Method and apparatus for resource allocation and scheduling

A method and apparatus for resource allocation and scheduling within a wireless communication system is provided herein. During resource allocation, a maximum total system transmit power (P), a maximum number of codes available (N), a maximum number of codes for each user in the system (N=(N1, . . . , Nd)), a maximum SINR value (S=(S1, . . . , Sd)) for each user in the system, and a SINR per watt of transmit power for each user in the system (e=(e1, . . . , ed)) is received by a scheduler. Scheduler then outputs an optimal number of codes per user (n) and power levels per user to (p).

FIELD OF THE INVENTION

The present invention relates generally to resource allocation and scheduling and in particular, to resource allocation and scheduling in an over-the-air communication system.

BACKGROUND OF THE INVENTION

Resource allocation and scheduling within communication systems is generally known in the art. During resource allocation and scheduling, a system controller determines channel parameters for each user, along with a schedule for data transmission. For example, each user within a communication system may be assigned a coding scheme, a power, a number of codes utilized, and a data rate. As known, a communication system generally comprises many users each having their own transmission parameters. A challenge becomes optimizing the communication system by appropriately scheduling each user, and picking appropriate system parameters for each user. Therefore, a need exists for a method and apparatus for scheduling and resource allocation within a communication system that generally optimizes system performance.

DETAILED DESCRIPTION OF THE INVENTION

To address the need for resource allocation and scheduling, a method and apparatus for resource allocation and scheduling within a wireless communication system is provided herein. During resource allocation, a maximum total system transmit power (P), a maximum number of codes available (N), a maximum number of codes for each user in the system (N=(N1, . . . , Nd)), a maximum SINR value (S=(S1, . . . , Sd)) for each user in the system, and a SINR per watt of transmit power for each user in the system (e=(e1, . . . , ed)) is received by a scheduler. Scheduler then outputs an optimal number of codes per user (n) and power levels per user (p) based on P, N, N, and S.

The present invention encompasses a method for resource allocation. The method comprises the steps of receiving a maximum total system transmit power (P), receiving a maximum number of system codes available (N), receiving a maximum number of codes for each user in the system (N), receiving a maximum SINR value (S) for each user in the system, receiving a SINR per watt of transmit power value for each user in the system (e), determining an optimal number of codes per user (n) and optimal power levels per user (p) based on P, N, N, S, and e, and scheduling users with operating parameters based on n and p.

The present invention additionally encompasses a method for resource allocation. The method comprises the steps of determining a value for an optimal number of codes per user (n) within a communication system, and determining an optimal rate per user (r) and an optimal power per user to) based on n.

The present invention additionally encompasses an apparatus comprising a scheduler receiving a maximum total system transmit power (P), a maximum number of system codes available (N), a maximum number of codes for each user in the system (N), a maximum SINR value (S) for each user in the system, and a SINR per watt of transmit power value for each user in the system (e), the scheduler outputting an optimal number of codes per user (n) and optimal power levels per user to) based on P, N, N, S, and e.

Turning now to the drawings, wherein like numerals designate like components,FIG. 1is a block diagram of transmission circuitry100. As shown, transmission circuitry100comprises scheduler/optimizer101, controller103, and plurality of transmitters105. During operation, system parameters enter scheduler101. Scheduler101then computes an optimized set of transmission parameters for each transmitter105and passes this information to controller103. During data transmission, controller103receives data destined to individual users, and utilizes the set of optimized transmission parameters to appropriately control transmitters105. When data is passed to transmitters105, transmitters105utilize the transmission parameters to appropriately transmit data to individual users.

As an example, scheduler/optimizer101receives a set of users from controller103and selects the users for transmission. For each of the users selected, scheduler/optimizer101chooses a physical-layer operating point (PLOP) which comprises a particular modulation and coding scheme (MCS), a particular transmit power, a particular number of codes, and a particular information rate. Each PLOP consumes different amounts of overall code and power resources.

Scheduler/optimizer101picks the “optimal” PLOP for each user such that the overall system is optimized. In particular, the optimal PLOP for each user is chosen so that a sum of a weighted combination of the rates assigned to users is maximized. The preferred value for the weight vector is the gradient of the utility function at the current throughput estimate

As discussed above, scheduler/optimizer101has the task of optimizing overall system performance based on a given set of input parameters. In the preferred embodiment of the present invention this is accomplished by optimizing a scheduling and resource allocation algorithm. The following text describes, 1) the generation of the resource allocation algorithm, and 2) the optimization of the resource allocation algorithm.

