Il presente lavoro di tesi analizza e sviluppa un innovativo algoritmo di scheduling degli utenti per sistemi a larga banda 4G LTE. La particolare implementazione adottata ha permesso l’evoluzione degli algoritmi di scheduling dal caso singola antenna al caso multi-antenna, senza alterare in alcun modo la struttura degli algoritmi stessi. Le prestazioni di tale algoritmo, denominato Smalloc (Smart Allocation) sono state valutate attraverso lo sviluppo di un simulatore al cui interno sono stati implementati anche altri algoritmi di scheduling giá noti in letteratura come Round Robin, Max Rate e Propotional Fair.

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to which user and vector

be allocated to each sub-carrier. The theorem proved in [3] showing that the data rate of a multi-user OFDM system is maximized when each sub- carrier is assigned to only one user that has the best channel gain for that sub-carrier. Many dynamic resources allocation algorithms and optimization techniques have been proposed to manage the future services that continue to evolve; it is very important that these techniques are able to provide high bit rates as possible with various quality requirements. In a OFDM system each sub- carrier can have a different modulation scheme which provides a trade- of between spectral efficiency and BER. If a fixed modulation scheme is CHAPTER 2. LTE LAYER 2 AND SCHEDULING TECHNIQUES 35 adopted in a OFDM system then it tries to maintain acceptable performance when the channel quality is poor. Using a fixed modulation, it can not be possible to increase the modulation when a channel gain of a sub-carrier improves; in this manner, it would maximize the overall spectral efficiency. On the other hand, adaptive modulation requires an accurate channel esti- mates at the receiver; if the channel changed faster than it can be estimated, adaptive modulation would perform poorly. Furthermore, overhead infor- mation needs to be updated regularly and exchanged so that transmitter and receiver know what modulation is being used. Two crucial issues in resource allocation for wireless communication systems are efficiency and fairness. A definition for spectral efficiency is the data rate per unit band- width; a user''s spectral efficiency is calculated by dividing the total band- width throughput by the user''s total bandwidth. If a system provides the highest throughput then it does not take into account the fairness among the users. There is a trade-of between efficiency and fairness in wireless re- source allocation. In [4], the definition of fairness is to allocate the resources to the users so that all the users achieve the same data rate. A fairness index is defined in [5] as a rate proportional constraints with the maximum value of 1 to be the fairest case in which all users would achieve the same data rate.

index; when ρk,n is 1, it means that the n-th sub-carrier is allocated to k-th

user, ρk,n is 0 otherwise. B N = 1 T is the bandwidth of each channel, T is the OFDM symbol duration. γk,n is the SNR of the n-th sub-carrier for the k-th

user, its expression is the following: γk,n = pk,nHk,n = pk,nh2k,n N0 B N (2.2) where pk,n is the power allocated for user k in sub-channel n, hk,n is the

channel gain and Hk,n denotes the channel-to-noise ratio for user k in sub-

channel n while N0 B N is the noise power on each sub-carrier where N0 is the power spectral density of AWGN channel. Equation 2.1 indicates the achieved data rate in a zero margin system. The total data rate RT of a zero margin system is given by: RT = B N K X k= 1 N X n= 1 ρk,nlog2(1 + γk,n) (2.3) CHAPTER 2. LTE LAYER 2 AND SCHEDULING TECHNIQUES 37 The following is the general form of the sub-carrier and power allocation problem with relative constraints that a scheduler should follow: Objective : max ρk,n,pk,n RT = B N K X k= 1 N X n= 1 ρk,nlog2(1 + pk,nh2k,n N0 B N ) or min ρk,n,pk,n PT = K X k= 1 N X n= 1 ρk,npk,n subjectto : C 1 : ρk,n '' 0, 1, ''k, n C 2 : K X k= 1 ρk,n = 1, ''n C 3 : pk,n 1 0, ''n C 4 : K X k= 1 N X n= 1 ρk,npk,n 0 Ptotal C 5 : User Rate Requirements. (2.4) The first two constraints ensure that each sub-carrier is allocated to only one user. The third and fourth constraints indicate that the power allocated to the users must not be larger than the total power. The fifth provides the fixed or variable rate required by the users. In relation to objectives and constraints, each algorithm belongs to a different class; in each class, the problem is formulated and the optimal solution is derived using different optimization techniques. As the optimal solutions have a high computa- tional complexity, it is adopted a solution that can be applied in real time applications, a sub-optimal solution. CHAPTER 2. LTE LAYER 2 AND SCHEDULING TECHNIQUES 38

( 1 '' 1 TPF )Rk(m) + 1 TPF Rk,n(m) if user k is selected, ( 1 '' 1 TPF )Rk(m) if user k is not selected.

in LTE

matrix channel is represented by way of example in Figure 3.1. Then the Figure 3.1: MIMO system with N transmit antennas and M receive antennas. M '' T signal R received over T symbol durations over this subcarrier can CHAPTER 3. BENEFITS OF MIMO TECHNOLOGY IN LTE 46 be conveniently written as:

ing antennas. We will use

referred to as the receive spatial signature of (i.e. corresponding to) the ith transmitting antenna. Likewise, the jth row of

mit spatial signature of the jth receiving antenna.

