (4).
The collection of channel sets included in the Master Prûgram is comprised of all the sohltion~ of the Subprogram. The k'h solution of the Subprograrn provides values for the binary variables Xk;. A channel set is defined in terms of the co-user cells it serves. The collection of channel sets grows with every new solution of the Subprogram, and this growth helps improve the Masler Program25 solution. Growth in the collection of channel sets stops when the optimal solution is reached.

3 ~ 7 ~

- 7 -The overall structure of the ~cci,~nm~nt process comprising the Master Program and Subprogram is shown in the FIG. 4. The solution procedure, as shown in the flow process in FIG. 4, involves four major functions. These are: Channel~ccienmf~nt Tniti~1i7~tinn (block 410), a Master Program Solution (block 420), S Channel Set ~ngm~.nt~tion, and Subprogram Solution (closely related blocks 430and 440). In the first function, block 410, which is the initiqli7~tion of the channel ~csignm~nt, a feasible channel ~esignmpnt is obtained before we proceed with the;.--;,,U;s~n If the model is applied to an existing grid, the present channel pcci~nm~nt can serve as the initial channel assignment, provided it satisfies all 10 system COn~ . If it violates any of the constraints, it is mo~lifiP.d by the Initial Channel Ac.cignm~nt algorithm, as described below, to meet all constraints.
Once an initial feasible channel assignment has been obtained, the ..... ~h~h~g three functions are ex~cu~d in an iterative s~ucnce. First comes the solution of the Master Program in block 420, whose solution furnishes the system15 values of g, Nk, ~, and ~p ~ is a simplex multiplier cc, .~,i")onding to constraint (5) and ~j is a simplex muldpler co.-~ ,ollding to the jth constraint in (4). This in~....~lit)n is used by the Channel Set Augmentation algorithm in block 430 which invokes the Subprogram Solution algorithm in block 440 several times in order togenerate new channel sets.
The Channel Group Augmentation algorithm is a heuristic process that el-h~ -res soludon of the problem. It revises the values of Nk and ~j, which are used in the next soludon of the Sul,l).u~ ... The Subprogram soludon furnishes the values of v and x kj-Once a srecifi~d number of channel sets has been ~enelat~d~ optimality 25 is checked as prescribed in decision block 450. If the soludon is optimal as t .~ f A in decision block 450, the algorithm terminates and the aC~cignml nts are u~ided in block 460. Otherwise, the cycle repeats again with the solution of thet~i.,t~,d Master Program in block 420.
The following condition in-~in~ s opdmality: Let K- 1 be the current 30 cycle, and let x Kj be the optimal solution of the new Sub~ l. Let ~ be the simplex mllltirli~r coll~,s~nding to constraint (5) of the relaxed Master Program. If ~ XK; ~j C ~ (7) then the current soludon is optimal for the relaxed Master Program.

~ ~ ?3 ~ ~ ~ 3

- 8 -The solution procedure described herein is finite as the number of different channel sets is finite, and each solution of the Subprogram contributes a new channel set to the Master Program. That the channel set entering the Master Program at each cycle is new is based on the following observation. The simplex S m~1ltip1iP.rs of the relaxed Master Program at cycle K- 1 satisfy the conditions: (5) ~, Xkj~ SO fork= l,...,K-l (8) If the new Subprogram solution x Kj iS added to the Master Program, it cannot meet the con-litif~n in (7), for that would lead to the termin~t~ of the process. Since it 10 violates the re4ui~ vn~ in (7) it cannot be identical to any of the K- 1 solutions encounlc.~,d previously, by contlition (8). Hence, XKj represents a new channel set.
Given that the number of cells in a grid is finite, the number of distinct cell groupings that lG~ ,senl different channel sets is also finite. Hence, the solution procedure is finite.
The solution procedure must start with a feasible channel acsignm~nt~
that is a channel pCcignm~nt that covers all cells and meets the channel availability collsLlaint and co-channel intclrc.cnce consllaints. For an existing cellular grid, the channel accignmpnt in place may serve as the initial channel acsignm~nt~ provided it is feasible. If the existing channel ~ceignm~on~ is not feasible (infeasibility would 20 arise typically from the violation of the intrvlrcllvnccv COIISIlailllS), or if there is no existing channel ~eejgnmPnt, it is necess~y to generate an initial feasible channel pcci~nmlq.nt The m-ethod for deriving an initial channel ~ccignmlo.nt is based on a v - - of the Channel Group Augm~nt~tis~n algorithm. In the most general case, 25 as shown in FIG. 5, the existing channel acsignm~nt violates the inte~fivl,vnce co..C~,~;nl~ In this case, Channel ~csignmf nt Tniti~1i7~tion consists of two phases.
In Phase I we modify (Block 507) the channel sets in the existing channel ~cSignm~nt one at a time by c h:-n~ing values for N k and ~p If a channel set violates the intelr~,lcllce con~l~ainl (decision Block 502), cells are removed (Block 30 504) until it satisfies the h~tclf~ nce collsllaint. If the illle.r~ ~nce COll:~lldilll iS met by an existing channel set, the algorithm will assign as many adrlition~l cells as possible (Block 505), provided that the interference constraint is satisfied. If the resulting channel sets cannot cover all cells, the second phase is implemented. In Phase II ~rlition~1 channel sets are generated until all cells are covered (Block 506) 7 ~

