Chapter 4. Radio Resource Allocation using Resource Scheduling in LTE: Fourth Generation (4G) 4.1 Introduction

Transcription

1 Chapter 4 Radio Resource Allocation using Resource Scheduling in LTE: Fourth Generation (4G) 4.1 Introduction LTE is popularly called a 4G technology. It is an all-ip technology based on orthogonal requency-division multiplexing (OFDM), which is more spectrally eicient and can deliver more bits per Hertz. LTE also brings subscribers a true mobile broadband that enables a quality video experience and media mobility. It is predicted that out o approximately 2 billion people, who will be having broadband by 2012, some two third will be mobile broadband users and majority users will be served by High Speed Packet Access (HSPA) and Long Term Evolution (LTE). 3GPP LTE is the evolution o the Third-generation o mobile communications [22]. LTE is designed to increase data rates and cell edge bit rates. Radio resource management attracts great attention while utilizing available resources to provide users with enhanced system throughput. Radio resources management includes transmission power management, mobility management, and scheduling o radio resources. An intelligent radio resource management is at the heart o LTE to make it a robust technology to meet the broadband mobility needs o upcoming years. This will schedule the available resource in a best way and provide to the users with the enough transmission capability to achieve the decided QoS, even while they move reely and also will make sure that these assigned resources would not interere 88

2 with already assigned resources. Orthogonal Frequency Division Multiple Access has been adopted in emerging broadband wireless access networks such as 3GPP UMTS/LTE and IEEE x (WiMAX) due to its inherent immunity to inter-symbol intererence and scheduling lexibility in resource allocation. This lexibility allows the exploitation o requency, temporal and multiuser diversity oered by the wireless broadcast channel. By employing sophisticated multiuser scheduling algorithms, which transmit data to dierent users on avorable resources, a high system capacity can be achieved. In this chapter Dynamic Radio Resource Allocation schemes are discussed and a new scheme, Cyclic Switching Scheduling Scheme (CSSS) is designed. It perorms the probability computation on the radio resources to determine which resource can be assigned to the cell centre users and which resources can be assigned to the cell edge users. It is also conversed that how Multiuser Scheduling with adjustable airness is used or maximizing throughput. The problem o allocating resources to multiple users on the downlink o a Long Term Evolution (LTE), cellular communication system under a desired airness constraint is addressed [66]. A method or multiuser scheduling is proposed, that operates on the boundary o the achievable multiuser rate region while guaranteeing a desired long term average airness. This method is based on a sum utility maximization o the α -air utility unctions. 4.2 Overview o the 3GPP LTE Air Interace Basic concepts o 3GPP LTE Air Interace The starting point o LTE study was irst ocused on the inormation about the targets or data rate, capacity, spectrum eiciency and latency. Also commercial aspects like costs or installing and operating the network were considered. Based on these requirements, the key eatures o LTE are the usage o multiple access schemes, adaptive modulation and coding, multi antenna techniques (MIMO), hybrid automatic 89

3 repeat request (HARQ) technology and distributed or localized radio resource allocation techniques Key Technologies o the 3GPP LTE Air Interace OFDM OFDM is requency-division multiplexing scheme utilized as a digital multi-carrier modulation method that has been used successully in wire-line access applications, such as Digital Subscriber Line (DSL) modems and cable modems. Recently, wireless systems such as 3GPP LTE have also adopted OFDM-based transmissions to overcome the challenges o Non Line o Sight (NLOS) propagation because OFDM is a technology that has been shown to be well suited to the mobile radio environment or high data rate and multimedia services. For uplink and downlink, dierent transmission schemes are selected in 3GPP LTE due to certain characteristics. OFDMA has been selected or downlink (or transmission rom enodeb to UE) and SC-FDMA has been selected or uplink (rom UE to enodeb). Downlink Orthogonal Frequency Division Multiplexing Access (OFDMA) OFDM is already in use by cellular and non-cellular wireless transmissions like mobile WiMAX and WLAN. It is selected as multiplexing scheme or 3GPP LTE. OFDM is a spectral eicient transmission system which divides a high-bit-rate data stream into a number o parallel narrowband low-bit-rate data streams. It is termed as sub-carriers or tones. Division is made by using such a technique that sub-carriers are orthogonal to each other and eliminates the need o non-overlapping sub-carriers to keep away rom inter carrier intererence [67]. The irst carrier is selected so that its requency contains integer number o cycles in a symbol period. For making sub-carriers orthogonal to each other, adjacent subcarriers can be spaced by 90

4 B sc = W (4.1) L Where, B SC =Bandwidth o subcarrier W= nominal bandwidth o high-bit-rate data stream. L= number o sub-carriers Transmission on orthogonal sub-carriers is ine but only or the ideal situation such as there is no multi-path delay spread, but usually this situation does not exist in real world. To make transmission completely Inter Symbol Intererence (ISI) ree it is also needed to place a time guard in between the sub-carriers and their spacing. Making this time guard enough, larger than the maximum expected delay spread, makes transmission completely ISI ree. This time guard also cause the power and bandwidth consumption and o course reduce the spectrum eiciency but this is dependent on the time guard raction o symbol duration. Peak to Average Power Ratio (PAPR) PAPR is characterized as the peak power within one OFDM symbol normalized by the average signal power [70] [71]. When several OFDM sub-carriers align themselves in phase, there occur a large PAPR, which is the most diicult concern in radio requency engineering o traditional OFDM. The value o PAPR is directly proportional to the number o sub-carriers [72] and is given by, PAPR db ( ) 10log( L) Where L = the number o sub-carriers Signals with a large PAPR necessitate highly linear power ampliiers to avoid excessive inter modulation distortion and to achieve this linearity, ampliiers have to operate with a large back o rom their peak power which results in low power eiciency. 91