1. Generation of the Resource Allocation Algorithm

Simply stated, optimizing a scheduling algorithm involves maximizing the dot product of the “gradient of utility” (as a function of the throughput and the queue length) defined as ∇U(Wt, Qt):=φ∇wU(Wt,Qt)−∇QU(Wt,Qt) and the rate vector rtto be selected at each scheduling time t, where:

U is a utility function,

∇wU(W1, Q1) is a vector of partial derivatives of U with respect to W,

∇QU(W1, Q1) is a vector of partial derivatives of U with respect to Q,

d is the number of users.

That is, we would like to pick the rate vector from the state dependent rate region R(et), which has the highest projection on the gradient of the utility. The rate region depends on the channel state. While the channel state is not perfectly known we assume there is some estimate of it available through a quality (e.g., CQI) feedback, etc. In particular, we assume that we know the predicted SINR per watt of transmitted power ei,tfor each user i and that et=(e1,t, . . . , ed,t) captures the channel state

maxrt∈ℛ⁡(et)⁢∇U⁡(Wt,Qt)T·rt=maxrt∈ℛ⁡(et)i⁢U.i⁡(Wi,t,Qi,t)⁢ri,t
For a certain class of utility functions we have

ciis the QoS weight associated with the throughput for useri,

diis the QoS weight associated with the queue length for user i,

φ is filter coefficient associated with the throughput,

α is a fairness parameter associated with the throughput,

p is a fairness parameter associated with the queue length.

Thus the optimization problem results in

maxr∈ℛ⁡(e)⁢∑i⁢wi⁢ri
where wiis given by equation (1) above and where we have suppressed the dependence on time t for convenience. Note that selection of the rate riis coupled with the selection of the physical layer operating point (PLOP) that includes the number of codes niand the power pi. These PLOP variables need to satisfy system and per user constraints such as

ni≤Ni∑i⁢ni≤N∑i⁢pi≤P
and these are part of the description of the state dependent rate region R(e). As described in U.S. Patent Publication No. US 2002/0147022 “Method for Packet Scheduling and Radio Resource Allocation in a Wireless Communication System,” by Agrawal, et al., the rate per code can be written in terms of the signal to noise ratio (SINR) per code so that

rini=Γ⁡(SINRi)
where the SINR per code is given by

SINRi=pini⁢ei
and where Γ is some appropriate function. A reasonable choice of the function Γ is the well known information theoretic channel capacity formula Γ(x)=Blog(1+x). Such a functional relation between the rate and the SINR also provides a good curve fit to the High-Speed Downlink Packet Access (HSDPA) MCS table with B equal to the symbol rate (chip rate/spreading factor) which for HSDPA is B=3840000/16=240000 symbols/sec. Note also that for the best curve fit, the SINR is decreased by a factor of A=1.7, i.e., Γ(x)≈Blog(1+x/A) is used. Plugging in this formula results in the following equation for the rate riin terms of ei, ni, pi:

ri=ni⁢B⁢⁢log⁡(1+pi⁢eiAni)(2)
Note that the SINR per watt of transmit power on a HS-PDSCH code is given by:

ei=(EcNt)pilot⁢16Ppilot
For notational simplicity eiis redefined to be ei/A the “effective” SINR per watt of transmit power on a HS-PDSCH code, i.e.,

ei=(EcNt)pilot⁢16Ppilot⁢1A
The rate region is then given by

ℛ⁡(e)={r≥0⁢:⁢⁢ri=ni⁢B⁢⁢log⁡(1+pi⁢eini),⁢ni≤Ni⁢∀i,∑i⁢ni≤N,∑i⁢pi≤P}
By redefining wito be

ciis the QoS weight (possibly 0) associated with the throughput for user i,

diis the QoS weight (possibly 0) associated with the queue length for user i,

φ is filter coefficient associated with the throughput,

α is a fairness parameter associated with the throughput,

p is a fairness parameter associated with the queue length,

B is a scaling constant to match up the formula to bits.