Both phases employ the Channel Set Allgm~nt~tion algorithm. They differ in terms of the initial values used for ~p In Phase I, ~j equals I for all cells j covered by the existing channel set, and zero for the ~ g cells. In Phase II, iS cc.~... ....p,.t.,d by the equation (10) (li~clc!s~-d herein below.
S The Master Program is a linear program involving the integer variables Nk, which assume values ranging from 0 to N -- the number of available L~uencies, a number which is normally between 300 and 400. Given the magnitl~clç of the integer variables, one can obtain near-optimal solutions to this mixed-integer linear program by solving the relaxed linear program without the 10 integer re~lui~ el.~s as per Block 601 in FIG. 6. For the purposes of channel ~signm~nt, integer solutions must be provided.
The ~lgonthm yielding an integer solution to the Master Program shown in FIG. 6 uses the fact that the optimal channel ~si~nm~nt will use all of the Navailable channels. Given an optimal solution to the relaxed problem (the linear15 program without the integer l~uih~ nl~), the algorithm starts by making the channel set sizes equal to the integers closest to the relaxed solution (Block 601). It t~,.---.nates if the integer set sizes add up to N (Blocks 605, 607, 609). If not, it illCI~,aSes (or decl~,ascs) by 1 the sizes of the channel sets with the greatest positive (or negative) deviation from the optimal non-integer value (Blocks 611, 615). The 20 steps of the ~ rithm are shown in the FIG. 6 and are described below in detail.
The term N k denotes the channel set sizes in the optimal solution, and by _ k their closest integers. The procedure for obtaining an integer solution to the Master Program is outlined in FIG. S as follows:

Step 1 Set _ k equal to the integer closest to Nk. (Block 603) 25 Step 2 Compute the difference D = ~ _ k - N. (Block 605) If D = 0, terrninate (Block 607). Otherwise go to Step 3.
Step 3 If D < 0, go to Step 5. Otherwise go to Step 4. (Block 607) Step 4 Find D channel sets with the largest difference ~k = Nk - Nk Decrease the size of each of the D channel sets by 1.
Tenmin~t~ (Blocks 611, 613) Step5 Find lDl channelsetswiththelargestdirr~ nceok = Nk - Nk Increase the size of each of the I D I channel sets by l .
Tçnnin:~te (Blocks 615, 617) ~ ~ f~

It is easy to verify that, given a non-negative solution to the relaxed linear program, the resulting integer solution will also be non-negative.
Once the colllple~ily caused by the integer constraints has been removed, the solution of the Master Program becomes straightforward. Standard S linear prs)~ ihlg software can be used. By linear l~lu~ fing standards, the relaxed Master Program is a reladvely small linear program, having a number of con~ s equal to one plus the number of logical cells in the grid, and number of variables equal to one plus the number of channel groups. It is exrec~.çd that a large grid would have no more than 500 logical cells. Seven hundred and fifty channel 10 sets would more than exceed the number needed to yield an optimal solution.
The number of cycles of the Master Program is reduced by g~ eld~ g lists of channel sets with the channel group ~ugm~nt~ti~n heuristic. One of the factors contributing to the cc,---pulalional effort in ",~ll.P.."~ti~l pro~ lingJ'~ is the repeated solution of the Master Program. Since the optimal 15 channel a~ignm~nt is derived from the last Master Program solution, and all previous Master ~U~;lalllS serve only to generate a list of desirable c~n~
channel sets, g~,n~.ating a larger number of c~n~ tes at each cycle would tend to reduce the number of Master Program solutions while still yielding an optimal solution. Therefore, between any two conseculive solu~ion~ of the Master Progrann, 20 the method used g_llc.at~,s several new channel sets. The number to be generated is specififfl by the user.
The criterion used in generating new channel sets is that they must have the po -1 to improve the Master Program objective value. The first channel set ~_n~,~ut~,d after the solution of the Kth Master Program has this potential since it has 25 a negative reduced cost by con-litic-n (7). In order to obtain heuristically additional channel sets with a negative reduced cost, the simplex ml-ltirli~r ~j is needed.Typically, ~j is supplied by the solution of the Master Program. Since our aim is to generate more than one channel set between consecuLi~e solutions of the Master Program, it is nccessa,y to revise the ~j values before each Subprogram solution30 without re-solving the Master Program.
The revision of ~j is based on properties that would hold if the Master Program were solved. They are derived from the following ComplP,.--~,nL~y Slackness conditions defined by equation (9):