5 Uplink SC-FDMA Single Carrier Frequency Division Multiple Access (SC-FDMA) is used as 3GPP LTE uplink transmission technique (MS to enodeb). It is a customized structure o OFDMA and it has comparable throughput perormance as OFDMA [71]. Power luctuations in SC-FDMA signals are prevented by transmitting subcarriers in sequence. ISI might be caused in SC-FDMA signals with severe multipath propagation environment. The adaptive requency domain equalization is used by base station to cancel the inter symbol intererence. 4.3 LTE Architecture Figure 4.1: LTE Architecture 3GPP Evolved Packet System (EPS) ramework includes Evolved Packet Cores (EPCs) and Evolved UMTS Terrestrial Radio Access Networks (E-UTRAN) as shown in Figure 4.1. EPCs communicate with each other and with E-UTRANs. EPC contains a Mobile Management Entity (MME) and a System Architecture Evolution Gateway (SGW) together with a Packet Data Network Gateway (PDN GW). E-UTRAN solely contains Evolved Universal Terrestrial Radio Access Network Base Stations (aka enodeb or enb) where the User Equipment (UE) communicates with enb and enbs 92

6 communicate with each other and with the EPCs [79]. There is one-to-one communication between UE and enb but there is one-tomany communication among enb, MME, and SGW. Both WiMAX and the UMTS successor technology LTE use Orthogonal Frequency Division Multiplexing (OFDMA) as the core modulation technology on the air interace in downlink direction. Objectives o LTE include a radio-interace physical layer to support transmission bandwidth up to 20 MHz together with new transmission schemes and advanced multi antenna technologies. Perormance requirements o LTE are presented in Table 4.1. LTE s perspective or mobility considers optimum perormance or mobile speeds 0 15 km/h. LTE is being designed to ensure high perormance between 15 and 120 km/h and still expected to maintain mobility at speeds between 120 and 350 km/h even up to 500 km/h or some requency bands. LTE is expected to support voice and real-time service quality without interruption over entire speed range. Mobile speeds above 350 km/h are mainly or trains. Perormance criterion is uninterrupted operation below 120 km/h or vehicular and pedestrian speeds [36]. Table 4.1: LTE Perormance metrics LTE Perormance metrics Peak data Rate DL/UL:100/50 Mbps or 20Mhz Full Mobility Upto 500 km/h Latency in control/user plane < 100 ms(idle to active)/<5 MHz Capacity 200 users per cell (5 MHz) Cell sizes km Spectrum 1.25, 2.5, 5, 10, 15 and 20 MHz LTE Downlink Physical Layer overview LTE radio interace protocol architecture The LTE access network is simpliied and reduced to only the base station (enodeb) and the LTE radio interace covers the interace between the User Equipment (UE) and the network. The LTE radio interace architecture is made up o the layer 1, 2 and 3. Layer 1 is the physical layer and its speciications are described in the TS series. Figure 93

7 4.2 shows the E-UTRA radio interace protocol architecture around the physical layer. Figure 4.2: Radio interace protocol architecture around the physical layer. The LTE air interace consists o physical channels and physical signals which are generated by the LTE physical layer [36]. Physical channels carry data rom higher layers including control, scheduling and user payload. Physical signals are used or system synchronization, cell identiication and radio channel estimation. The types o downlink physical channels are Physical Downlink Shared Channel (PDSCH), Physical Broadcast Channel (PBCH), Physical Multicast Channel (PMCH), Physical Control Format Indicator Channel (PCFICH), Physical Downlink Control Channel (PDCCH) and Physical Hybrid ARQ Indicator Channel (PHICH). The types o uplink physical channels are PRACH (Physical random access channel), PUCCH (Physical uplink control channel) and PUSCH (Physical uplink shared channel). There are two types o signals, Reerence signal and Synchronization signal concerned to physical signals. The physical layer interaces the Medium Access Control (MAC) o Layer 2 and the Radio Resource Control (RRC) o Layer 3. The physical layer presents a transport 94

8 channel to MAC and a transport channel is characterized by how the inormation is transerred over the radio interace. MAC oers dierent logical channels to the Radio Link Control (RLC) o Layer 2 and a logical channel is characterized by the type o inormation transerred. Thus, the physical layer perorms the ollowing unctions in order to enable data transport service: LTE physical layer unctions applied to transport channels: Error detection on the transport channel and indication to higher layers. FEC encoding/decoding o the transport channel. Rate matching o the coded transport channel to physical channels and mapping o the coded transport channel onto physical channels. LTE physical layer Functions applied to physical channels: Power weighting o physical channels and modulation and demodulation o physical channels. Other LTE physical layer Functions: Hybrid ARQ sot-combining Power weighting o physical channels. Frequency and time synchronization. Radio characteristics measurements and indication to higher layers. Multiple Input multiple Output (MIMO) antenna processing. Transmit diversity (TX diversity). Beam orming and RF processing LTE Downlink Transmitter The layout o the transmitter is shown in Figure 4.3. Based on User Equipment (UE) eedback values, a scheduling algorithm allocates Resource Blocks (RBs) to UEs and sets proper mobile modulation and coding schemes, (coding rates between and with 4, 16, or 64-QAM modulation), the MIMO transmission mode (Transmit Diversity (TxD), Open Loop Spatial Multiplexing (OLSM), or Closed Loop Spatial Multiplexing (CLSM)), and the precoding/number o spatial layers or all served users. 95

