Efficient mapping of voice calls in wireless OFDMA systems

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Efficient mapping of voice calls in wireless OFDMA systems Yehuda Ben-Shimol, Eldad Chai and Itzik Kitroser

Abstract— We address the problem of efficient resource allocation and its description for constant bitrate traffic (e.g., voice calls) in wireless OFDMA systems. In such systems resources are allocated to users in a two-dimensional map. The representations of the allocated resources have to be broadcast, thus generating a substantial amount of overhead transmission. Here we present an efficient mapping and allocation representation algorithm that increase the total resource utilization by reducing the mapping overhead of the uplink frame for constant bitrate voice sessions. We use the IEEE802.16 standard for a system model and investigate by simulation the performance of the proposed solution. The results show that the required overhead can be reduced greatly.

Index Terms WiMAX, Efficient Mapping, Resource Allocation I. I NTRODUCTION We consider the problem of efficient mapping and allocation representation in Orthogonal Frequency Division Multiple Access (OFDMA) based systems. The OFDMA modulation technique presents a two dimensional allocation scheme where each resource is a two dimensional entity having both time symbol space and sub-channel space (where each sub-channel is comprised of a set of sub-carriers). Resources are allocated by the base station (BS), according to subscriber stations (SSs) requirements in fixed time intervals called frames. The allocation process is called mapping and is applied by using a mapping algorithm. Each allocation is represented in an allocation map which is broadcasted to all SSs at the beginning of the frame. The information contained in the maps is crucial for system operation, therefore they are usually transmitted with low modulation and repetition coding. This usually generates a substantial overhead in each frame, namely the mapping overhead. IEEE802.16 based systems are examples of such implementation [1]. There is a strong motivation to increase system throughput by decreasing the size of the allocation maps. However, the map size is dependant on the number of served SSs, traffic characteristics and the mapping algorithm. We focus on the allocation maps for resources used to transmit data from the SSs to the BS noted as uplink (UL) resources. The allocation map for UL resources is noted as the uplink map (ULMAP) [1]. In order to reduce the size of the UL-MAP, less information concerning resource allocations should be sent to the served set of SSs. We achieve this by differentiating between variable and constant bitrate (CBR) traffic types. A CBR session, for example a voice session, generates packets of identical size in fixed time intervals, hence allowing the BS to know in advance the SS’s resource requirements (e.g., UGS allocation mode in [1]). For the set of CBR sessions, each SS

receives a fixed set of resources within each frame (namely, fixed allocation) for UL data during a session. This enables the BS to notify an SS of its allocation only at the beginning of the session and, whenever the allocation changes, eliminating almost all mapping overheads. To the best of the authors knowledge, this letter is the first research on resource allocation in OFDMA systems in the sub-channel variant from the perspective of minimizing the map size. The algorithm presented here shows that a considerable amount of overhead can be saved without any effect on the efficiency of the mapping algorithm. We show stable performance under high traffic load and high repetition rate. We compare the mapping overhead resulting from our algorithm to that which is enforced by the technique given in the standard [1] showing substantial improvements under identical conditions of served calls and the mapping algorithm in use. In Section II we present the system model and the objective. Section III presents our mapping and allocation representation approach and the algorithm used to solve the problem. Section IV presents the simulation model and its results. Section V presents our conclusions and directions future for research. II. S YSTEM M ODEL A. Notations and Definitions We consider an OFDMA UL mapper with a set of resources to be allocated. Our resources are OFDMA sub-channels and time symbols, where each combination of sub-channel and time symbol is called a slot. We look at this configuration as an M × N resource table, where M is the number of sub-channels and N is the number of OFDMA time symbols, together forming M × N allocatable slots each having indices i and j for the corresponding sub-channel and time symbol. Allocations take place in fixed time intervals called frames, each forming an M × N allocation table. The allocation table is noted A[k], where k is the frame index. A call request r arriving at frame index tr is characterized by the number of slots required for each transmission, Nr ∈ N, its duration dr (expressed in terms of number of frames) and the time period between successive packets. An allocation instance for a request r is a set of allocated slots in A[k], S kr = {si,j }, holding |S kr | ≥ N r , for some k ∈ {tr + ∆, tr + dr + ∆}, and ∆ ∈ N is the delay until the first allocation instance is performed. An allocation for a request r is a set of allocation instances, Sr = {Srk1 , Srk2 , ..., Srkl } for all relevant A[ki ]. An allocation set is a set of all allocation instances P for some frame A[k], S k = {Sik |Sik ∈ Si }, and |S k | = S k ∈S k |Sik |. i An allocation map M [k] associated with the allocation table

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A[k] is the mapping of S k , where mkr ∈ M [k] is the mapping of Srk ∈ S k . A cost for an allocation COSTr,ki in frame A[ki ] is defined as COSTr,ki = |mkr i | (1)

known to be NP-hard. Therefore any algorithm that solves the off-line problem is also NP-hard since it solves the three dimensional strip packing problem.

