This application claims priority under 35 U.S.C. §119 to European Patent Application No. 10191589.0 filed on Nov. 17, 2010, the entire content of which is hereby incorporated by reference.
The present invention is related to wireless communication and, particularly, to the task of resource allocation for transmitter/receiver nodes in a wireless network.
Reference is made to the problem of finding an efficient proportional fair rate assignment, denoted by the vector of transmission rates r=[r1, . . . , rK]TεR+K, for the set of users K, in the coverage area of the network.
The rate assignment for the users in the network is illustrated in
In order to allow for real time implementation of the algorithm its convergence speed and complexity is a main issue. The computational complexity of the Algorithm is dominated by the complexity to solve the Weighted Sum-Rate optimization
c*i=argmaxcεR{λiTc},
carried out in each iteration. Additionally when users in a network with more than one base station are coordinated each iteration causes signalling overhead among the base stations. As the complexity for solving the Weighted Sum-Rate optimization is constant for each iteration a main issue is to reduce the number of iterations necessitated to find the solution, or a rate configuration that is provable within a factor ε of the solution. The number of iterations needed depends on the update method for the dual variables and most frequently used methods for the update of the dual variables are
Subgradient Methods, are the most popular update rules, see for example, as they have a simple closed form expression for the update,
The drawback of subgradient methods however is the poor convergence, especially in case high accuracy is necessitated.
Cutting Plane Methods, build on the fact that the dual function is convex and can therefore be lower bounded by hyperplanes. Iteratively hyperplanes are used to cut off halfspaces of points from the candidate points until the solution is found.
Ellipsoid Method [2] use Ellipsoids that contain the candidate points. Iteratively the Ellipsoid is cut into two half-ellipsoids and one is discarded. As an update the center of a new ellipsoids containing the remaining half ellipsoid is used. The new center λi+1 is calculated by
Kelley's Cutting Plane Method [3], approximates the dual function by hyperplanes and uses the minimizer of the linear approximation as an update. The new dual variables are the solution of the following optimization problem
Various variants of adding hyperplanes to the linear approximation exist. Additionally, a method is considered, which is named Multi-Cut, where one hyperplane per user is added in each iteration. The Multi-Cut method drastically improves the convergence speed, however the costs for the dual update increases largely in each iteration.
Aitken's method [4] adds an acceleration mode to subgradient methods, resulting in faster convergence, however stability of the algorithm becomes an issue. The update rule calculates one subgradient step, thereby finding an intermediate dual vector
With the intermediate dual vector one can compute
{tilde over (r)}=argmaxr≧0{U(r)−{tilde over (λ)}Tr},
and
{tilde over (c)}=argmaxcεR{{tilde over (λ)}Tc}
to obtain a further sub-gradient step
Finally, use {tilde over (λ)} and {circumflex over (λ)} to compute
One can observe that convergence speed is improved when more computational complexity is invested for the dual update. Some methods have closed form expressions for the update, while others necessitate to solve an optimization problem. The complexity and the convergence speed is summarized in
As one can see, the state-of-the-art methods have either high complexity to calculate the dual update or suffer from poor convergence which again is computationally complex, due to the large number of Weighted Sum-Rate problems that need to be solved.
U.S. 2009/232074 A1 discloses an auction-based resource allocation in wireless systems. Systems and methods to assign one or more resources in a multi-user cellular Orthogonal Frequency-Division Multiple Access (OFDMA) uplink include specifying a resource allocation problem for one or more resources; converting the resource allocation problem into an assignment problem; solving the assignment problem through an auction; and allocating one or more resources to cellular users to maximize a system utility.
According to an embodiment, an apparatus for allocating resources to nodes in a communication system may have: an iteration controller for performing an iterative processing, characterized in that the iteration controller being configured: for using iteration resource weights to obtain a resources allocation result for an iteration step, and for updating the iteration resource weights to obtain updated iteration resource weights for a further iteration step using a weighted combination of the resources allocation results for the iteration step and for at least one earlier iteration step.
According to another embodiment, a communication system may have: an inventive apparatus for allocating resources; nodes being mobile terminals; and base stations, wherein the mobile terminals or the base stations have multiple antennas to implement spatial channels.