This is a specific instance of the weight vector w=(w1, . . . , wd); however, in general wicab be any function of the throughput Wiand queue length Qiwhich is non-increasing in the throughput and non-decreasing in the queue length. The function may also take as parameters various QoS related information such as delay requirement, QoS class, bandwidth requirement, etc.

The optimization problem can be rewritten as
V*:=max(n,p)εχV(n,p)  (3)
subject to

n is a vector of code allocations, i.e. a vector comprising codes per user,

p is a vector of power allocations, i.e., a vector comprising power levels per user,

w is the vector of wis, and

e is the vector of eis.

Note that the constraint set χ is convex. It can also be verified that V is concave in (n,p). In case of a retransmission for a user i the “effective” SINR per watt per code eiof that user may be bumped up by a suitable factor.

In addition to the constraints captured above, the following per user power constraints are allowed, any of which may be rendered redundant by a suitable setting of the parameters.peak power constraint:
pi≦Pi, ∀i.SINR constraint:

SINRi=pi⁢eini≤Si⇔pi≤Si⁢niei,∀i.rate per code (note that the encoder rate assuming a fixed modulation order is a constant times this, viz. the encoder rate is the rate per code divided by the coded output rate which itself is the product of modulation order (2 or 4) times the symbol rate (240000 symbols/sec for HSDPA))rate

All of the above per user power constraints are special cases of

SINRi=pi⁢eini≤si⁡(ni),∀i,(6)
where the function siis also dependent on the fixed (for the optimization problem) parameters Pi,ei,Si,Ri,(R/N)i. In fact all of the above constraints can be combined into the single constraint (6) above with

si⁡(ni)=min⁢{Pi⁢eini,Si,(ⅇ(R/N)i-1),(ⅇRi/ni-1)}
Two special cases of this of interest are:1. si(ni)≡sidoes not depend on ni.2. si(ni)≡si=∞.

With the per user power constraints, the constraint set χ is further restricted to
χ:={(n,p)≧0:ni≦Ni, pi≦si(ni)ni/ei∀i}(7)

The constraint set continues to be convex if si(ni)niis a concave function of ni. Note that si(ni)niis indeed a concave function of nifor the two special case (1-2) mentioned above. However, for the rate constraint case (equation 18), si(ni)niis convex in ni.

As mentioned earlier, users with retransmissions need to be treated differently in two respects:1. Their effective SINR per watt per code needs to be increased.2. They have an equality constraint on their rate ri=Ri

The first can be handled easily by adjusting their eiappropriately. To handle the latter constraint, we observe that the rate constraint is equivalent to

Scheduler/optimizer101receives a set of parameters and solves for V* by optimizing the resource allocation algorithm of equation (3). More particularly, scheduler/optimizer101receives

P=Maximum total system transmit power,

N=Maximum total codes available to the system,

N=Vector comprising the maximum number of codes (e.g., spreading codes) for each user in the system,

R=Vector comprising the maximum data rate for each user in the system,

R/N=Vector comprising the maximum data rate per code for each user in the system,

P=Vector comprising the maximum transmit power for each user in the system,

S=Vector comprising the maximum noise (e.g., SINR) for each user in the system,

e=Vector comprising the noise (e.g., SINR) per power (e.g., SINR per watt) for each user in the system,

W=Vector comprising the estimated throughput vector for each user in the system,

Q=Vector comprising the queue length vector for each user in the system,

c=Vector comprising the QoS weight associated with the throughput for each user in the system, and

b=Vector comprising the QoS weight associated with the queue length for each user in the system.

In the preferred embodiment of the present invention scheduler/optimizer101determines optimal values of ri, ni, and pifor each user i, outputting vectors r, n, and p for communication system100. As discussed above, vectors r, n, and p for communication system 100 are determined by solving for V* in equation (3) given the set of input parameters described above. Scheduler/optimizer101solves for V* subject to the additional constraints described above in (7).