mapping function

ble MIMO transmission methods results, each yielding a different combi- nation of the diversity, array and multiplexing gains. Meanwhile, the so- called spatial rate of the chosen MIMO transmission method is given by the ratio P T . Note that, in the most general case, the considered transmit (or receive) antennas may be attached to a single transmitting (or receiving) device (base station or UE), or distributed over different devices. The symbols in (x1, x2, ..., xp) may also correspond to the data of one or possibly multiple users, giving rise to the so-called single-user MIMO or multi-user MIMO models.

under the current channel conditions and modulation scheme; and a

coding matrix for the current channel conditions. Finally, the UE provides a CQI given the RI and PMI, rather than basing CQI on the current operation mode. This allows the eNodeB to quickly and effectively adapt the trans- mission to channel conditions. Closed loop operations are particularly im- portant for spatial multiplexing, where MIMO offers the greatest through- put gains.

times and known to both the transmitter and the receiver. Here, hij is the channel gain from transmit antenna j to receive antenna i. There is a total power constraint, P, on the signals from the transmit antennas. In the nota- tion of matrices, the matrix

matrix whose diagonal elements are non-negative real numbers and whose off-diagonal elements are zero. If we define: '

calculated as: CHAPTER 3. BENEFITS OF MIMO TECHNOLOGY IN LTE 58 SINR(f) = GBS '' GMS '' ( Ptx BS /Nt Ncarrier ) '' |'|2 N + I (3.12)

from single-antenna to

multi-antenna solutions

where GBRj '' G(1 6 j 6 NGBR). Let A be the GBR matrix allocation where

each element of the matrix aj,n is 1 if the n-th sub-channel is allocated to

the j-th GBR user. 1. Calculate Mn = maxk(CQInon''GBR k ,n ) , ''n1 6 n 6 Nsch. 2. Create the Ratio matrix R where the element rj,n = CQIGBR j ,n Mn is the ratio related to the j-th GBR on the n-th sub-channel. 3.

1 if rj'',n'' = maxj,n(rj,n) 0 otherwise

the GBRs in that n-th sub-channel in which maxkCQInon''GBR k ,n ''k( 1 6 k 6 Nnon''GBR), is a low value. Figure 4.1 shows the described algorithm. CHAPTER 4. SMALLOC: FROM SINGLE TO MULTI ANTENNA SOLUTIONS 63 Figure 4.1: Smalloc algorithm diagram.

used in our simulations. In each TTI we have Hn Matrix where n is the number of link from BS to Figure 5.3: Generation of H matrices. MS, the matrix''s row represents the RBs while the columns represents the users like it''s shown in figure 5.4. CHAPTER 5. SIMULATION SCHEME 71 Figure 5.4: H matrix structure.

in Single Antenna case. Figure 6.2: Urban-Macro, achieved bit rate for each user for different algorithms in Single

Antenna case. of smalloc algorithm.

Antenna case. Figure 6.4: Urban-Macro, achieved bit rate versus different number of users RB constraints

in Transmit Diversity case.

distance between antenna element at BS. In Figure 6.6 shows the total bit rate achieved by the algorithms when the distance between antennas at BS is 8 λ.

in Closed-Loop Spatial Mult. case. Figure 6.7 shows the performance of the Smalloc when the antennas, at BS, are at different distances. Figure 6.7: Urban-Macro:Smalloc performance in Open-Loop Spatial Mult. with different

distance between antenna element at BS. Figure 6.8 shows the total bit rate achieved by the algorithms when the distance between antennas at BS is 8 λ. CHAPTER 6. NUMERICAL RESULTS 81 Figure 6.8: Urban-Macro: achieved bit rate versus different number of users RB constraints

in Open-Loop Spatial Mult. case. Figure 6.9 shows the performance of the Smalloc Algorithm with dif- ferent transmission mode in Urban-Macro scenario. In this figure is more noticeable the difference in throughput between the various transmission mode. Figure 6.9: Smalloc performance in different transmission mode. In Figure 6.10 the various transmission modes were compared at dif- CHAPTER 6. NUMERICAL RESULTS 82 ferent distances from BS in Urban-Macro scenario. It is important to note that for distances greater than 210 meters Smalloc algorithm, in Tx diver- sity case, has better performance than Round Robin in Closed-Loop Spatial Multiplexing. Smalloc algorithm, in Tx diversity case, is better than Propor- tional Fair in Closed-Loop Spatial Multiplexing, for distance exceeding 430 meters. For distances of 230 meters Smalloc algorithm,in Single-antenna case, is better than Round Robin in Closed-Loop Spatial Multiplexing. The BS, according to the considerations made, could change allocation al- gorithm or transmission mode, depending on the quality of the channel and depending on the distance of the users. Figure 6.10: Transmission mode performance at difference distance from BS.

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