The mapping overhead of request r is quantified by l P COSTr,ki . The effective area for frame A[k] (noted as

At each frame, sessions having a former allocation use the same set of slots unless notified otherwise in the UL-MAP. Define a forward scan (F-SCAN) as a scan of the resources table from left to right and bottom to top, and reverse scan (R-SCAN) as a scan from right to left and top to bottom. We use the term “hole” to describe sets of successive slots in the EA[k] which are not allocated to any voice session. F-SCAN is used to find all holes, and during this scan, each hole found is assigned to a new request requiring resources equal to hole size. If there is no such request(within the FSCAN), R-SCAN is used to find the allocations that are above the hole and are identical in size with the current hole. The first allocation meeting this criterion is then re-allocated to the hole, and R-SCAN terminated and F-SCAN resumed. If a hole is not assigned a matching request, F-SCAN is terminated and allocations are compacted to eliminate remaining holes (if any). The reason that allocations are compacted in each frame with no relation to the total size of holes is that holding time for voice session is relatively long compared to frame time, usually minutes againts several milliseconds. This suggests that a certain mapping will remain unchanged for long periods, during which holes not eliminated create more overhead than the overhead required by the compacting procedure. Therefore a one time overhead due to compacting is preferred. At the end of the compacting phase, remaining unassigned new requests are then allocated resources sequentially, starting with the first unallocated slot. The rest of the allocation table can then be used by another mapping algorithm for the other traffic types without any change in efficiency or complexity, but this is not of the concern the current work. Basic allocation algorithms for non CBR traffic can be found in [3]. Allocations in the UL-MAP are described by a slot offset and the number of allocated slots, as defined in [1]. In our scheme only new or updated allocations are described in the UL-MAP. Thus, it is clear that even in the worst case scenario, the proposed algorithm will not create more mapping overhead than the standard mapper and will not exceed the UL-MAP size basic mapper. From the above discussion one concludes that η ≤ 1 in Equation 2.

i=1

EA[k]) for a given allocation set is defined as the sum of |S k | and the empty resources that became unusable for allocation by the mapping algorithm. B. The Objective Given allocation tables A[k], k = 0, 1, 2, ..., K, and a series of requests R = {r1 , r2 , ..., rl }, find a set of non overlapped allocations S = {S1 , S2 , ..., Sl } (i.e., Sik ∩ Sjk = ∅, ∀i 6= j), such that the mapping overhead is minimized. III. T HE M APPING A LGORITHM In the standard mapping scheme ([1]) each allocation is represented by an entry of identical size in the map. In the standard scheme, slots are indexed from the lowest numbered sub-channel and the first OFDMA symbol up to the last. When the last OFDMA symbol is reached, the indexing continues from the next sub-channel and the first OFDMA symbol. At each frame SSs are allocated a successive set of slots (considering their index). Each allocation is represented in the UL-MAP by the slot offset and the number of slots in the allocation. We note the overhead of this standard scheme as the Standard Mapping Overhead. We propose extending the standard mapping scheme to support semi-fixed resource allocations. Only a single CBR traffic type is considered. Our main approach is to assign a set of slots to new sessions and to change that set the minimum number of times. Ongoing sessions always use the last allocation they have been notified about, unless a new allocation is explicitly given in the UL-MAP. Thus, the ULMAP is reduced in size for any allocation sets that do not change. It should be emphasized that mapping CBR traffic does not interfere with the mapping of other traffic types since a different allocation space is used for non-CBR traffic. We evaluate the performance of the mapping algorithm with η=

Algorithm Overhead Standard Mapping Overhead

(2)

Expression 2 compares the total mapping overhead of the proposed algorithm and the basic mapping scheme. For each frame η < 1 if our algorithm uses less resources and η > 1 otherwise. The effective area of any optimal mapping algorithm is equal to |S k |. The proposed algorithm is designed to maintain this property, thus the effective area is not relevant for the performance measure given in Expression 2. The fact that the packet size for each session is constant and each allocation is a successive set of slots allows us to model the off-line problem as a three dimensional strip packing problem where item fragmentation (with a certain cost) is allowed [2]. The three dimensional strip packing problem can be reduced to the one dimensional strip packing which is