According to another embodiment, a method for allocating resources to nodes in a communication system may have the steps of: performing an iterative processing using a plurality of successive iteration steps; characterized by, within an iteration step, using iteration resource weights to obtain a resources allocation result for the iteration step, and within the iteration step, updating the iteration resource weights to obtain updated iteration resource weights for a further iteration step in the plurality of successive iteration steps using a weighted combination of the resources allocation results for the iteration step and for at least one earlier iteration step.
Another embodiment may have a computer program for performing, when running on a computer or processor, the inventive method for allocating resources to nodes in a communication system.
The present invention is based on the finding that a much higher convergence speed of the iterative process is obtained when the update step of the iteration resource weights is performed using a weighted combination of the resource allocation results for this iteration step and for at least one earlier iteration step. All earlier resources allocation results are combined for calculating the updated iteration resource weights necessitated in a Primal-Dual algorithm.
Specifically, the update of the Dual variables λk is performed as a weighted combination of the earlier resources allocation results, where each earlier allocation result has an associated weighting factor. The weighting factor is a solution to a further optimization problem in that the sum of the weights for weighting the earlier iteration result is equal to 1.
The resources allocation result for the iteration step is determined based on an optimization of the weighted sum of the individual resources, where the iteration resource weights λ are the weights for the individual resources, and where the optimization is performed using an optimization target and the resource region. The resource region is defined by a condition of the communication system or the nodes. In an embodiment, the condition of the communication system or the nodes comprises a transmission channel between a node and a receiver or inner characteristics of the nodes, transmission power constraints of the nodes, mutual interference between the nodes, physical layer constraints or transmission protocols. The resources allocated through the nodes are transmission rates, frequency channels, time slots, code slots or spatial channels.
The iteration controller is configured for calculating, in an iteration step, a new combination weight α based on an optimization of a weighted sum of the resources allocation result of an earlier iteration step multiplied by a combination weight of the earlier iteration step and the resources allocation result of a current iteration step multiplied by the new combination weight, under the condition that the combination of the new combination weight and the combination weight of at least one earlier iteration step is equal to the predefined constraint value.
The apparatus comprises a memory for storing the resources allocation results obtained in earlier iteration steps up to a current iteration step and for storing combination weights for the weighted combination from earlier iteration steps up to the current iteration step.
The apparatus comprises an input interface for receiving information on the resource region defined by a condition of the communication system or nodes and an output interface for outputting the resources allocation result of a final iteration step performed by the iteration controllers so that the nodes are configurable using the resources allocation result of the final iteration step.
The nodes are mobile terminals, and the system comprises base stations, wherein the apparatus for allocating is configured for providing the resources allocation result of the final iteration step to a base station.
Embodiments of the present invention constitute an efficient proportional fair rate assignment for multi-user systems. The invention provides a novel dual update method and apparatus for dual decomposition based algorithms, used to compute an efficient proportional fair rate assignment for multi-user systems. The new concept offers a superior convergence speed compared to existing methods. Contrary to existing methods, embodiments of the present invention strictly improve the performance in each iteration. By causing minor additional costs, the inventive concept drastically reduces the number of iterations needed and, therefore, enables an overall reduction of complexity.
The present invention is useful in the field of wireless communications, in the field of transmission technologies, in the field of coordinated multi-point (CoMP) transmission and when a proportional fair rate assignment is necessitated.
Embodiments of the present invention will be detailed subsequently referring to the appended drawings, in which:
It has been found that the computational complexity of the dual variable update in conventional methods is too high and that many iterations are necessitated, leading to a high overall computational complexity where the main complexity lies in solving the weighted sum rate problem and in case of cooperation between cells, a high signaling overhead is necessitated.