2.1 First Embodiment

In case

∑i⁢Ni≤N,ni=Ni
is the optimal code allocation, we are left with just a power optimization problem which can be solved very easily as shown later. Henceforth, we will tackle the case when this is not the case, i.e.,

∑i⁢Ni>N.
Also, we allow nito take on non-integer values as a relaxation to the integer optimization problem. We find that in most cases, the optimal solution turns out to assign integer values to ni. We solve the optimization problem by looking at the dual formulation. Define the Lagrangian

χ is set of valid choices for (n,p) given by the constraint set (7),

λ is Lagrange multiplier for the power constraint, and

μ is Lagrange multiplier for the code constraint.

The dual problem is to find
L*:=min(λ,μ)≧0L(λ,μ)  (10)
Also, define
L(λ):=minμ≧0L(λ,μ)=max(n,p)εχL(p,n,λ,μ)  (11)

For this part of the solution we will ignore the rate constraint (5) ((8) for retransmissions) or replace it with a linear constraint as described below in “Handling rate restrictions.”

Note: Handling Rate Restrictions

The constraint set with the rate restriction (5) or (8) is non-convex, which would not allow us to optimize over nivery easily. To simply matters, we may assume that ni=Niin the second term on the right. Thus we assume that (5) is replaced by

pi≤niei⁢(eRi⁢ln⁢⁢2BNi-1)
In case of constraint (8), we can replace it by

This may be justified on a few different grounds. First, we have observed that in many cases the optimal ni=Ni. Secondly substituting ni=Nimakes things a bit worse for this user, but the bump up in ei(for the case of retransmissions) will increase the wieiof this user which should probably still help select this user. We could also try putting a different linear approximation to the above constraint. Note that this constraint is only needed for the code allocation part. Some other heuristics are also possible. For instance we may replace the rate constraint as above and if we still pick this user and it gets ni=Ni, then we have most likely not sacrificed anything. Similarly we could try ni=1 in the second term which should make the user more likely to be selected. If it is still not selected, once again we have probably not sacrificed anything by this approximation. However for the cases in between (which would probably be rare), we may want to explicitly vary the nifor this user explicitly and optimize. Note that once the code allocation is made, we can work with the original rate constraint for the optimizations over powers.

Since the objective function is concave and the constraint set is convex, there is no duality gap allowing us to use the solution of the dual to compute the solution of the primal.

Based on this the scheduler/optimizer101determines appropriate values for r, n, and p via the following steps (also illustrated inFIG. 2):1. Collect all the input parameters P, N, N, R, R/N, P, S, e, W, Q, c, b. (Step201)2. For a fixed λ and μ find the optimal (n,p) analytically. (Step203)3. Then keeping λ fixed, find the optimal μ*(λ). (Step205)4. Also, keeping λ fixed, calculate L(λ) as defined in equation (11). (Step207).5. Numerically search for the optimal λ=λ*, in other words, search for the value of λ that minimizes L(λ) to obtain L*. (Step209)6. Calculate n=n*(λ*,μ*(λ*)) (Step211)7. Calculate optimal p and r keeping n fixed. (Step213)

FIG. 2is a flow chart showing operation of scheduler/optimizer101. The logic flow begins at step201where e, P, N, N, and S are collected by the optimizer101. At step203n and p are calculated analytically by keeping λ and μ fixed. In particular λ and μ are fixed but arbitrary and n and p are calculated as a function of λ and μ to optimize the Lagrangian in order to obtain the dual function as shown in equation (9).

At step205λ is fixed but arbitrary and an optimal μ*(λ) is determined so that we minimize the dual function L(λ,μ) to obtain L(λ). L(λ) is calculated per equation 23 at step207and a numerical search for an optimal λ=λ* occurs at step209. In other words, at step209λ=λ* is determined so that L*=L(λ*)=minλ≧0L(λ). At step211n=n*(λ*,μ*(λ*)) is calculated per equation (14). The vector R is collected and r and p are calculated keeping n fixed (step213). In particular n is fixed to the value obtained in step5, and p and r are calculated as per equations (21) and (2) taking the actual rate constraint R into account. Finally, at step215values for n, p and r are output to controller103and utilized to schedule and transmit data via transmitters105.

The following discussion further details the steps taken above inFIG. 2.