9 In the irst step o the transmitter processing, the user data is generated depending on the previous Acknowledgement (ACK) signal. I the previous user data Transport Block (TB) was not acknowledged, the stored TB is retransmitted using a Hybrid Automatic Repeat request (HARQ) scheme. Then a Cyclic Redundancy Check (CRC) is calculated and appended to each user's TB. The data o each user is independently encoded using a turbo encoder. Each block o coded bits is then interleaved and ratematched with a target rate depending on the received Channel Quality Indicator (CQI) user eedback. Similarly to HSDPA, the rate-matching process in LTE already includes the HARQ process.. Figure 4.3: LTE downlink transmitter structure The encoding process is ollowed by the data modulation, which maps the channel-encoded TB to complex modulation symbols. Depending on the CQI, a modulation scheme is selected or the corresponding RB. Possible modulations or the DL-SCH are 4-QAM, 16-QAM and 64-QAM. The modulated transmit symbols are then mapped to up to our transmit antennas. 96

10 Downlink reerence symbols and synchronization symbols are also inserted into the OFDM symbol assembly. The assignment o a set o RBs to UEs is carried out by the scheduler based on the CQI reports rom the UEs LTE Downlink Receiver LTE receiver is shown in igure 4.4. Each UE receives the signal transmitted by the enodeb and perorms the reverse physical-layer processing o the transmitter. First, the receiver has to identiy the RBs that carry its designated inormation. The estimation o the channel is perormed using the reerence signals available in the time-requency resource grid. Based on this channel estimation, the quality o the channel may be evaluated and the appropriate eedback inormation calculated. The channel knowledge is also used or the demodulation and sot-demapping o the OFDM signal.. Figure 4.4: LTE downlink receiver structure 97

11 Finally, the UE perorms HARQ combining and channel decoding. In order to cut down processing time, at every turbo iteration a CRC check o the decoded block is perormed and i correct, decoding is stopped.the impact o the additional CRC checks is negligible, as a turbo decoder iteration requires a computation time three orders o magnitude bigger than the CRC check Channel decoding consists o our dierent types o channel estimators, (i) Least Squares (LS) (ii) Minimum Mean Squared Error (MMSE) (iii) Approximate LMMSE (iv) Genie-driven (near) perect channel knowledge based on all transmitted symbols. LTE requires UE eedback in order to adapt the transmission to the current channel conditions. The LTE standard speciies three eedback indicators or that purpose. The channel quality indicator (CQI), rank indicator (RI) and precoding matrix indicator (PMI). CQI is employed to choose the appropriate MCS, such as to achieve a predeined target BLER, whereas the RI and the PMI are utilized or MIMO pre-processing. Speciically, the RI inorms the enodeb about the preerred number o parallel spatial data streams. Ater each evaluation, the receiver provides the inormation necessary to evaluate the igures o merit, including user and cell throughput, Bit Error Ratio (BER), and Block Error Ratio (BLER) LTE MAC layer The MAC layer services and unctions contain mapping between logical channels and transport channels. It multiplexes the RLC PDUs into transport blocks or demultiplexes the RLC PDUs rom transport blocks in the reception side. Measurement reporting or 98

12 traic and error correction through HARQ is also done in MAC layer. Main unction o MAC layer is scheduling that dierentiates between logical channels and dierent UEs HARQ HARQ ramework in LTE considers incremental redundancy and special case o chase combining. HARQ can be synchronous or asynchronous. Synchronous HARQ requires that transmission occurs at known time instants. No explicit signalling is required; on the other hand, or asynchronous HARQ, explicit signalling is required to accommodate HARQ process that happens anytime. HARQ can also be adaptive or nonadaptive; adaptive HARQ has the ability to change the modulation, resource block allocation, and duration o transmission. Note that synchronous operation requires less control signalling and has signiicant advantage when it is nonadaptive since sot-combining can be perormed. This mode is selected or uplink. However, in the downlink, asynchronous and adaptive HARQ mode is considered Scheduling The enb has a scheduler to manage the time/requency resources or a given time or uplink and downlink. The scheduler dynamically allocates resources to UEs at each TTI (Transmission Time Interval). A UE always monitors the L1/L2 control channel(s) to search possible allocation. Predeined resource allocation is also possible where UE is notiied by the coniguration and then the allocation is done without Cell- Radio Network Temporary Identiier (C-RNTI), where UE blindly does the decoding. Depending on the channel conditions, scheduler selects the best multiplexing or UE. The decision depends upon any combination o the QoS parameters, buered payloads, pending retransmissions, CQI reports rom the UEs, UE capabilities, UE sleep cycles, measurement gaps/periods and system parameters such as bandwidth and intererence level/patterns. Downlink LTE considers the ollowing schemes as a scheduler algorithm: FSS: Frequency Selective Scheduling assigns transmission resources to a user using the 99