In accordance with the present invention, the update rule for dual variables is enhanced in that for updating the iteration resource weights the iteration resource weights λi+1 are updated using a weighted combination of the resource allocation results for the current iteration step and for at least one earlier iteration step. Approximations of the rate regions are iteratively improved and used for updating the dual variables (weights of the rate distribution among users). The new update rule has a small computational complexity and leads to a high convergence speed. Therefore, the new concept has a reduced overall complexity. This is summarized in the last line of
For the simulations in
The final allocation result may comprise transmission rates, frequency channels, time slots, code slots or spatial channels. When, for example, a certain minimum bit error rate is necessitated for a certain bit rate, then the transmission power has to be set to a certain value. When, however, the transmission power remains the same, then assigning a higher or lower minimum signal to noise ratio which can, for example, be controlled by different modulation methods having higher or lower constellation diagrams, a rate assignment can also be performed. Therefore, a resource allocation will manifest itself within a transmitter in a certain transmission power setting and/or in a certain selection of a mapping rule (constellation diagram), in a certain amount of forward error correction coding, i.e., that a higher redundancy means a lower transmission rate but an enhanced signal to noise ratio. More complex issues can be included into the rate assignment such as certain available retransmission rules, etc.
Hence, the final allocation result is communicated via the output interface to an individual transmitter in a transmission network or is first transmitted to a base station 210 of
For the update of the dual variables, the following is proposed
where α* is the solution to the following optimization problem:
The problem is to maximize a twice differentiable concave function over a simple constraint set, for which very fast and efficient algorithms exist. The Primal-Dual Algorithm with the new update mechanism is summarized in
The main contribution of the novel dual update method are:
Embodiments comprise a concept for updating dual variables in algorithms aiming at maximizing some utility function in a communications system with multiple users, comprising the solution of a utility maximization program assuming a piece wise linear approximation of the rate region, and further comprising the element wise inversion of the resulting user rates.
The present invention comprises an iterative execution of the dual variable update rule to improve the quality of the piece wise linear approximation of the rate region. The utility function is done in accordance with a proportional fair rate allocation. Furthermore, the invention is applied to a communication system, where the base stations are cooperating and where base stations and mobile nodes have multiple antennas.
Finding an efficient proportional fair rate assignment for a multi-user system is cast by the utility maximization problem
This problem is solved by dual decomposition, where the dual function d(λ) is
As UP is a convex optimization problem, that attains its maximum, the dual problem has the same optimal value U*D=U*P. The dual problem UD is
which is equivalent to
as a closed convex set can be characterized as the intersection of closed half-spaces. In general the number of halfspaces needed to fully describe R is infinite which prohibits to solve UD directly. One can therefore adopt Algorithm 1 and in each iteration one can formulate an alternative problem,
that works with a finite set of points {c*0, . . . , c*i}, which are obtained from the weighted sum-rate optimization problem c*m=argmaxcεR{λmTc} solved in each iteration. Clearly the optimum of AP is a lower bound on the optimum of problem UP, which has less degrees of freedom. In the following it is mathematically proved that iteratively using the optimizers of AP as update of the dual variables tightens the bound until eventually A*P(i)=U*D=U*P, or D=U*P−A*P(i)<ε which is an ε−optimal solution.
Solution to the Approximation Problem
In this section it is discussed how to compute the solution of A*p(i), which is a convex optimization problem. The Lagrangian Function is
Proposition 1: The dual function θ(α), which is the minimum of the Lagrangian Function for a given dual variable α, is given by
Explanation: As z is unconstrained one can make it arbitrary small and therefore θ(α)=−∞unless Σm=1mα≠1. In this case,
and from
Plugging this into Equation (1) one can conclude that in case Σm=1mα=1,
From Proposition 1 one can conclude that the dual problem AD(i),
is equivalent to the following problem
The problem means to find the convex combination of the rate points, c1, . . . , Ci, that maximizes the proportional fairness utility. Plugging the solution a* of AD (i) into Equation (2), leads to proposed update rule. Finally, it is possible to prove that the algorithm strictly improves the utility in each iteration until it converges to the solution.
Simulation Results
The algorithm is also investigated in a larger network with the fractional reuse scheme. The subgradient, ellipsoid, and cutting-plane algorithm are not applicable for this scenario as the number of iterations becomes too high (1,000-1,000,000).
Subsequently, the algorithm illustrated in
Now, as illustrated in
Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus.
Depending on certain implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be performed using a digital or non-transitory storage medium, for example a floppy disk, a DVD, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed.
Some embodiments according to the invention comprise a non-transitory data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.
Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier.
Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.
In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.
A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein.
A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet.
A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein.
A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.
In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are performed by any hardware apparatus.
While this invention has been described in terms of several advantageous embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.
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