Resource Allocation Strategies Based on Ant Colony Optimization for Next Generation OFDMA Wireless Systems

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University of Pisa

Department of Information Engineering

Master’s Thesis in

Telecommunication Engineering

Resource Allocation Strategies

Based on Ant Colony Optimization

for Next Generation Wireless

Systems

Author:

Riccardo Andreotti

Supervisors: Prof. Filippo Giannetti Ing. Vincenzo Lottici Ing. Ivan Stupia July 20th_{, 2009}

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Abstract

Next generation wireless systems aim at providing an high spectral efficiency, with indoor traffic up to 1 Gbit/s and outdoor traffic up to 100 Mbit/s, offering, at the same time, several multimedia applications, each one marked by its own QoS.

In such a dynamic situation, where the number of users, the type of applications and the channel conditions of each user vary rapidly, raises the problem of how efficiently manage the system resources in order to satisfy these requirements.

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Scheduling Overview

The advent of 3rd _{Generation (3G) mobile radio systems has made}

schedul-ing one of the most challengschedul-ing and interestschedul-ing features. In fact, wireless systems until 2nd_{Generation (2G) were characterized by hard capacity (i.e.,}

a deterministic number of users can be served by a given base station) and only vocal application was supported, meaning that link requirements to be met were only set in terms of block error rate and delay. 3G wireless systems offer instead several multimedia applications, each one marked by its own QoS, raising the problem of how efficiently manage the system re-sources in order to satisfy these requirements. Moreover, the offered traffic continuously changes according to the number of users and the specific mix of applications required, since each user can request different applications. So, in such a situation, QoS cannot be achieved through a static configura-tion of the system, but it is dynamically pursued by a set of funcconfigura-tionalities grouped under the term Radio Resource Management (RRM).

1.1 Scheduling definition and properties

RRM is the set of functionalities whose aim is to provide services accord-ing to the QoS negotiated for each application over the area covered by the system and to optimize the system capacity through the choice of the best resource sharing among users. Scheduling, together with some other well known functionalities such as Power Control (PC), HandOver (HO),

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mission Control (AC), Congestion and Load Control and Link Adaptation (LA), belongs to RRM.

In particular, scheduling could be defined as an RRM functionality per-formed at the Medium Access Control (MAC) sub-layer, whose aim is to evaluate the set of resources available and distribute them among competing flows according to their priority in order to guarantee the QoS negotiated by the flows, where a flow can be defined as one of the possibly several parallel data streams supported by a certain user (fig. 1.1).

Figure 1.1: A Typical Wireless Scheduling

A general definition of the radio resource that the scheduler should assign is quite hard to give, because it depends on the particular wireless system. However, a Radio Resource (RR) could be defined as the signal format nec-essary to define how a certain amount of data can be transmitted over the wireless medium.

For instance, in a Time Division Multiple Access (TDMA) system, an RR is identified by all the following dimensions: the time slot over which trans-mission is allowed, the carrier frequency and the relevant bandwidth, the modulation and coding format, the power level and the transmitting spatial dimension.

According to the definition of Radio Resource previously provided, a Re-source Unit (RU) can be consequently defined as the minimum amount of RR assignable or, alternatively, the RR allowing the minimum amount of

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data to be transmitted. However, since a RR (and consequently a RU) is composed of both discrete (e.g., time slot) and continuous (e.g., power level) dimensions, it is actually impossible to define a numerable set of resources offered by a certain system.

For this reason, it is useful to give a reduced definition of Radio Resource, which includes only the set of discrete dimensions, so that the problem of scheduling consists in distributing orthogonal resources among competing users, where the orthogonality implies that each resource can be allocated to at most one user.

It is now possible to introduce the concept of Adaptive Radio Resource Assignment, as the allocation of a specific set of Radio Resources to a certain flow according to the contingent state of the system, which can include wireless channel conditions, the state of the queues, the number of users, QoS requirements etc. It is thus worth noting that the terms scheduling and resource allocation are often used in literature as synonyms but, according to the definitions provided, it is evident that while scheduling implies resource assignment, the contrary does not hold. In fact, the latter does not consider, for instance, neither the temporal axis or the multiuser environment. On the other hand, while the RR assignment have to be aware of the air interface to adapt the system parameters (or, to allocate radio resources) to the channel conditions in order to maximize system performances, the scheduler can be air interface unaware. In fact, it could decide to serve a certain flow receiving information only from application side, such as the state of the buffers queues or the QoS requirements.

Though, in recent years, the knowledge of the air interface structure and of channel dynamism at the resource assignment module, and of application parameters at the scheduler, allow the real implementation of a cross-layer approach. Thus, as shown in fig. 1.2, we can define the scheduling problem as an allocation problem aimed to optimize a particular objective function subject to constraints that are specific of the system scenario.

The reminder of this chapter will provide a description of the IEEE 802.16 QoS classes and an overview of the main scheduling algorithms pub-lished in the literature.

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Figure 1.2: Generical Scheduling Algorithm

1.2 QoS Classes

In the IEEE 802.16 standard, four classes are provided [1] to describe the most common applications in terms of quality of service (see also tab. 1.1).

1. Unsolicited Grant Service (UGS) supports constant bit rate or fixed

throughput connections such as VoIP. This service provides guarantees on throughput and latency.

2. Real-time Polling Service (rtPS) provides guarantees on throughput

and latency but with greater tolerance on latency relative to UGS. MPEG video conference and video streaming are examples of applica-tions supported by this class.

3. Non Real-time Polling Service (nrtPS) provides guarantees in terms

of throughput only and therefore best suits with applications as File Transfer Protocol.

4. Best Effort (BE) does not provide guarantee neither on delay nor

throughput and is therefore used for HTTP and e-mail.