13 selective resource blocks to give the best perormance. Channel-side inormation is necessary or FSS and it can increase capacity over TDS (Time Domain Scheduling). PFS: Proportional Fair Scheduling is the most used scheduling mechanism, which basically is a C/I scheduler but with a delay component to address the delay sensitive traic. Link adaptation is perormed through adaptive modulation and coding. A user uses the same coding and modulation or all PDUs. However, in case o MIMO, dierent streams may use dierent modulation and coding. FDS: Frequency Diverse Scheduling does not need channel-side inormation since it allot resources distributed across the transmission bandwidth. 4.5 LTE System Level Simulator Structure o LTE Simulator The overall structure o the LTE System Level Simulator (SLS) is explained in this section (Figure 4.5). In LTE, such a network comprises o a multitude o enodebs that cover a speciic area in which many mobile terminals are located and/or moving around [25]. Figure 4.5: Schematic Diagram o LTE System Level Simulator 100

14 Simply perorming physical layer simulations o the radio links between all terminals and base-stations is uneasible or system level investigations because o the large amount o computational power required. Thus, the physical layer has to be abstracted by simpliied models capturing its essential dynamics with high accuracy at low complexity [83] LTE Simulator Overview Simulating the totality o the radio links between the User Equipments (UEs) and enodebs is an impractical way o perorming system level simulations due to the vast amount o computational power that would be required. Thus, in System Level Simulations, the physical layer is abstracted by simpliied models that capture its essential characteristics with high accuracy and simultaneously low complexity. Core part o LTE system-level simulatort consists o: i) A link measurement model and ii) A link perormance model. The link measurement model abstracts the measured link quality used or link adaptation and resource allocation. On the other hand the link perormance model determines the link Block Error Ratio (BLER) at reduced complexity. As igures o merit, the simulator outputs traces containing throughput and error rates, rom which their distributions can be computed. Implementation-wise, the simulator low ollows the pseudo-code below. The simulation is perormed by deining a Region o Interest (ROI) in which the enodebs and UEs are positioned and a simulation length in Transmission Time Intervals (TTIs). It is only in this area where UE movement and transmission o the Downlink Shared Channel (DLSCH) are simulated. Link measurement and Link perormance model The link measurement model abstracts the measurements or link adaptation and resource allocation and aims at reducing run-time computational complexity by pre-generating as many o the needed parameters as possible. This shits most o the computational burden to an o-line task that pre-generates and stores the results in trace iles that can be re-used 101

15 at simulation time. Special care has been taken as to account or the spatial and time correlation o the channel present in a wireless cellular system. To this eect, the link quality model has been splited into three parts. (i) macroscopic pathloss, (ii) shadow ading, and (iii) small-scale ading (SISO and MIMO). The scheduling algorithm assigns resources to users to optimize the perormance o the system (e.g., in terms o throughput) depending on this eedback. Following the link measurement model, the link perormance model predicts the BLER o the link, based on the receiver SINR and the transmission parameters (e.g., modulation and coding). In order to generate the network topology, transmission sites are generated, to which three NodeBs (sectors) are appended, each containing a scheduler. A scheduler assigns PHY resources, precoding matrices, and a suitable MCS to each UE attached to enodeb. The actual assignment depends on the scheduling algorithm and the received UE eedback. At the UE side, the received subcarrier postequalization symbol SINR is calculated in the link measurement model. The SINR is determined by the signal, intererence, and noise power levels, which are based on the cell layout (deined by the enodeb positions, large-scale (macroscopic, macro- scale) pathloss, shadow ading and the time-variant small-scale (microscopic, micro-scale) ading. The CQI eedback report is calculated based on the subcarrier SINRs and the target transport BLER. The CQI reports are generated by an SINR-to-CQI mapping and made available with adjustable delay. At the transmitter, the appropriate MCS is selected by the CQI to achieve the target BLER during the transmission. Implementation-wise, the simulator ollows the structure shown in Figure 4.6. Each network element is represented by a suitable class object. 102

16 Figure 4.6: Relation between the several components comprising the LTE SLS 4.6 Dynamic Radio Resource Management Radio Resource Scheduling Schemes Dierent radio resource scheduling algorithms have been studied and Cyclic Switching Scheduling Scheme is proposed. Proportional Fairness (PF) Resource Allocation Scheme The priority or each user at each resource block is premeditated irstly in PF scheduling algorithm or OFDMA and then the user with maximum priority is assigned the RB. Then the algorithm continues to assign the Resource Block (RB) to the user with next utmost priority. This process goes on till all RBs are assigned or all users have been served with RBs. ollows In time n the priority o th k user or j-th resource block is premeditated as P ( n) RDR ( n) R ( n) k, j = k, j k (4.1) 103