~3~7~

K

, x k; N k -- y j g ) = O for j -= 1, .. ., J

A conse~uencv of the above conditions is that the simplex multiplier ~j, which is required to be non-negative, will be positive only if the correspon-iing primal 5 con~l.aihil in equation (1) is binding or, equivalently, whenever the capacity ratio of cell j equals the grid capacity factor. We refer to such a cell as a binding cell.
The con-lition of equation (9) is employed to update tne ~j values of binding cells as follows. A new channel set K, derived from the last Subprogram solution, will receive in the next iteration a portion of the available ch~nn~lc This 10 implies that if set K covers cell j, cell j will typically not be binding in the next iteration. By equation (9), the corresponding simplex multiplier ~j would becomezero. Hence, the following revision rule is used:

_ Jo if x Kj e~ if XKj = O (10) 15 This revision causes channel sets gvnvlatvd by subse luvnl solutions of the Su)J~ a.l- to favor binding cells that were not covered by the last channel set, as they vill have positive ~j values.
The above revision rules deal with the binding cells as they become non-binding. Rules are needed also for the cells that are not binding in the Master 20 Program solution but, as new channel sets are added, may become binding. Suchcells should be coverd by subsequent channel sets. With ~j assigned zero value by eql-Q~ion (9), however, they do not have a chance, unless ~j is updated. An altv...aLi.v way is to cc.""""oi~Qt~ to the Subprogram the binding status of a cell by handing over the new channel set si~s N k . The Subprogram considers the binding25 status of a cell together with simplex multiplier ~j values in deriving a new channel set.
There are several ways to revise N k In this implementation of the algorithm we assume that the new channel set K will receive one K'h of the available channels, while the si~ of the existing K - 1 channel sets will be adjusted 30 accordingly. That is, ~f~ s33 ~ ~ ~

NK = K (11) If the existing channel sets had si~e N' k. their new si_es will be 5 Nk = N'k (K K ) for k = 1, .. , K- 1 (12) The algori~hm for generating F new channel sets is shown in flow form in FIG. 7.

Step 1 Set ~j and Nk equal to the values obtained by solving the Master Program. (Block 701) Step 2 Repeat Steps 3 through 6, F times. (Blocks 702, 713) Step 3 Solve the Subprogram to obtain Xkj. (Block 704) Step 4 Revise ~j by equation (10). (Block 705) Step 5 Compute NK by equation (11) (Block 709), and revise Nk fork = 1, ~-, K - 1 byequadon(12). (Block711) 15 Step6 Inc~ elltK. (Block711) Given the difficulty of pursuing a globally optimal solution method, we have devised an efficient heuristic algorithm for the solution of the Subp-o~n. It con~l.ucls a solution by selecting among the cells in the grid those that will m~ imi7~. the Subprogram objective value without violating the interference 20 consllaints of equadon (6). Such a set is constructed by adding one cell at a time, giving priority to the cells with the greatest ~j value. A cell can be added to the set if it does not interfere with the cells already in the set. For cells with equal ~j values the order in which cells are considered is hllpol~ because the inclusion of one cell might preempt, through the intelr~ ce it generates, more cells than another.
25 P~ef~ ce is given to cells with low pre-emptive potential. The pre-emptive pot ':~l would change at each step, as new cells are added to the set. Therefore, the criterion function used for including a cell in the solution is updated after the addition of each cell.
The ~lgorithm logic can be described as follows. At each step, the cells 30 are partitioned into three subsets. The set C, which consists of the cells included in the solution (i.e., Xj = I); the set C, which consists of the cells excluded from the solution (i.e., x; = 0); and the set U, which consists of the cells whose fate has yet not been determined. At the start of the algorithm, U con~ains all the cells, and C