2.1.1 Step203, for Fixed λ and μ Find the Optimal (n,p) Analytically

Optimizing the Lagrangian (in the dual) for a fixed λ, μ, and n (this includes the optimization over powers assuming a fixed feasible n) we get

pi*=niei⁡[min⁢{wi⁢eiλ-1,si⁡(ni)}]+.(12)
The resulting SINR per code is given by

The last case is vacuous when we have no per user constraints on the powers, i.e., si(ni)=∞. Note that in case si(ni)≡sidoes not depend on ni, the resulting SINR per code also does not depend on the number of codes niand the power requirement scales linearly in the number of codes.

Define

h⁡(wi⁢ei,si⁡(ni),λ):={0,wi⁢ei≤λ[λwi⁢ei-1-ln⁢⁢λwi⁢ei],wi⁢ei1+si⁡(ni)≤λ<wi⁢ei[ln⁡(1+si⁡(ni))-λwi⁢ei⁢si⁡(ni)],λ<wi⁢ei1+si⁡(ni)
Then for case (1) si(ni)≡sidoes not depend on ni. Additionally,
h(wiei, si(ni),λ)=h(wiei, si, λ)
also does not depend on ni. For this case it is easy to further optimize the Lagrangian over nito calculate the dual function. In particular, we find that

ni*=ni*⁡(λ,μ)={0,wi⁢h⁡(wi⁢ei,si,λ)<μ0≤ni≤Ni,wi⁢h⁡(wi⁢ei,si,λ)=μNi,wi⁢h⁡(wi⁢ei,si,λ)>μ(14)
Note that for the case μ=wih(wiei, si, λ) any 0≦niNiis optimal. Then the dual function is given by

In order to optimize the dual function (15) over μ, we sort the users in decreasing order of μi(λ). Let j* be the smallest integer such that

∑i=1j*⁢Ni≥NL⁡(λ):=minμ≥0⁢L⁡(λ,μ)⁢=∑i=1j*-1⁢μi⁡(λ)⁢Ni+μj*⁡(λ)⁢(N-∑i=1j*-1⁢Ni)+λ⁢⁢P(16)
and the minimizing μ is given by

Note that μj(λ)≧μj+1(λ) by the above ordering. Thus μ*(λ) is a threshold; users with their μi(λ)>μ*(λ), get their full code capability and those with μi(λ)<μ*(λ) get none. Also note that when wi≧wjand ei>ej, μi(λ)≧μj(λ), and user i will be given a full code allocation before allocating any codes to user j. This implies that when the fairness parameter α=1 (the “max C/I scheduler”) and all users have the same QoS weight, wi's are constant and identical across users and thus packing users into the code budget in order of their ei's is optimal. This is illustrated below with respect to description of the alternate embodiment of the present invention.

In case μj−1*(λ)>μj*(λ)>μj+1*(λ), there is a unique feasible n* that satisfies the sum code constraint with equality and that optimizes the Lagrangian for μ=μ*(λ). It is given by

ni*={Ni,i<j*N-∑i=1j*-1⁢Ni,i=j*0,i>j*.(18)
However, if this is not the case, there is a tie and there are multiple n* that optimize the Lagrangian. However, not all of these choices of n* and the resulting p* given by (18) and (12) will be feasible. In order to achieve feasibility we must also satisfy the additional code and power constraints. Let n*(λ) denote any of the maximizing n constructed above.

We have just shown that the optimal code allocation has the following properties:

1. For the case of Ni=N at most two users will be scheduled.

2. If all Niare equal, then at most ┌N/Ni┐+1 users will be scheduled. All but two users will have their full code allocation.

3. In general all but two users will have their full code allocation.

2.1.3 Step213Calculating r and p While Keeping n Fixed.

In step213we solve for the optimal powers given a code allocation n. It should be noted that n may be derived as discussed above with reference to steps203and205, or alternatively, n may be pre-determined and provided as an input into the power-optimization algorithm. Denote by
V*(n):=max{p≧0: pi≦si(ni)ni/ei∀i}V(n,p)
subject to

This is solved by finding λ*(n) using the dual formulation and then computing the optimal p*(n) as described before. Since n is fixed there are no restrictions on the function nisi(ni) except that it has to be non-negative. Thus, we can incorporate the rate constraints in the calculations performed in this step.

