RESOURCE ELEMENT-LEVEL DIMENSIONING OF LONG TERM EVOLUTION NETWORKS

Long Term Evolution (LTE) of Universal Mobile Telecommunications System (UMTS) is the latest cellular technology coined by the third Generation Partnership Project (3GPP) and is currently being deployed worldwide. a crucial step towards the successful deployment scenarios of LTE networks is through the use of accurate budgetary and coverage dimensioning formulas of LTE’s physical air-interface channels and signals to guarantee favourable cell footprint and other capacity targets. In this paper, the total physical downlink resources along with their associated powers are derived and computed. Their corresponding overheads are also presented. The provided formulas serve in various network dimensioning campaigns of the LTE systems.


INTRODUCTION
After being ratifi ed by the International Telecommunication Union (ITU) as the fourth generation (4G) technology, The 3 rd Generation Partnership Project (3GPP) long term evolution of Universal Mobile Telecommunications System (UMTS) 1 (Kattan, 2009) has broken all records as the fastest cellular technology being embraced and deployed worldwide (The Global mobile Suppliers Association (GSA), 2011a, 2011b, 2011c, 2011d). 1 LTE is also referred to as Evolved UMTS Terrestrial Radio Access Network (E-UTRAN) Based on the specifi cations (3GPP TS 25.942, 2008;3GPP TS 36.211, 2007;3GPP TS 36.300, 2006;3GPP TS 36.410, 2010), LTE air-interface gives rise to large transmission bandwidths of 1.4 MHz up to 20 MHz in which several physical common 2 control channels, synchronization and pilot signals are transmitted and received along with user data. Similar to UMTS (3GPP TS 25.211, 2002;3GPP TS 25.221, 2002), these channels and signals profoundly decide cell coverage and capacity targets. Nevertheless, owing to LTE-to-UMTS bandwidth and data rate ratios, their overhead and power requirements are quite different from those of UMTS, i.e. they have larger powers, and therefore precise dimensioning of the channels and signals becomes extremely imperative and decisive for effi cient intake of cell power and physical resources as well as controlled coverage and capacity targets.
Notably, the physical layer resources and its corresponding overhead analysis are poorly covered in the standard (3GPP TS 36.211, 2007). Nonetheless, dimensioning of downlink physical channels and signals are neither suffi ciently nor effi ciently covered.
The objective of this manuscript is to address these limitations in the standard in the related literature by proposing accurate formulas for the calculations of downlink channels and signal resource elements numbers of an LTE evolved Node-B (eNodeB), their associated overhead and their corresponding power intakes before and after reception. Furthermore, to accurately account for the various clutter types and variable cell range, an improved propagation model is proposed for the modelling of physical channels received powers. The fi nding of this work can thus be effi ciently used to bolster up cell coverage and capacity campaigns for a wide range of transmission possibilities.

RELATED WORK
This section aims at leveraging reader's insights on latest research activities, and specifi cally, the ways they are employed to characterize and model physical cell resources in OFDMA-centric systems particularly in LTE networks.
At the heart of any eNodeB, the physical layer and air-interface schemes and their corresponding control channels and signals (RS, PBCH, SS, PDCCH, and PDSCH) are the main drivers of the whole transmission process and thus, are the controllers of coverage, capacity and actual cell throughput in LTE (3GPP TS 36.211, 2007). They are therefore, the key elements in many decisive LTE dimensioning processes.
For these reasons and many others, there has been a wave of research activities dedicated to the design and characterization of LTE's PHY layer channels and signals.
Unfortunately, the 3GPP does not provide a complete modelling procedures of the LTE's frame structure and its built-in control channels (3GPP, 2007;3GPP, 2008). A natural extension of this shortage is a wide spectrum of inputs from the literature fi lling in the gaps left by the standard.
Accordingly, the authors, Ball, Hindelang and Kambourov (2008) provided brilliant design and performance comparisons between LTE and its rival WiMAX. After exposing a complete picture of the PHY layer channels and signals of both technologies, they illustrated that the overall radio performance of both systems is similar, with LTE slightly outperforming WiMAX. The authors albeit their in-depth treatment, provided no models to account for the channels resource utilization or inputs pertaining to channel overhead except for Reference signal (RS) and Physical Download Control Channel (PDCCH). In the same context, the work by Cui (2009) validated the results in the standard and went beyond the theory of LTE by concluding that the new protocol's practical DL/UL data rates are only (257/41) Mbps, as opposed to (300/71) Mbps in theory, provided that of 20 mhz of bandwidth with 4x4 mimo antenna confi gurations are used. This paper does not include resource elements calculations, and the simulated system was limited to FDDmode only.
In contrast to Cui (2009), the investigation by Rezaei, Hempel and Sharif (2011) revealed that LTE's (Rel.8.0) DL-to-UL speed is (300-to-75) Mbps. The results were collected by the modelling and simulation of LTE-PHY layer system operating in both FDD and TDD modes. The study, however, is shortened by the lack of control of channels overhead.
Similarly, the fi ndings of Basit (2009), Ratasuk, Ghosh, Love, Nory andClasson (2008), Rezaei (2010), Sanchez, Morales-Jimenez, Gomez and Enbrambasaguas (2007) are of similar nature. They provided some insights into some theoretical performance metrics of LTE. Nevertheless, apart from the impractical assumptions they relied on in their studies, the provision of no analytical models of calculating resource elements and overheads were the common features noted in these studies. Figure 1 depicts A Long Term Evolution (LTE) signal fl ow diagram in which the physical download resources along with their associated phases of transmission and reception are proposed. Interestingly, the methodology employed can BE basically broken down into the following:


The transmission power of LTE frame resource element is calculated fi rst. This power is determined in line with the transmission power of LTE base station antenna port;  Matlab ® programming language is used as the simulation tool, where the parameters in Table 1 along with formulas in section 4, 5 and 6 are used together to determine the LTE downlink signals and channel powers.
Interestingly, three mediums have been defi ned in Figure 1: transmitter, transmission medium and receiver. The diagram is further subdivided using points A-to-S, which include various factors affecting the transmission and reception of the LTE downlink frame (together with its signals and channels). In this regard, several Matlab ® simulation runs are performed to evaluate the performance of an LTE eNodeB. Effects of the common channels and signals overhead on traffi c channels and the use of multiple transmission antenna ports at the base station for various channel bandwidths are investigated together.

RESOURCE ELEMENT TRANSMISSION POWER
An LTE eNodeB transmits power that is shared equally by all antenna transmission ports. the Antenna port power is then used to feed the transmission of a frame by sharing its power with all physical downlink resource elements. Analytically, the following holds true for any number of antenna ports supported by an eNodeB: (1) Where P ant is the antenna port maximum transmit power in Watt, P eNodeB is the maximum transmit power of an eNodeB in Watt and N ant is the number of antenna ports supported by the same cell. In LTE release 8.0, which is currently being deployed worldwide, P ant is equally divided over frame resource elements: ( Where P re is the power of a single resource element, P ant is found in Eq.(1), and is the total number of RE(s) in a frame and is expressed as follows: ( Where 12 is the number of subcarriers in one timeslot, 20 is the number of timeslots per one frame, is the number of OFDM symbols in one timeslot, which is 7 or 6 for normal or extended cyclic prefi x, respectively, N RB is

LTE PHYSICAL DOWNLINK CHANNELS AND SIGNALS POWERS
This section embarks on the formulation of physical downlink channels and signals powers, as illustrated in Figure 1. The objective here is to derive power formulas that are applicable to any Frequency Division Multiplexing (FDD) type of frame in any LTE system and for a wide range of system-specifi c parameters. interestingly, the same formulas can be used for the time division multiplexing (TDD) type of frame; however, some additional frame-type constraints found in 3gpp ts 36.211 (2007) have to be respected. To end of this work, Figure 2 is employed in which two major phases, namely, points a and s are used for demonstration purposes. These phases, i.e. a and s, correspond to transmission and reception respectively.