and C are empty. At each step a member of U is placed in C. Its inclusion in thesolution may pre-empt other ~ of U from inrlllcion The pre-empted of U are moved to C. The ~lgorithm tto.rrninotlos when U becomes empty.
Among cells with equal ~j values, the cell to be moved from U to C is S chosen based on its po~ 1 to block other l,l~,.ll~l~ of U from entering C. There are several ways to measure this po: 1 In the i~ k .,...n;.lion described in this paper we define the pre-e.l,~ c: - -1 function pj as the inverse of the "slack" a in the i~tc.fl,.ence con~llaint in equadon (6), which Ille~ul.,s the margin for a~l~liti--n~l contributions to the ~ ~ ncc ~i~-;enced in cell j.

10 pj =-- (13) The solution of the Subplu~;lalll is expanded to include cells with zero . This is necess~u~ in order to deal with the non-binding cells that become binding as more channel sets are g~n~lat~d. Moreover, the inrlllci~n of the largest possible 15 number of cells in the solution of the SublJlo~aln is ~e~ blr for the h~lcdsed system planning flexibility it affords. Hence, cells are chosen in order of descending value of the following criterion function fj:

fj = ~j -- E ~=I -- E pj Yi (14) 20 where K is the last channel set ~ ,Iat~,d, and E iS a very small posidve number.
Given a suffi~i~ntly small value for E, the cells with positive ~j values will be given priority. The l~jl"~ cells will be considered only when all cells with positive ~j have been conside.ed. Among cells with positive and equal values, the choice of a cell to be included in set C is based on the pre-emptive25 potential p j since, according to condition (9), the capacity ratio in the second terrn of (14) is the same for all such cells -- it equals the grid capacity factor. For cells with zero ~j values, the capacity ratio ~lomin:lt~o.s the choice of a cell to be included into C.
The ~lgorithm for the solution of the Subprogram is shown in flow 30 process form in FIG. 8.

Step 1 Place all cells in set U, and make sets C and C empty. (block 801) Step 2 For each memb~r j of U, compute fj by equation (14). (block 803) Step 3 Select j to be the mem~er of U with the greatest f j value. (block 805) Remove jlt from U. (block 306) S Step 4 Compute aj for each member j of C s~c~nming that j (block 807) is also in C.
Step 5 If aj < 0 for any j in C, place j in C and go to Step 8. (block 809) Otherwise, place j in C (block 811) and go to Step 6.
Step 6 Foreachmember jofUcomputeaj. (block813) 10 Step 7 Remove from U any of its members j with aj < 0 and place them in C. (block 815) Step 8 If U is empty, t~ lh~ale. (block 817) Otherwise, go to Step 2.

The c~lrul~tion of the pre-emptive potential pj in the solution of the Sul~lu~al~"li~c~l~se~ above, involves the i~ ,lÇ~,Ie.lce con~ h-t slack aj, which 15 measures the margin for additional contributions to the i~.t~,lr~l~,nce e~l;.,nced in cell j. The slack will vary with the CGll.pO ,ilion of C, the collection of cells covered by the channel set.
To compute the slack aj we convert the probability 5lot~ t of eq~l~tion (6) into an equivalent dete-lllinistic consLlaint for each ceil j in U, the 20 collpctinn of ~ Aet~ cells. The COll~llaillt in equation (6) can be written as follows:

Prob i 2 T 2 1 ~ or j ~ U
i~, ~C (15) To write the above as an equivalent de~ isllc inequality, we need to know the 25 probabili~ distribution of the signal-to-interference ratio. Let Y be the value of this ratio, eA~ ,ssed in decibels. That is, S
y = 10 1~glo ~ I
' i~j, EC , ( 1 6) Following other tre~tm~ns~, we assume that Y is norrnally distributed. Let ~ y and ~3~

c~2 be the mean and vanance of Y, respectively, and let R be the signal-to-h,t~,.r~lG.~cf ratio threshold value T GA~ s~l in clecibelc Equation (15) can bewritten as follows:

Prob [ Y 2 R] = 1 - Prob z < 2 1 - a for j ~ U
S (~Y (17) where z is a normal random variable. The equivalent df tu....;nictic con~laint is the following:

