Analytical average throughput and delay estimations for LTE uplink cell edge users

Abstract

Estimating average throughput and packet transmission delay for worst case scenario (cell edge users) is crucial for LTE cell planners in order to preserve strict QoS for delay sensitive applications. Cell planning techniques emphasize mostly on cell range (coverage) and throughput predictions but not on delay. Cell edge users mostly suffer from throughput reduction due to bad coverage and consequently unexpected uplink transmission delays. To estimate cell edge throughput a common practice on international literature is the use of simulation results. However simulations are never accurate since MAC scheduler is a vendor specific software implementation and not 3GPP explicitly specified. This paper skips simulations and proposes an IP transmission delay and average throughput analytical estimation using mathematical modeling based on probability delay analysis, thus offering to cell planners a useful tool for analytical estimation of uplink average IP transmission.

Introduction

Nowadays IP based multi-service wireless cellular networks mobile handsets are requesting reliable data transmission from QoS perspective point of view [1], [2], [3], [4]. In 3GPP standards four negotiated QoS profiles are defined based on four existing QoS classes [3]. These QoS classes define specific attributes related to traffic integrity which QoS profiles should include, which among others are mean and peak throughputs, precedence, delivery delay and Service Data Units (SDU) error ratio [3]. A new generation of wireless cellular network since 2010, called Enhanced UTRAN (E-UTRAN) or Long Term Evolution (LTE) workgroup of 3GPP, has been evolved providing advantages to services and users [4], [5]. LTE requirements, compared to previous mobile broadband networks (HSPA, 3G), pose strong demands on throughput and latency, requesting new multiple access techniques over air interface and simplified network architecture [6], [7]. Using OFDM/SC-FDMA technology a minimum group of 12 sub-carriers of total 180 kHz bandwidth is known as Resource Block (RB). In a frequency-time domain resource grid a Schedule Block (SB), a unit of resource allocated by MAC scheduler, is defined as a resource unit of total 180 kHz bandwidth (12 sub-carriers of 15 kHz each) in the frequency domain and 1ms sub-frame duration (known also as Transmission Time Interval (TTI)) in time domain.

From cell planning perspective uplink is always the weakest link in the power-link budget and throughput analysis, for both outdoor and indoor to outdoor coverage. MAC scheduler, residing in eNodeB, is responsible for dynamically allocating uplink/downlink resources [8]. The primary goal of uplink scheduler is the ability to allocate an appropriate amount of consecutive resources in the SC-FDMA with the appropriate transport format, modulation to appropriately map symbols to bits and coding to protect data and transmitted power per TTI. The secondary goal of scheduler functionality is to appropriately manage the transmission of uplink SB among neighbor cells to suppress as much as possible the inter-cell interference (ICI). Mobile operators face quite often QoS problems in case of bad coverage (coverage limited environment) or interference (Interference limited environment), due to low scheduling decisions of the uplink scheduler. A lot of research has been performed on international literature regarding ICI and scheduling decisions focusing on throughput estimations and coverage cell range probabilities. In [9] authors performed a survey of the Inter Cell Interference Cancellation (ICIC) 3GPP feature [10] for interference coordination on LTE MAC scheduler. Interference coordination has also been proposed on [11] where network planning issues have been considered together with remote radio head by the authors. Resource allocation on LTE uplink has been also extensively studied on international literature so far in conjunction with throughput performance and expected delay of service. To analyse allocation of resources is not easy since MAC scheduler functionality is not standardized by 3GPP; it is rather left on vendor (Ericsson, Nokia, HUAWEI, etc.) implementations trying to make more efficient use of available resources for good coverage users. 3GPP describes only the general procedures for scheduling functionality and standardizes three functional blocks to be implemented, Scheduler block, Signal to Interference and Noise Ratio (SINR) estimation block and Link Adaptation block. Uplink Scheduler block and SINR block exist in eNodeb; however for uplink transmission Link Adaptation block is implemented on user equipment (UE). In order to depict the MAC functionality from vendor specific solutions, system simulations or drive tests are extensively used on papers in international literature. Indeed authors in [12] proposed a new resource allocation method well-suited for the uplink scenario of LTE allocating frequency spectrum among cell users with the goal of maximizing the system’s overall throughput. In [13] authors used power and packet delay as two important metrics to propose an innovative resource allocation technique for LTE uplink. Authors in [14] proposed a new resource allocation scheme based on the knowledge of buffer statuses and channel conditions to reduce the waste of system resources and improve the aggregate throughput. Although all these research papers have been considering MAC functionality, their proposals are validated based on general or public simulators which do not depict reality since the vendor specific MAC software implementation is not public released.