17 ( n) RDR k, j = requested data rate or the th k user over the j-th RB in time n. Rk ( n ) = the low-pass iltered averaged data rate o the th k user. RDR is estimated using Adaptive Modulation and Coding (AMC) selection which is based on current transmission channel condition. RDR or retransmissions is clearly separated rom the RDR o new resource requests as retransmissions must be treated specially to guarantee their successul reception at the receiver and in that case RDR is estimated as ollows Where, RDR = R ( SNR ) k, j MCS AC (4.2) R MSC = the rate estimation unction and SNR is the accumulated signal to AC noise ratio over the transmission channel. Rk ( n ) is updated on each interval o scheduling as ollows, R ( n 1 ) = ( 1 a) R ( n) + a RDR ( n) + (4.3) k k. k Where a = average rate window size and RDR k ( n) is the aggregate data rate o user time n. th k in Soter Frequency Reuse based Resource Scheduling Algorithm For reducing the requency selective scheduling gain loss and to increase the data rate at cell edge, the soter requency reuse scheme is used. In this scheme the requency reuse actor both at cell centre and cell edge is 1. The high power requency band is dierent between neighboring cells. The designed requency scheduler runs in a way that the cell edge users have the greater probability to use the requency band with higher power and the cell centre users have the higher probability o using requency band with lower power. 104

18 Modest modiication in PF scheduling algorithm is needed as ollows, ( ) ( ) ( ) P n = RDR n R n * F (4.4) k, j k, j k k, j Where, F k, j is the priority actor and can be one o the ollowing k j F 1,1, User k at cell centre, RB j is low power F 1,2, User k at cell centre, RB j is high power F 2,1, User k at cell edge, RB j is low power F 2,2, User k at cell edge, RB j is high power F, can have the value between 0 and 1. ` Thus we can easily assign the values to F k, j to control the resource assignment to users at cell center and cell-edge. Round Robin Scheduling Scheme In a round-robin approach radio resources are assigned to users. The irst arrived user is served with entire requency spectrum or a speciic time period and then these resources are revoked back and assigned to the next user or another time period. The previously served user is kept at the end o the waiting queue so that it can be served with radio resources in next round. The new arriving requests are also positioned at the tail o the waiting queue. This scheduling continues in the same manner. It oers a great airness among the users in Radio Resource Allocation (RRA). It is not realistic in Long Term Evolution technology as only one user is served at a time and it degrades the entire system throughput drastically. Resource Scheduling Scheme based on Maximum Intererence Maximum overall intererence (MOI) is key actor in this method. The users are scheduled to utilize radio resources based on MOI. In this scheme users are ranked according to their practiced intererence. It means that, the user with worst CQI is ranked up on the top and scheduled to utilize the physical resource blocks or the 105

19 speciic time. The user with the next worst CQI condition is then scheduled to utilize RBs. The ranking K can be calculated using the ollowing equation. K ( γ ( t) ) = arg max (4.5) k Here γ is the vector o experienced intererences by the cell users in time t. Resource Scheduling Algorithm based on Dynamic Allocation In dierent types o network traic, this scheme executes competent radio resource utilization. Conversational class traic is transmitted on the network in small portions which are noticeably smaller than the packets o streaming class traic. In this algorithm the equal allocation o the radio resources is ensured but not the capacity o traic that they can handle with these physical resource blocks (PRB). Algorithm is outlined as below. Algorithm Initialization N=100 (1, 2, 3, 4, 100) Until N=0 For each k in U RB->k; the user k selects inest physical resource block (PRB) rom N depending on N = N RB End or each k End Until channel condition Where, N = Total number o available physical resource blocks U = Total users to multiplex on a physical resource block RB = Resource block which are assigned to k user 106

20 4.6.2 Design and Implementation The dierent Probabilistic Equations are identiied rom [73]. In next subsections these equations are used or numerical analysis o dierent resource allocation schemes. Probabilistic Equations A 3GPP LTE network is considered to derive dierent equations and ind probabilities which are needed in numerical calculations and network implementation simulation. In the network the requency band o L subcarriers is partitioned into C sub channels each containing M subcarriers, or instance M = L/C (4.6) Allocated subchannels in interering cells is characterized by a vector K K = { K 0, K 1, K 2, K n} It is a set o vectors representing number o allocated subchannels in n cell where K 0...K n represent the number o allocated subchannels in cell numbers (0.n) Collision Probability Collisions o the cell subcarrier with the subcarrier allocated in the interering cell are the intererence in a network. Load in the target cell must be ound out to realize collision probabilities. X i K C ( K ) = 1 K i π i (4.7) C i Where, 107

21 X i = the cell load, C = the number o available sub channels, K = the number o allocated subchannels in the cell numbers I, and ( ) i π is the probability o having K subchannels allocated in the cell number i. K i Where, The probability o having exactly k collision in a subcarrier in a homogeneous network can then be ound using the binomial law as ollow, n k = x x k n k k n k, Pr( ) (1 ) 0 (4.8) Where n is the number o interering cells, k is the number o collisions o subcarrier allocated in the target cell with the subcarrier allocated in the interering cell, and x is the load in the target cell (0 x 1). The intererence with dierent rings can be ound as ollows: n1 n2 k k Pr( k + k ) = P ( k + k ) r 1 2 n1 + n2 k + k 1 2 (4.9) Where, Pr (k 1 +k 2 ) can be ound using equation (4.4) The probability o having exactly k j collisions in a heterogeneous network is premeditated as ollows. Interering cells are classiied into L sets. Set j contains n j equally-loaded cells, and whose load is denoted by x j. The probability o having k j collisions between a given subcarrier o cell 0 and subcarrier belonging to cells in set j is, 108