~Y + Za ~y 2 R (18) I

10 where Za is the a-quantile of a normal random variable. aj is the slack variable of the above inf~ lity. Therefore, aj = ~IY + Za ~y - R (19) The values of '~1 y and ~ y depend on the composition of set C. They are 15 co..~l~uS~,d using the ~C~..,,~p~ n that the signals of all antenna faces, when expressed in df~ihelc~ are in-lr p~ ~/lr..u normally distributed random variables and that the cum.~ ive intelf~ incf, ~ . ;f,nnf~ in cell j is also normally distributed, wheneA~ Gd in decibels [9]. Let 20 Y = P--L (20) where I

¦ i~J.~C ¦ (21) 25 P = 10 loglO Sj (22) If ~lL the mean of the cum~ tive interfence L in cell j, eA~IG;~sed in decibels ~L2 the variance of L ,up the mean of the power signal P in cell j, is GA~ scd in decibels as ~p2 the variance of P then, the mean and variance of Y are given by:

~y = E(Y) = E(P) - E(L) = llp - l1L (23) 5 c~y2 = Var(Y) = Var(P) + Var(L) = ~Sp2 + C~L2 . (24) llp and C~p2 are speçifi~d as input to the model. I1L and ~L2, which vary with the composition of the set C, are co,l-~u~tid in each step of the Subprogram Solution ~lgorithm by a power-summing procedure.

Claims (23)

Claims:

1. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of optimizing the assignment of radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communications system;
comprising the steps of:
comprising an initial feasible channel assignment scheme covering all cells and which assignment scheme obeys channel availability, blocking and interference constraints;
decomposing the method of optimizing of the channel assignment into Master Program and a Subprogram, initially solving the Master Program in order to determine values for a capacity factor, channel set sizes, a first simplex multiplier corresponding to the channel assignment constraints for each cell, and a second simplex multiplier corresponding to the radio channels availability constraint;
solving the Subprogram to generate additional channel sets using output values from the Master Program;
hueristically providing new values of channel set sizes and the second simplex multiplier, and resolving the Subprogram to generate further channel sets.

2. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of optimizing the assignment of radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communication system, as claimed inclaim 1;
comprising the further steps of:
resolving the Master Program for determining new channel sets;
checking the resulting assignments for optimality; and terminating when optimality is achieved.

3. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of assigning radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communication system as claimed in claim 1;
wherein the steps of computing an initial feasible channel assignment scheme includes the steps of:
modifying channel sets in an original assignment one at a time by changing values for N K and .lambda. j;
determining if the modified channel set violates interference constraints and removing cells until the interference constraint is satisfied; and assigning additional cells and generating additional channel sets until all cells are covered.

4. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of assigning radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communications system as claimed in claim 1;
wherein the steps of solving the Master Program include the steps of:
converting a channel group size provided by the Master Program to its nearest integer value;
determining if the integer group sizes add up to the number of available channels;
if the integer group sizes exceed the number of available channels reduce the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels;
if the integer group sizes are less than the number of available channels increase the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels; and if the number of integer group sizes equal the number of available channels accepting the channel group size to be integerized.

5. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of assigning radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communication system as claimed in claim 1;

wherein the steps of solving the Subprogram include the added steps of:
placing all cells in a set U and initializing sets C and ~ to be empty, computing a criterion function f j for each member j of set U, selecting aj * having the greates f j value to be a member of U, removing j * from U and adding it to C, computing the term a j for each member j assuming J * is in C, placing j * in C if a j is less than zero and placing j * in ~ if a j is equal to or greater than zero, computing a j for each member j of U when a j is equal to or greater than zero from the previous step, and removing members j from U where a j is less than zero from U and placing them in ~, and terminating when U is empty.

6. In a wireless communications system, in which service areas are partitioned into a plurality of contiguous cells which are non-regular to each other with respect to cell shape/size and their respective traffic loads, a method of assigning radio channels to the cells for achieving maximization of traffic handling capacity of the wireless communications system as claimed in claim 1;
wherein the steps of hueristically providing new values for the solution of the K th Master Program include the added steps of:
starting with a channel set X Kj;
revising .lambda. j to 0 if x Kj is 1, and leaving it unchanged if x Kj is 0.
computing NK and revising NK for K ranging from 1, through K-l.