A major metric, not considered so far on international literature, is the evaluation of overall IP packet transmission delay as a function of scheduler resource allocation decisions and channel conditions. Prediction evaluation is considered to be split into three distinct delay contributions:

• N, number of allocated SB from uplink scheduler: The number of allocated SB is directly related to throughput or in other words to packet delay. This delay is also affected by the selected spatial multiplexing mode (MIMO or Transmission diversity), number of expected retransmissions, size of IP service packets and the selected MAC packet size. Many research papers exist in international literature using either theoretical simulations or analytical probabilistic models trying to combine packet delay and resource allocation principles. In [15] a semi-analytical macroscopic probabilistic model has been proposed trying to capture channel conditions and MAC resource allocations for different cell load conditions. In [16] authors try to analytically model expected interference and expected channel conditions and combine it with MAC scheduler decisions and throughput. End-to-end QoS performance of Bandwidth and QoS Aware (BQA) scheduler for LTE uplink, together with delay sensitive traffic thresholds, is evaluated in heterogeneous traffic environment in [17]. A very good approach has been proposed on [18] where packet delays may be deduced from buffer status reports (BSR) from UE’s in LTE uplink. However these delays have not been directly correlated to the expected throughput conditions neither the MAC scheduler IP buffering. Although all aforementioned papers have studied the expected number of resources allocated from MAC decisions they do not consider the reality since allocation of resources from MAC scheduler is vendor specific and only vendor official simulators [19] or drive tests could depict the reality; consequently there is not much work on such a topic on international literature. One important such drive test reference is on [20] which will be used later on the mathematical analysis.

• n, Scheduler decision: Second expected transmission delay contribution relies on the fact that MAC scheduler never schedules each UE every TTI = 1 ms due to capacity reasons, QoS service priority issues and finally due to Channel Quality Index (CQI) reports per UE radio channel conditions; hence an inherent delay has to be considered in the total delay calculation. Again this is vendor specific and any analytical estimation has to rely either on public simulators or analytical mathematical modeling. Few papers exist on international literature. One very good research paper is [21] where authors have derived a mathematical model for delay estimations. An oldest approach [22] indicates also an innovative algorithm to consider end-to-end delay constraints on MAC scheduler decisions.

• Π₀, UE transmission buffer delay: Third expected transmission delay contribution is the buffer delay on UE transmission buffer due to QoS class identifier (QCI) scheduling core network priorities. This is a topic considered in seldom in other papers in international literature; however its contribution to transmission delay calculations is vital.

All aforementioned research papers never combine predicted delays with cell planning principles and constraints and most of predicted results are generated from public LTE simulators not following vendor specific solutions; thus estimations are not accurate for specific network equipments. This paper proposes an analytical mathematical model to predict buffer delay as an integral part of overall packet transmission delay estimation; uplink delay is considered as a cell planning constraint, according to 3GPP QoS restrictions, realizing a very interesting metric for operators to understand how the cell planning and coverage conditions affect the uplink packet transmission delays [15]. Moreover average transmission uplink throughput is predicted to be considered as analytical tool for cell planning algorithm.

Rest of the paper is organized as follows. On Section 2 an analytical mathematical model, using one Lemma and one important Theorem, is proposed calculating the probability of n packets existing in the system either in scheduled blocks or in the transmission buffer. On Section 3 an explicit calculation for non-delay probability on UE buffer is proposed and a mathematical Theorem is also stated. On Section 4 an overall uplink average IP throughput formula, considering uplink air interface transmission delay as input, is proposed for cell planning analytical predictions. Applications on cell planning and parameter justifications are analytically presented on Section 5 and final conclusions on Section 6. Finally on Appendix A, Appendix B formal mathematical proofs on delay probabilities for Lemma and Theorems of Sections 2 IP packet probability modeling, 3 Non-delay probability estimation are explicitly provided.