22 nn ( ) ( )( ) ( ) kj nj kj Pr k, x = x 1 x, 0 k n (4.10) j j k j j j j j The probability o having exactly k j collisions with each set numbered j is then ound with the ollowing equation Pr,... =, (4.11) l ( k kl) P( k j x j) 1 1 Steady-State Probabilities The System state (S) is deined by the number o the users U in a cell: { U U C} S = : (4.12) Where, S= System state U = the number o users in the cell C = the number o subchannels in the cell. To calculate the system perormance it is necessary to calculate the user s arrival and departure rate irst to/rom the cell. Let, D T = instantaneous throughput o a call. Then D T depends on bandwidth W, modulation scheme eiciency e, and Block Error Rate (BLER) in such a way T ( 1 ) D = M W e BLER (4.13) Where, e = Eiciency o used modulation. The eiciency e and error rate BLER depends on the SINR, which is also written as C/I. Then, 109

23 e (1 BLER) = e( C I ) (1 BLER( C I ) = B( C I) In this last step is the deinition o a unction B, in this way, instantaneous throughput becomes D ( C I) = M W B( C I) (4.14) T SINR depends on propagation conditions, distance between transmitter and receiver, the shadowing and requency selective ading. In this way in OFDMA systems where a set o parallel, lat, and non-selective ading channels are used, their transmission channels is merely impacted by slow ading. The SINR in the target cell is calculated as C X I 0 ( ) = i= 1 X p q p i n qi DT + N 0 (4.15) X i = 1 means that there is a collision between a call in cell i and the user in target cell. N o is the background noise, p is the power and q is pathloss.[22] D q T i is the pathloss between the interering base station i and the corresponding receiver such as, Where, D ξ T c i qi = r α i 10 (4.16) 10 r i = distance rom base station in a cell i to the receiver in target cell. ξ i = a normal random variable due to shadowing, with zero mean and variance α [2, 4] is a constant. c 2 ζ and 110

24 Call s Mean Service Time Service Time o a call allocated to one subchannel is calculated using the harmonic mean o throughput D T when reuse o 1 is used. T E[ Z] = (4.17) D T Harmonic mean o throughput is given by, 1 DT = P x T I DT ( x ) is the throughput given the vector o collisions X: 1 r ( ) (4.18) x D ( x) ( ) D x = M. W. E T ro 1 C B I ( X ) 1 (4.19) Mean Service Time o a call (T ) in cell 0 is calculated as, T = E T [ ( X )] = Z M. W E ro 1 C B ( X ) I (4.20) Where, M = Number o sub-channels assigned to a call Z = Size o the ile to be downloaded W =Channel bandwidth E r0 = Expectation over surace o cell 0 Ater inding mean service time o a call we can calculate steady-state 111

25 probabilities means probability o having U calls in the system as ollow: ( λt ) 1 π ( U ) = (4.20) G U! Normalized constant G can be gained as ( λt ) U G = (4.21) U! U C Here, U= number o users (subscribers) in a cell C = subchannels in the cell λ = the intensity o arriving calls (Poisson Process) Steady-state probabilities are calculated with the help o departure rate in the target cell and departure rate is calculated using the steady-state probabilities in the interering cell. The mean-time that a session spends in the system is calculated using the Little s Formula: E[ U ] T= λ ( 1 b) (4.22) Where, [ ] = π( U) is the average number o calls in a cell. E U U S 112

26 Power in UPLINK The minimal transmission power procedure, P e is calculated with the help o the ollowing i) Calculate Signal to Intererence plus Noise Ratio ( SINR) achievable when signal is transmitted with maximum power P max ii) Identiy the Modulation and coding schemes (MCS) corresponding to above calculated SINR iii) Calculate the minimum transmission power P e able to achieve above identiied MCS. Assume that, there are X collisions in the target cell and the intererence experienced by a user in target cell because o a user in cell i is calculated as ollows Where, (, ) i i i I ( i ( i, θi )) q ( r ) U P l r U i ( ri, i ) U o i θ = (4.23) l r θ is the distance between base station and user in interering cell. ( i ( i, i )) U P l r θ is the mean transmit power in interering cell at distance l rom the base station and U q o is the pathloss between user and base station in the target cell. The maximum achievable SINR by the target user is calculated as below. SINR max ( q, X, r, θ ) 0 U Pmax / q0 ( ro ) U = X ii ( ri i + N i, θ ) = n i 1 0 (4.24) Where, p max is the maximal transmitted power o the target user U qo ( r o ) is the pathloss experienced by the target user at distance r o rom its base station. An average minimal transmittable power is required to account or changes in intererence, thus it can be calculated as ollows 113

27 = Pe( r ) Er, e 0 [ P ( r, X, r, θ) ] P ( ) 0 r X X θ (4.25) Where, r and θ = distance vector and angle between base station and interering user in the target cell and P ( ) r X is the collision probabilities o collision vector X and the transmitted power is averaged over interering cell suraces Multiuser Scheduling With Adjustable Fairness Two-user Rate Region Theoretical two-user rate region is considered (Figure 4.7). Figure 4.7: Hypothetical two user rate region o a wireless ading channel User 1 has a high Signal to Noise Ratio (SNR) that allows him to get a rate o up to 2 bits per channel use while User 2 s maximum rate equals 1 bit per channel use. As channel has ading nature, it is possible to achieve a sum rate higher than the single user rate by developing multiuser diversity. The maximum sum rate is marked with a 114