Without loss of generality we remove any users with zero code allocations. Let M be the number of users with positive code allocation. We first need to check if the sum power constraint is inactive, i.e.,

∑i⁢pi=∑i⁢niei⁢si⁡(ni)≤P.
If this is the case the optimal power allocations are just the individual power constraints

pi*=niei⁢si⁡(ni)
and we are done.

Henceforth, we proceed when this constraint is active. In this case we can show that the sum power constraint must be satisfied with equality for the optimal powers (otherwise at least one of the users' powers can be increased resulting in a higher primal value function). We can now construct the Lagrangian in the sum power constraint alone.

Lp⁡(p,λ):=∑i⁢wi⁢ni⁢⁢ln⁡(1+pi⁢eini)+λ⁡(P-∑pi)
In case

∑i⁢ni=N,
the two Lagrangians are equal. The dual function is given by
Lp(λ):=max{p≧0: pi≦si(ni)ni/ei∀i}Lp(p,λ).

Note that for optimizing over powers, the constraint set is always convex regardless of the function si(ni)ni. Maximizing Lp(p,λ) over p is essentially the same as the problem for L(p,n,λ,μ) as covered in the previous section. The optimal p is given by (12) as before, i.e.,

In Agrawal et al. it was shown that λ*(n) optimizes Lp(λ) if and only if the corresponding p*(n,λ) satisfies

∑i⁢pi*=P.
Substituting from (19) we get that λ*(n) is given by any solution of the equation:

Then the optimal power allocation vector p*(n) is given by

pi*⁡(n)=pi*⁡(n,λ*⁡(n))=niei⁡[min⁢{wi⁢eiλ*⁡(n)-1,si⁡(ni)}]+.(21)
Since λ occurs on both sides of equation (20) solving for λ*(n) may seem hard. We provide an algorithm solution to this as follows:

∑i⁢pi*⁡(n,λ)≥P,
i.e., find the smallest l such that

∑i⁢pi*⁡(n,x⁡[l])≥P.
In the paper “Joint Scheduling and Resource Allocation in CDMA Systems,” by Agrawal et al., we have shown that λ*(n) ε [x[l],x[l−1]) and is given by the solution of equation (20). Moreover for λ in the above range, the indicators in equation (20) are not dependent on the particular value of λ and hence we have an easily computable expression for λ.

Below we provide pseudo-code for an algorithm that finds the solution to the above equation (20). The algorithm complexity is O(MlogM) due to a sort.

Pseudo-code for Preferred Embodiment of Solution λ*(n)

If for some user i, the inequality pi≦eisi(ni)niis replaced by the equality constraint pi=eisi(ni)ni, as may happen for instance in a retransmission when the rate is fixed, we may simply remove this user from the problem after subtracting pifrom P and proceed as before.

2.1.3.2 No Per User Power Constraints

For the case that si(ni)=∞, the following simpler algorithm finds λ*(n). First, without loss of generality, assume that the users are numbered in descreasing order of wiei. Calculate the following

Any algorithm that minimizes or attempts to minimize L(λ) over λ is considered here. In the preferred embodiment we do so iteratively, where in each step k of the iteration we narrow the range [λkLB,λkUB] of the optimal λ* in a manner such that starting at k=0 with 0≦λ0LB≦λ0UB<∞ and for some d≧1 and 0≦ρ<1,
[λ(k+1)dUB−λ(k+1)dLB]≦ρ[λkdUB−λkdLB] ∀k≧0.

A plurality of such schemes may be designed all of which guarantee geometrically fast convergence to the optimal λ*. Two such embodiments are described below.

2.1.4.1 First Embodiment for Finding λ*

The algorithm makes use of the functions L(λ) (11), n*(λ) (18) and the tie resolution, λ*(n) (20), p*(n) (21), and V(p,n) (4) defined earlier. The function r(p,n) is simply the rate given the powers and codes given in (2). Pseudo-code for calculating λ*(n) is also given in Step213.

In “Joint scheduling and resource allocation in CDMA systems,” by R. Agrawal, V. Subramanian, R. Berry, G. Casheekar, A. Diwan, B. Love, it was shown that L(λ) is convex and that the optimal λ*=argminλ≧0L(λ)ε[λmin,λmax] where λmin=0 and λmax=maxiwiei.