7. In a wireless communications system having a plurality of cell areas, each having a central base station for radio communication with a plurality of mobile radiotelephones and an assigned set of transmit/receive radio channels different from those of a nearby cell area but shared with a distant cell area so as to permit channel reuse with out interference, a method of partitioning a plurality of available radio frequencies and assigning these radio frequencies into non-overlapping sets of frequencies assigned to optimal groupings of co-user cells in a non-regular cellular arrangement;
comprising the steps of:
preliminarily assigning channel sets to all cell areas using conventional regularity assumptions and complying with channel availability and interference constraints;

establishing an initial capacity factor defining a limiting capacity ratio of assigned channels to channels needed to meet blocking requirements;
maximize the capacity factor and defining channel group sizes and generate dual variable terms specifying channel group sizes and a coverage logicvalue by using linear programming techniques;
decomposing the linear program into a Master Program and a Subprogram;
solving the Master Program to obtain new values of the capacity factor, channel group sizes and dual variable terms reflecting channel assignment constraints and channel availability constraints, solving the Subprogram using the new values provided by the Master Program to obtain new channel sets;
hueristically augmenting the Subprogram to provide new channel sets and iteratively resolve the Subprogram;
testing the solution for optimality and beginning with the Master Programs iteratively solve the Master Program, the Subprogram and hueristically augment until optimality is achieved.

8. In a wireless communication system having a plurality of cell areas, each having a central base station for radio communication with a plurality of mobile radiotelephones and an assigned set of transmit/receive radio channels different from those of a nearby cell area but shared with a distant cell area so as to permit channel reuse with out interference, a method of partitioning a plurality of available radio frequencies and assigning these radio frequencies into non-overlapping sets of frequencies assigned to optimal groupings of co-user cells in a non-regular cellular arrangement; as claimed in claim 7;
wherein the step of preliminarily assigning channel sets to all cells include the steps of:
modifying channel sets in the original assignment one at a time by adding as many cells as possible, provided the interference constraint is satisfied;
for those channel sets in the original assignment for which the interference constraint is not satisfied, removing cells until the interference constraint is satisfied; and generating additional channel sets until all cells are covered.

9. In a wireless communications system having a plurality of cell areas, each having a central base station for radio communication with a plurality of mobile radiotelephones and an assigned set of transmit/receive radio channels different from those of a nearby cell area but shared with a distant cell area so as to permit channel reuse with out interference, a method of partitioning a plurality of available radio frequencies and assigning these radio frequencies into non-overlapping sets of frequencies assigned to optimal groupings of co-user cells in a non-regular cellular arrangement as defined in claim 7;
wherein the steps of solving the Master Program include the steps of:
converting a channel group size provided by the Master Program to its nearest integer value;
determining if the integer group sizes add up to the number of available channels;
if the integer group sizes exceed the number of available channels reduce the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels;
if the integer group sizes are less than the number of available channels increase the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels; and if the number of integer group sizes equal the number of available channels accepting the channel group size to be integerized.

10. In a wireless communications system having a plurality of cell areas, each having a central base station for radio communication with a plurality of mobile radiotelephones and an assigned set of transmit/receive radio channels different from those of a nearby cell area but shared with a distant cell area so as to permit channel reuse with out interference, a method of partitioning a plurality of available radio frequencies and assigning these radio frequencies into non-overlapping sets of frequencies assigned to optimal groupings of co-user cells in a non-regular cellular arrangement as defined in claim 7;
wherein the steps of solving the Subprogram include the added steps of:
placing all cells in a set U and initializing sets C and ~ to be empty, computing a criterion function f j for each member j of set U, selecting a j* having the greatest f j value to be a member of U, removing j* from U j and adding it to C, computing the term a j for each member j assuming J * is in C, placing j * in ~ if a j is less than zero and placing j * in C if a j is equal to or greater than zero, computing a j for each member j of U when a j is equal to or greater than zero from the previous step, and removing members j from U where a j is less than zero from U and placing them in ~, and terminating when U is empty.

11. In a wireless communications system having a plurality of cell areas, each having a central base station for radio communication with a plurality of mobile radiotelephones and an assigned set of transmit/receive radio channels different from those of a nearby cell area but shared with a distant cell area so as to permit channel reuse with out interference, a method of partitioning a plurality of available radio frequencies and assigning these radio frequencies into non-overlapping sets of frequencies assigned to optimal groupings of co-user cells in a non-regular cellular arrangement as defined in claim 9;
wherein the steps of hueristically providing new values for the solution of the K th Master Program include the added steps of:
starting with a channel set x Kj;
revising .lambda. j to 0 if x Kj iS 1, and leaving it unchanged if x Kj is 0.
computing N K and revising N K for K ranging from 1, through K-l.