28 cross in igure 4.7. The other extreme, leading to equal rates o the users, is the solution to the max. min. scheduling problem (marked with a plus symbol) [31]. Let us next impose a airness constraint applying Jain s airness index [89] given by: J ( D T ) = K D k = 1 K k = 1 2 K D T (k) T (k) 2 (4.26) Here, D T is a vector o expected user throughputs (expectation over channel realizations). DT ( k ) is the kth entry o DT and k is the number o users. Jain s airness index ranges rom 1 K (only one user is served) to 1 (all users are served at the same rate). The constraint J DT JO Second Order Cone Constraint (SOCC). ( J O is the desired airness) can be reormulated as a K ( k = 1 D T ( k ) ) K D ( k ) K 2 k = 1 T 2 J 0 D 1 T D T (k) J K D (k) T 0 2 (4.27) Two examples are shown in Figure 4.7, as the two shaded cones. The constraint J 0.72 corresponds to the large cone (ranging rom the line with an angle o approximately 80 0 to the line with 15 0 ). The constraint J 0.85 is shown as the inner cone. Increasing J O shrinks the aperture o the cone until it converges to a line or J O = 1 going through the max. min. solution. The scheduling diiculty is to allocate resources (transmission time, bandwidth) to users in such a way that the rate tuple, that maximizes the sum throughput while lying in the intersection o the rate region and the cone given by the airness constraint is achieved. This proposes ormulating the scheduling problem as a Second Order Cone 115

29 Program (SOCP). Maximize: K k = 1 D T ( k ) D Subject to: J K D T T (k) 1 D T (k) (4.28) 0 2 The complexity in this ormulation is that the resource allocation must be perormed or the entire time-requency interval o interest at once in order to get an optimal solution. Naturally this is not possible because the channel qualities are not known in advance. Thereore instantaneous values are ed back. This allows solving the SOCP or every time instance, leading to a loss o temporal diversity. In order to achieve advantage rom temporal diversity, another approach to the problem is required. By solving a weighted sum rate maximization problem, points on the boundary o the multiuser achievable rate region can be achieved. Varying the individual users weights, it is possible to trace out the complete boundary. Directly applying such weighted sum rate maximization in ramework, with a desired airness constraint, requires to ind the weights o all users that ulill the airness constraint and simultaneously maximize the sum rate. To avoid the diiculty o inding so many weights, it is better to alternatively apply a utility maximization. A user s utility rates his satisaction with respect to the resource allocation. The important task then is to ind suitable utility unctions that allow to trade o network airness versus network throughput Adjustable Fairness Scheduling Maximization problem is ormulated in this section in a general context. It is specialized to the requirements o 3GPP LTE by applying the ramework presented in [31]. Moreover ocus is on inding the appropriate utility unctions in order to maximize the network throughput and attain a desired airness speciied in terms o Jain s airness index. 116

30 General Formulation Let, C r is the achievable rate region and J is the region corresponding to the Second Order Cone Constraint( SOCC). The sum utility maximization problem is then given by: max imize : U ( D T (k)) a subject to : D T C J K k = 1 r (4.29) The utility o a user is rated with the α -air utility unctions [90]. U α (x) = 1 α x 1, α 0, α 1 log, α = 1 α ( x) (4.30) It is dependent on the user s average throughput and the parameter α The solution o problem (4.30) achieves special points on the boundary o the rate region [90]. By varying α rom 0 to, the line segment in between the max. throughput solution and the max. min. solution is traced out ( Figure 4.7). Points on this line segment are guaranteed to be Pareto optimal [90], meaning that other points achieving the same airness do not achieve a larger sum rate. It means that in igure 4.7, the two points marked a) and b) both ulill the constraint J 0 = 0.86, but only the point marked b) attains the maximum sum rate. The points marked c) and d) both satisy J 0 = 0.72, but neither o the two is optimal because a higher sum rate is possible at an even higher airness, given by the maximum throughput solution. In both cases the optimal point lies on the considered line segment. With an appropriate value o α, the desired trade-o between airness and throughput. α -air utility unctions yield the The problem o utility maximization depends on the expected user throughputs DT ( ) k. In [92] it is revealed that how such a problem is reormulated to an online algorithm that converges to the true solution using standard stochastic approximation techniques. For that purpose the expected throughput D T is 117

31 replaced with an average throughput D Tn at the time instance n using the stochastic approximation recursion 1 1 D = 1 D ( 1) + D β β Tn T n T n (4.31) Where, D Tn is the instantaneous throughput and the step size β > 1. The recursion is equal to averaging utilizing an exponentially decaying window unction. The parameter β determines the decay rate o the window. Substituting (4.31) into (4.29) and approximating (4.29) with a Taylor expansion o irst order [93] guides to the online utility maximization problem at time instant n. ' max imize: U ( D T ( n 1) (k))d (k) ( T ) subject to: J D J K k= 1 α O T n (4.32) It has to be maximized with respect to the resource allocation. Jain s airness index still depends on the expected throughput. The irst derivative speciied by: ' U α o the utility is ' U (x) = α α 0 α x 1 (4.33) For α = 1 and ignoring the airness constraint in (4.33) this problem reduces to the well known ormulation o proportional air scheduling. The diiculty arising rom the stochastic approximation is the question o how to deal with the airness constraint.. In the ollowing analysis the airness constraint is not considered explicitly in the maximization problem anymore but chooses the parameter is met. α such that the constraint 118