At the kthiteration we identify λ* in the range [λkLB,λkUB] with the estimate of λ* given by λk*. The state of the algorithm at any time k is given by
Sk={[λkLB,LkLB], [λk*,Lk*,nk*], [λkUB,LkUB]}
with the assumption that Lk*=L(λk*)≦min (LkUB=L(λkUB),LkLB=L(λkLB)).

Step0initializes the state of this algorithm and provides an exit check in case we got lucky to hit the optimal allocation.

Step1does the iteration on the above state of the algorithm and also uses an exit check.

Step2polishes up by taking additional constraints into account and reoptimizing the powers, calculating rates/TBS etc.

The algorithm works as follows.

Step0: Initialize(a) λ0LB=0(b) If there are no per user power constraints on at least one user then L(λ0LB)=+∞.(c) Else calculate L(λ0LB).(d) Sort users in decreasing order of wiei.(e) Find smallest j* such that

n0,i*={Nii<j*N-∑i=1j-1⁢Nii=j*0i>j*(g)In case of a tie for j pick the user with the larger wiand if the wis are also equal, pick either.(h) If nj,0=Nj* then

Step2:(a) Round n*—note two users may have non-integer allocations in the case of tie. In that case round down the one with the greater power per code requirement and round up the other one.(b) Recalculate p*(n*) taking all constraints including rate constraints into account.(c) Calculate the rate r*=r(p*,n*) given by

ri*=240000ln⁢⁢2⁢ni*⁢⁢ln⁡(1+pi*⁢eini*)
and TBS=ri×0.002. Round down to nearest byte or some even coarser quantization.
We can also skip steps (b)-(g) in Step1to get a pure bisection based search algorithm.
2.1.4.2 Second Embodiment for Finding λ*

The second embodiment for finding the optimal λ* uses subgradients of L(λ) to aid in its minimization. For any given λ, a subgradient can easily be found as follows:1. First find n*(λ) in equation (18). In case of a “tie” all feasible code allocations which satisfy the sum power constraint with equality and optimize the Lagrangian (as described after equation (18)) are considered.2. Next, using n*(λ) find the corresponding p* as given by equation (12)3. Then

P-∑i⁢⁢pi*
is a subgradient to L(λ) at λ.4. Since L(λ) is convex, λ* will be optimal if and only if 0 is a subgradient of L(λ*).5. Thus, we can find the optimal λ* that minimizes L(λ) by numerically searching for λ with a 0 subgradient.
2.2 Other Embodiments

Based on the above results scheduler/optimizer101determines appropriate values for r, n, and p as follows:1. Collect all the input parameters P, N, N, R, R/N, P, S, e, W, Q, c, b. (Step301)2. Calculate n. (Step303)3. Calculate optimal p and r keeping n fixed. (Step305)

This is illustrated inFIG. 3, whereFIG. 3is a flow chart showing operation of scheduler/optimizer101in accordance with another embodiment of the present invention. The logic flow begins at step301where P, N, N, R, R/N, P, S, e, W, Q, c, and b are collected by the optimizer101. Note that steps 2-5 in the first embodiment were really aids to calculating the optimal n. We consider any other method to calculate n based on the input parameters P, N, N, R, R/N, P, S, e, W, W, Q, c, and b (Step303). Then, r and p are calculated keeping n fixed (step305). In particular n is fixed to the value obtained in Step303, and p and r are calculated as per equations (21) and (2) taking the actual rate constraint R into account. Finally, at step307values for n, p and r are output to controller103and utilized to schedule and transmit data via transmitters105.

An alternative method of calculating n based on the input parameters e, P, N, N, and S, is presented below:1. Sort users based on any metric that is a function of the input parameters including wiand ei.2. Find smallest j* such that

n0,i*={Nii<j*N-∑i=1j-1⁢⁢Nii=j*0i>j*4. In case of a tie for j* pick the user with the larger wiand if the wis are also equal, pick either.5. Optionally, we can also run one or more iteration of the algorithm described in the previous section.

While the invention has been particularly shown and described with reference to particular embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. For example, although examples where given above with respect to implementations within an HSDPA system, one of ordinary skill in the art will recognize that the above embodiments may be implanted in any communication system where codes and/or power need to be allocated. It is intended that such changes come within the scope of the following claims.