Power at point A
Point A is the point where the resource elements are assigned to their perspective physical channels and signals, i.e. They are powered up. However, at this point no signal attenuation is undergone as shown in Figure 2.
Power models of physical channels and signals at point A are as follows: a) Downlink Reference Signals At point A in Figure 2, reference signal (RS) power is the power of RS prior to any loss. This power (in Watt) can be expressed as follows: (4) Where P re is the resource element power (in Watt) as found in Eq. (2), and is the number of reference signals used and silent resource elements, respectively in one frame and are found as follows: In one timeslot, there are 4 used reference signals resource elements for 1 and 2 transmit antenna ports respectively, and 6 RE(s) for the case of 4 ports. However, unlike used resource elements, there are 0, 4 or 8 silent ones for 1, 2 or 4 antenna ports respectively. For per frame, this gives: The mapping of the Primary Synchronization Signals (PSS) and Secondary Synchronization Signals (SSS) resource elements is bandwidth-independent as they are only transmitted through the middle six resource blocks. Accordingly, the number of resource elements per each synchronization signal is 144, which gives a total of 288 for both synch signals. The power (in linear units) of synchronization signals (SS) is thus: Where P re is the power (W) of single resource element, as found in Eq. (2).

c) Physical Broadcast Channel
The Physical Broadcast Channel (PBCH) takes up 4 OFDM symbols in the second timeslot of the fi rst downlink subframe, i.e. subframe #0 in Figure 1. Additionally, PBCH resource elements overlap with those of reference signals and therefore have to be deducted as below: Where 288 is the number of PBCH resource elements in a frame and Y denotes the number of RS overlapped resource elements, that is 12, 24 or 48 for antenna ports number of 1, 2 or 4 respectively. Accordingly, SS power is defi ned (in W) as:

d) Physical Downlink Control Channel
The Physical Downlink Control Channel (PDCCH), Physical Hybrid ARQ Indicator Channel (PHICH) and Physical Control Format Indicator Channel (PCFICH) together set up the control region in a frame and are mapped into one, two or three symbols of the fi rst timeslot of any subframe. Like some other physical signals and channels, the control channels resource elements overlap with reference signals resource elements and thus have to be subtracted.
Having known that, the following expression defi nes the number of resource elements used by the control region:

N s y m K N
Where is the number of resource elements taken up by control region, 12 represents the 12 subcarriers of a resource block, sym is the number of symbols occupied by the control region in one timeslot, K represents/indicates the number of RS resource elements that overlap in the control region. It is thus: K= 2 (when 1 antenna port is confi gured), K= 4 (when 2 antenna ports are confi gured), K= 4 (when 4 antenna ports are confi gured and sym= 1), K= 8 (when 4 antenna ports are confi gured and sym= 2 or 3), N RB is the number of resource blocks per a frame (6 to 100) for 1.4 MHZ to 20 MHz, respectively and 10 is the number of subframes in one frame. From Eq.
Where is the number of PDSCH resource elements in one frame, as found in Eq. (3), is the total RS (used plus silent) physical resources in a frame as found in subsection 5.1(a), 244, , and are the number of physical resources of synchronization signals, PBCH and control region respectively, as defi ned by subsections 5.1-(b),(c) and (d) respectively. Therefore, the downlink shared channel power at point A is expressed as follows: (11)

Power at point S
Basically, point S is where an LTE frame is successfully received. This is considered true after the frame (including its associated physical channels and signals) has experienced a series of gains and losses across the transmissionreception path, i.e. from point A to S in Figure 2. Major gains and losses are: Where , , , and are received power levels (in dBm) of RS, SS, PBCH, control channels region and PDSCH, respectively, is the antenna gain of transmitter (Tx), is MIMO gain of Tx and equals , where N MIMO is the number of MIMO antenna terminals, PL is the pathloss between the transmitter and receiver, M is the margin of interference plus shadowing, L building is the building penetration loss, L Body is the body loss and is the antenna gain of receiver.
At this point, it is extremely important to understand the difference between the transmission antenna ports and the MIMO unit of an LTE eNodeB as they are not the same. Essentially, an antenna port is a new concept introduced G by the 3GPP to act as a logical port that does not necessarily correspond to an antenna. The objective is to relieve the pressure from the user equipment to detect beamforming-centric transmission from an eNodeB by means of assisting signals (pilots). In other words, pilots (RS) are used when MIMO is used at the eNodeB to inform the user terminal on any beamforming operations being carried out at the transmitter (eNodeB) (3GPP TS 36.211, 2007;Sesia, Toufi k, & Baker, 2011). Furthermore, MIMO denotes multiple physical antennas usage at the eNodeB. However, for MIMO to work, logical antenna ports have to work as well to impart the number of physical MIMO antennas used by means of pilot signals, i.e. RS.