The Algorithm

A. System Model

IV. S IMULATION

We use the OFDMA frame model presented in [1] to model the UL frame and estimate the overhead. The system uses 70 sub-channels and 10ms frame length. The UL frame time was set to 5ms and each OFDMA symbol time is 190µs. We consider the unsolicited grant service (UGS) as presented in [1]. Each SS generates a load of 0.1 Erlang where the average holding time is three minutes. This specific user model is commonly used for performance evaluation of practical wireless systems. Each SS uses a G.729 vocoder [4] that generates a load of 40 bytes every 10ms (including headers). The modulations and coding rates simulated are QPSK with

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B. Simulation Results Our simulations show that a great deal of overhead can be avoided by using the proposed mapping and allocation representation techniques. Figure 1 shows the mapping overhead generated by both mapping schemes for each frame. The system load was generated by 260 registered users and each map is transmitted twice. One can see that, significantly, substantially less resources are required when using our algorithm in most cases. Moreover, the mapping overhead of our algorithm is always less than the overhead generated by the mapping scheme used in the standard (i.e., in Equation 2, η < 1). Mapping Overhead Standard Mapping Overhead @SlotsD

40

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10 Our 0 50000

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Fig. 1. Mapping overhead per frame for traffic generated by 260 users and map repetition = 2

Figure 2 shows that on average our algorithm uses less resources. The average number of slots used by our algorithm is less by about 15 slots. This implies that the excess resources saved by our algorithm can be used to serve additional voice calls or data streams. This difference is linearly proportional to the map repetition rate. The standard [1] allows several repetition rates. Figure 3 displays the percentage of the long-time average of the total resources (i.e., the sum of mapping overhead and actual allocated slots for the voice calls) occupied by our algorithm compared with the standard mapping scheme for a varying number of users. The results show that the traffic load has no significant effect on the relative total allocation table occupancy. With no repetition our algorithm uses only ∼ 84% of the standard mapping representation. With two map repetitions the relative occupancy decreases to ∼ 73%, improving to 61% and 53% for 4 and 6 repetitions, respectively.

Average Mapping Overhead

Mapping Overhead @SlotsD

17.5 Standard

15 12.5 10 7.5 5 2.5

Our

0 50000

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Fig. 2. Average mapping overhead for traffic generated by 260 users and map repetition = 2 Relative resource usage

90 Relative Resource Usage @%D

coding rates 1/2 or 3/4, 16-QAM with coding rates 1/2 or 3/4, or 64-QAM with coding rates 2/3 or 3/4, respectively. The modulations and coding rates for each SS are derived from a uniform distribution and remain fixed throughout the session. The number of bits per slot for each SS is calculated from multiplying the modulation rate with the coding rate and the number of sub carriers in each time symbol. The modulation rates are 2, 4 and 6 for QPSK, 16-QAM and 64QAM modulations respectively. The number of sub-carriers in a time symbol is set at 48. The UL-MAP header has 18 bytes of data and each allocation represented requires 4 bytes of data. We simulated 180 minutes of traffic for several scenarios with varying number of users and different number of repetitions of the UL-MAP. To ensure statistics stability only the last 30 minutes were used.

No Repetition

80 Repetition 2

70 Repetition 4

60 Repetition 6

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Fig. 3. Relative resources occupancy for different number of users and different repetitions

V. C ONCLUSIONS AND F UTURE R ESEARCH We showed that discriminating between the voice and other traffic types is beneficial due to the specific characteristics of voice calls. We present a new algorithm for mapping and allocation representation that takes advantage of these characteristics. This algorithm uses semi-fixed resource allocations to reduce the UL-MAP size. We have shown that using this algorithm saves a substantial amount of resources that can be used to increase the system’s throughput, a saving of up to 47% when high repetition is used, and allowing the saved resources to be used for other needs. This infers that under the same user behavior model, a system using the proposed mapping algorithm would be able to double the number of served voice calls. The inclusion of our algorithm in existing OFDMA standards would require a minor change in the way that BS and SS work, inferring that this work is prospective and would increase the potential applicability of wireless OFDMA systems in the near future. An addendum to the standard based on the present work will be submitted soon. On-going research is directed to the applicability of the proposed mapping and allocation representation techniques to other traffic types with several vocoder types, and mobility. R EFERENCES [1] 802.16: IEEE Standard for Local and metropolitan area networks Part 16: AirInterface for Fixed Broadband Wireless Access Systems, 2004. [2] F. K. Miyazawa and Y. Wakabayashi, “An algorithm for the threedimensional packing problem with asymptotic performance analysis", Algorithmica, Vol. 18,pp. 122–144, 1997. [3] Y. Ben-Shimol, I. Kitroser and Y. Dinitz, “Two Dimensional Mapping for Wireless OFDMA Systems," IEEE Transactions on Broadcasting (To be published). [4] Coding of Speech at 8 kb/s using Conjugate-Structure Algebraic Code-excited Linear Predictive Coding, ITU-T Draft Recommendation G.729, (1995).