12. In a wireless communications system a having service areas partitioned into a plurality of substantially contiguous cells a method of assigning radio channels to the cells;
comprising the steps of:
determining the available cells and frequencies;
determining interference and system constraints for the cells;
determining existing traffic patterns for the cells; inputing the cells, frequencies, interference and system constraints, and traffic patterns into a computing device;
programming the computing device to optimize the assignment of radio channel sets to the cells by:
decomposing a calculation for optimizing of the radio channel set assignment into Master Program and a Subprogram, initially solving the Master Program in order to determine values for a capacity factor, channel set sizes, a first simplex multiplier corresponding to the channel assignment constraints for each cell, and a second simplex multiplier corresponding to the radio channels availability constraint;
solving the Subprogram to generate additional channel sets using output values from the Master Program;
hueristically providing new values of channel set sizes and the second simplex multiplier, and resolving the Subprogram to generate further channel sets;
resolving the Master Program for determining new channel sets;
checking the resulting assignment for optimality;
terminating when optimality is achieved;
transmitting the assignments to the respective base stations; and tuning the radios of the base stations to the appropriate frequencies.

13. In a wireless communications system a having service areas partitioned into a plurality of substantially contiguous cells a method of assigning radio channels to the cells as recited in claim 12;
comprising the further steps of:
comprising a channel group size provided by the Master Program to its nearest integer value;
determining if the integer group sizes add up to the number of available channels;
if the integer group sizes exceed the number of available channels reduce the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels;
if the integer group sizes are less than the number of available channels increase the size of selected channel groups by one until the integer group sizes add up to the number of available channels; and if the number of integer group sizes equal the number of available channels accepting the channel group size to be integerized.

14. In a wireless communication system a having service areas partitioned into a plurality of substantially contiguous cells a method of assigning radio channels to the cells as recited in claim 12;

wherein the steps of solving the Subprogram include the added steps of:
placing all cells in a set U and initializing sets C and ~ to be empty, computing a criterion function f j for each member j of set U, selecting a j * having the greatest f j value to be a member of U, removing j * from U j and adding it to C, computing the term a j for each member j assuming J * is in C, placing j * in ~ if a j is less than zero and placing j * in C if a j is equal to or greater than zero, computing a j for each member j of U when a j is equal to or greater than zero from the previous step, and removing members j from U where a j is less than zero from U and placing them in ~, and terminating when U is empty.

15. In a wireless communications system having service areas partitioned into a plurality of substantially contiguous cells, a method of assigning radio channels to the cells, comprising the steps of:
determining the available cells and frequencies;
determining interference and system constraints for the cells;
determining existing traffic patterns for the cells; inputting the cells, frequencies, interference and system constraints, including blocking requirements, and traffic into a computing device;
programming the computing device to optimize the assignment of radio channel sets to the cells wherein the improvement comprises;
decomposing a calculation for optimizing the radio channel set assignment into aMaster Program and a Subprogram, initially solving the Master Program in order to determine values for a capacityfactor, channel set sizes, a first simplex multiplier vector corresponding to the channel assignment constraints for each cell, and a second simplex multiplier vector corresponding to the radio channels availability constraint; wherein the capacity factor represents a bottle neck capacity ratio of a number of radio frequencies assigned to a cell over the number of radio frequencies needed to meet blocking requirements;

solving the Subprogram to generate additional channel sets using output values from the Master Program which include channel set sizes and the simplex multiplier vector; by heuristically providing new values of channel set sizes and the first simplex multiplier vector to replace for calculation purposes these values for values initially determined by the initially solving of the Master Program, and resolving the Subprogram to generate further channel sets;
resolving the Master Program using channel sets determined by solving and resolving the Subprogram to maximize the capacity factor and for selecting channel sets and for determining new sizes of the channel set;
checking the resulting assignments for optimality by evaluating the second simplex multiplier;
terminating when optimality is achieved;
transmitting the assignments to the respective base stations; and tuning the radios of the base stations to the appropriate frequencies.

16. In a wireless communications system a having service areas partitioned into a plurality of substantially contiguous cells a method of assigning radio channels to the cells as recited in claim 15;
comprising the further steps of:
converting a channel group size provided by the Master Program to its nearest integer value;
determining if the integer group sizes add up to the number of available channels;
if the integer group sizes exceed the number of available channels reduce the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels;
if the integer group sizes are less than the number of available channels increase the sizes of selected channel groups by one until the integer group sizes add up to the number of available channels; and if the number of integer group sizes equal the number of available channels accepting the channel group size to be integerized.