PATHLOSS MODEL
The propagation or path losses PL used in Equations (12) through (16) are addressed by an enhanced Cost321-Hata model. The proposed model accounts for signal attenuation, clutter morphology, variable cell range and frequency ranges of (150-1500) MHz or (1500-2000) MHz as described in the following expression: where A and B are both constants, and their values are shown in Table 2 ( Medeisis & Kajackas, 2000): Table 2. f is the transmission frequency of the transmitter (in MHz), H TX is transmitter height (in meters), D is the distance between the transmitter and receiver (in Km), and a(h Rx ), S and L clutter are described as follows:

Values of Constants A and B
a(h Rx ) is the receiver height correction factor (in meters):

RESULTS AND DISCUSSIONS
Based on the proposed methodology, this section provides the research analytical results that show the impact of overheads as well as individual transmission and reception powers of each considered physical download signal and channels. Figure 3 depicts the amount of overhead imposed by common channels and signals on shared (traffi c) channels when 1.4 MHz bandwidth is employed by an LTE transmitter, i.e. eNodeB. Clearly, the physical resources (resource elements) taken up by shared channels (PDSCH) are the highest in population among all channels and signals. However, payload carriers are inevitably disrupted to a certain extent, by control channels resource elements that affect negatively the number of user data carriers. From the perspective of synchronization signals and broadcast channels, their corresponding overhead is highly comparable and appears to be the smallest among all other common channels and signals due to their limited physical resources consumption that is constant for SS over any bandwidth and slightly less for PBCH due to the overlap with reference signals resource elements.

Common channels and signals overhead
For the same number of antenna ports and sym, the control region overhead is remarkably the same, thus being bounded by the amount of overlap with RS resources and control region width, i.e. sym in Eq.(8). Similarly, RS overhead remains unchanged for the same number of antenna ports. However, the peculiarity of RS's silent resource elements gives rise to extra overhead, as seen in Figure 2.
Lastly, the effect of the higher number of antenna ports at the transmitter on the amount of overhead imposed by common channels and signals on useful user data is illustrated in Figure 4 whereby the higher the number of antenna ports used, the greater the amount of overhead. Moreover, the smaller the bandwidth (RBs), the more serious impact the overhead imposes.

Common Channels and Signal Powers
The power transmitted by the eNodeB of inputs and propagation conditions shown in Table 2 is calculated with respect to various antenna ports numbers, as illustrated in Figure 5. Based on the above, the received power corresponding to each control channel and signal is determined as depicted in Figure 5. Under the same propagation circumstances and for 1.4 MHz system bandwidth, channels and signals transmitted and received, powers tend to decrease linearly with the increased number of antenna ports. This is essential because the corresponding antenna port power signifi cantly decreases in the order of 40, 20 and 10 W for 1, 2 and 4 antenna ports respectively, due to the power sharing scheme. However, the RS signals shows an exceptional increase in their received powers as the antenna ports increase in number due to the added MIMO gain. Ultimately, the power allocation among subcarriers means that if the coverage is restricted by the transmitted power, the operator should increase the output power or decrease the channel bandwidth.

CONCLUSION
In view of the whole new bandwidth-agnostic 4G networks in general and LTE systems in particular, the link budget, capacity and coverage dimensioning calculations of such networks turn to be more intricate than that of legacy systems due to the peculiarities the LTE physical channels and signals possess during transmission and reception. In this paper, the resource element level computations of the LTE downlink physical layer channels and signals have been addressed in detail. The calculations proposed in this paper are quite benefi cial for low and high level dimensioning procedures of LTE networks. it has been shown in this study that the cell-specifi c reference signal (pilot) overhead depends on the number of active antenna ports. Furthermore, from the overhead and power consumption standpoint, silent reference signals resource elements do impose extra overhead on the user payload and thus consume additional power. However, from the channel estimation and transmission point of view, they don't transmit any power. Instead they lend their powers to their corresponding active or used RS resources and thus act as power boosting entities. To sum up, downlink control channels and reference signals are the most important factors affecting dimensioning and capacity results. The rest of the downlink physical channels and signals can be ignored. notably, and it is recommended that for future work, this work can be expanded to include the dimensioning methodology of LTE uplink. This, however, is different from the LTE downlink formulas in that it is involves the transmission and reception of A slightly different multiplexing scheme, i.e. SC-FDMA (Single Frequency Division Multiple Access), which in turn comprises different physical resources allocations and structures.