32 LTE Specialization 3GPP UMTS/LTE is an Orthogonal Frequency Division Multiple Access (OFDMA) system. It orces several constraints to be considered in multiuser scheduling [91][92]. Resource Blocks (RBs) which consist o several adjacent OFDM samples are obtained by dividing the time-requency grid spanned by OFDM. It is done by LTE. Dierent RBs can be allocated to dierent users. RB selective Channel Quality Indicator (CQI) eedback is provided by users, which inorms the base station about the achievable rates on every RB [93]. Scheduling decisions are carried out every subrame (1 ms duration) or the next subrame [94] [95]. A user utilizes the same Adaptive Modulation and Coding (AMC) scheme on all resources is scheduled onto [95]. The power allocation or all resources is equal and already accounted or in the CQI eedback. In this work, we utilize an approximate linear ramework that takes all LTE speciic constraints into account. The number o available RBs per subrame is denoted by R. With ( k ) R 1 c n R we reer to the vector o rates achievable by user k on the R RBs at subrame n. The vector ( k ) c is computed rom the CQI eedback vector n ( k ) CQI [31]. Denote by n ( k ) { } 1 b n 0,1 R the resource allocation vector o user k at subrame n. b ( k ) () 1 n i = means that resource i is allocated to user k at subrame n. Excluding multi user MIMO, the resource allocation vectors o the users are mutually orthogonal. With this notation the stochastically approximated utility maximization problem in (26) can be specialized to * * ( 1) ( ) { b b },... = arg max 1 K { n,..., n } ( i ) T ( j ) C T ˆ K (k)t (k) K n n n n a b b k = 1 n 1 (k) subject to : b b = 0 i n n i, j b (4.34) The problem o Linear Program (LP) is reormulated by initiating an equivalent matrix ormulation as discussed in [31]. 119

33 Evaluation o the Parameter α To achieve the objective o a desired airness, it is needed to adapt the parameter α to the channel statistics. The channel statistics are a-priori unknown but can be learned online by the scheduler basically by observing the User Equipment (UE) eedback. Specially we need to learn the probability mass unction ( pm ) o the achievable rates per resource (RB in LTE). ( ) Tn ( ) A lg orithm to compute α 1 : D ' l = D l 1 l 1,..., K Tm 2 : α 1 = α 3 : J 1 = J n ( D Tn ) 4 : m = 1 5 : stop = alse 6 : while stop = alse do 7 : or k = 1 to k do ' ( T ( m + 1) ) 8 : C om pute E D ( k ) utilizing (4.37) and (4.38) 9 : Update D T ( m + 1) ( k ) utilizing (4.31) 10 : end or ' 11 : C ompute Jain ' s airness index J m + 1 ( D T ( m + 1) ) utilizing (4.26) 12 : U pdate α utilizing (4. 39) 13: 14 : 15 : 16 : m = m : end 18 : end while 19 : α m i J has converged to J then m stop = true else = α In a practical wireless system there is just a inite number o achievable rates per resource, N AMC, corresponding to the dierent supported AMC schemes (each scheme AMC 1 has a speciic spectral eiciency), which we include in the vector C R. The achievable rate pm allows predicting the predictable throughput o each user or a 120

34 givenα. Then it is needed to adapt α such that the predicted expected throughputs meet the airness constraint. In order to learn the pm o the achievable rates per resource o user k, utilize the same recursive stochastic approximation as in (4.32). ( k ) p, we 1 D 1 (k) T D (k) = 1 D ( 1) (k) + c b β β (k) Tn T n n n (4.35) In case o LTE the length o the stochastically approximated pm vector ˆ P n ( k ) N 1 [ ] 0,1 AMC is equal to the number o dierent CQI values (16 including CQI zero). The vector ( k ) P is an instantaneous approximation o the pm computed rom the n eedback values at time instant n. For LTE this vector can be calculated rom ( k ) CQIn by 1 P i C Q I r i i N R (k) K n ( ) = N ( ) 0,..., A M C R = r = 1 { } (4.36) With, [i = j] being the indicator unction or i = j. An iterative algorithm is provided that computes the parameter α rom the approximated pm s. Utilizing the stochastic approximation [91], the adjustable airness scheduler assigns a resource to the user or which the ratio o rate and average rate raised to theα -th power is largest. It helps to predict throughput o user k at iteration instant m+1 in the ollowing way [91]. N A M C k { } ˆ T m + 1 = n i = 1 E (D ' (k )) P k is s e r v e d i.c (i).p (i). (4.37) K N AM C c ( j ) c ( j ) P { k is served i} = ˆ < P ' m ' m n j α α l = 1 j = 1 D ( ) Tm l D Tm ( k ) i k ( l ) ( ) (4.38) 121