17. In a wireless communication system a having service areas partitioned into aplurality of substantially contiguous cells a method of assigning radio channels to the cells as recited in claim 15;
wherein the steps of solving the Subprogram include the added steps of:
placing all cells in a set U and initializing sets C and ~, to be empty, computing a criterion function f j for each member j of set U, selecting aj* having the greatest f j value to be a member of U, removing j* from U and adding it to C, computing the term a j for each member j assuming J* is in C, placing j* in C if a j is less than zero and placing j* in C if a j is equal to or greater than zero, computing a j for each member j of U when a j is equal to or greater than zero from the previous step, and removing members j from U where a j is less than zero from U and placing them in C, and terminating when U is empty.

18. In a wireless telephone communication system, having a plurality of substantially contiguous cells; apparatus for assigning radio channels to cells comprising:
input apparatus for storing in a memory information concerning available radio channel constraints, cell identifications, interference and system assignment constraints and existing traffic patterns for the cells;
a computer including programmed instructions for developing radio channel assignments in response to data stored in the memory;
means for assigning to the cells the radio channel sets developed by the computer to enable radio transceivers at the cells to tune to frequencies in accordance with the channel assignments;
wherein the programmed instructions carry out the process of:
selecting a first collection of channel sets;
for the first collection of channel sets, determining values for a capacity factor representing a bottleneck capacity ratio of a number of radio frequencies assigned to a cell over the number of radio frequencies needed to meet blocking requirements, set sizes, a first simplex multiplier vector corresponding to channel assignment constraints for each cell, and a second simplex multiplier corresponding to the available radio channels constraint;
generating additional channel sets to improve the capacity factor using values obtained from the step of determining;
heuristically computing new values of channel set sizes and new values of simplex multiplier vectors;
repeating the step of generating a selected number of times each time including the heuristically selected new values in the generating process; and returning to the step of determining as long as a selected criteria is not met.

19. In a wireless telephone communication system, as claimed in claim 18;
wherein the step of selecting a channel set includes assigning a channel set to a cell using conventional regularity assumptions and complying with channel availability and interference constraints.

20. In a wireless telephone communication system, as claimed in claim 18;
wherein the step of determining a value for a capacity factor includes defining a limiting capacity ratio of assigned channels to channels needed to meet blockingrequirements.

21. In a wireless telephone communication system, as claimed in claim 18;
a channel set size is determined by its integer value.

22. In a wireless communication system in which a service area is partitioned into a plurality of non-regular contiguous cells; a method of dynamically altering assignments of radio channels to the cells comprising the steps of:
initially determining interference constraints, system constraints and availablechannel frequencies and entering the information into a memory of a computer;
storing an existing assignment of radio channels into the memory;
determining existing traffic patterns of mobile radio telephone usage within theservice area and entering the existing traffic pattern into the memory of the computer;

developing an improved assignment of radio channels to the cells; and communicating the improved assignment of radio channels to the cells, causing radio transceivers at the cells to operate at frequencies representing the improved channel assignments;
wherein the improvement comprises programming the computer to solve a calculation for optimizing radio channel assignments to the cells by decomposing the calculation into a Master Program and a Subprogram, and by:
initially solving the Master Program to determine values for a capacity factor representing a ratio of radio frequencies assigned to a cell to radio frequencies needed to meet blocking requirements, channel set sizes, a first simplex multiplier vector corresponding to interference and system constraints for each cell and a second simplex multiplier vector corresponding to available channel frequencies;
solving the Subprogram to generate additional channel sets using output values from the Master Program;
heuristically generating new values for use by the Subprogram of the first simplex multiplier vector and of channel set sizes; and resolving the Subprogram using the new values to generate further channel sets;
resolving the Master Program using results of the Subprogram for selecting additional channel sets to maximize the capacity factor;
checking resulting channel set sizes of the Master Program for optimally; and terminating when optimality is achieved.

23. In a wireless communications system having service areas partitioned into a plurality of substantially contiguous cells, a method of assigning radio channels to the cells comprising the steps of:
measuring traffic and interference data for the cells on a substantially real-time basis;
determining an allotment of the radio channels among the plurality of cells based on the measured traffic and interference data; and tuning radios in the cells to such channel allotments in real-time.