1.3 Schedulers Design Factors

For a scheduling algorithm, to be efficient, it is desirable to possess the following features [2],[3]:

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Min Reserved Tolerated Max Request Traffic

Traffic Rate Jitter Latency Tx Policy Priority

UGS Yes Yes Yes Yes No

rtPS Yes No Yes Yes Yes

nrtPS Yes No No Yes Yes

BE No No No Yes Yes

Table 1.1: QoS requirements

• Efficient link utilization: resources should be assigned to users with

good channel conditions;

• QoS Guarantees: the scheduler must be able to assure the QoS

re-quirements for various service classes;

• Throughput Optimization: the algorithm should provide guaranteed

short-term throughput for error-free sessions and long-term through-put for all sessions;

• Fairness: on the short-term, sessions with higher priority and better

channel conditions are furthered but, on the long-term, all sessions should receive resources to transmit;

• Scalability: the algorithm should operate efficiently as the number of

sessions sharing the channel increases;

• Implementation complexity: a low-complexity algorithm is a necessity

in high-speed networks in which scheduling decisions have to be made very rapidly.

1.4 Classification of Schedulers

Over the last fifteen years hundreds of scheduling algorithms have been published and it would be hard, if not infeasible, to find a way to exactly group them. In [3], however, a survey on the recent scheduler proposals

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for multi-carrier wireless systems, such as IEEE 802.16e, classifies schedul-ing techniques in two main categories: channel-unaware and channel-aware schedulers (see fig.1.3). Basically, the channel-unaware schedulers use no

Figure 1.3: Schedulers Classification

information of the channel state condition in making the scheduling deci-sion, assuming it error-free since it makes easier to prove assurance of QoS. However, in wireless environment where there is a high variability of radio link such as signal attenuation, fading, interference and noise, the channel-awareness is important. Ideally, scheduler designers should take into account the channel condition in order to optimally and efficiently make the alloca-tion decision.

1.4.1 Channel-Unaware Schedulers

Round Robin: it fairly assigns the allocation one by one to all connec-tions in a repeated periodic order. The fairness consideraconnec-tions need to include whether allocation is for a given number of packets or a given number of bytes. With packet based allocation, stations with larger packets have an unfair advantage, causing scheduling starvation. An-other version, called Weighted Round Robin, makes use of weights to menage throughput and delay constraints.

Fair Queuing: given a certain data rate R, N active flows are served with a rate R/N. In this way, scheduling starvation is avoided and fairness

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is obtained. Yet, there is no differentiation in QoS and the throughput is low.

Weighted Fair Queuing: the assignation of a weight to each connection allows priorities differentiation. If wk is the weight assigned to flow k,

it would transmit with a rate R wk N

P

i=1wi

. The weights can rely on different parameters as queue length, packet delay, minimum reserved rate etc.

Delay-based Algorithms: this set of algorithms is specifically designed for real-time traffic such as rtPS or UGS, for which the delay bound is the primary QoS parameter. Some examples are the Largest Weight Delay First [4] and Delay Threshold Priority Queuing [5].

Priority-based Algorithms: these algorithm, such as [6], are employed in order to guarantee the QoS to different classes of service. For example, the priority order can be: UGS, ertPS, rtPS, nrtPS and BE, respec-tively. Or, packets with the largest delay can be considered at the highest priority. An unwanted effect can be the scheduling starvation and a low throughput.

1.4.2 Channel-Aware Schedulers

The channel-aware schedulers can be classified into five classes according to the aim they pursue, which is described by the objective function.

Maximum Sum Rate Algorithm

The objective of the Maximum Sum Rate (MSR) algorithm is to maximize the sum rate of all users, given a total transmit power constraint. This algorithm is optimal if the goal is to get as much data as possible through the system.

Referring to fig. 1.2, the inputs required are the set of SINR perceived by each user, since they allow the calculation of the Shannon capacity. If

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function to maximize is: max PK k=1 N P n=1 BW N Log(1 + SIN Rk,n) s.t. PN n=1 K P k=1 P_k,l≤ P_max (1.1)

The sum capacity is maximized if the total throughput in each subcarrier is maximized. Hence, the max sum capacity optimization problem can be decoupled into N simpler problems, one for each subcarrier. The methods used to solve this problem are usually greedy optimization and water-filling power allocation.

Minimum Transmit Power

Another possible approach is to assign resources with the goal of minimizing the overall transmitted power in the system under different rate constraints for each user.

This is the approach developed for the OFDMA system in [7]. If P_k,nc is the power assigned to user k that transmits c bits on the n-th subcarrier and

γk,n=

(

1 if ck,n= c

0 otherwise (1.2)

is an indicator set to 1 if the subcarrier k is assigned to the user k (0 otherwise), the objective function is:

min γk,n K P k=1 N P n=1 C P c=1 Pc k,nγk,n for γk,n ∈ {0, 1} R_k= PM c=1 N P n=1 cγ_k,n for all k 0 ≤ PK k=1 M P c=1 γk,n≤ 1 for all n (1.3)

where Rk is the minimum rate guaranteed for k-th user.

The methods used to solve these algorithms are usually Integer Program-ming and Linear ProgramProgram-ming.

Maximum Fairness Algorithm

The maximum fairness algorithm aims at allocating subcarriers and power in such a way that the minimum users data rate is maximized. This essen-tially corresponds to equalizing the data rates of all users, hence the name

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Maximum Fairness. The Maximum Fairness algorithm can be referred to as a Max-Min problem, since the goal is to maximize the minimum data rate. The optimum subcarrier and power allocation is considerably more difficult to determine than in the MSR case because the objective function is not concave and, in particular, it is a NP-hard problem to simultaneously find the optimum subcarrier and power allocation. Therefore, low-complexity suboptimal algorithms are necessary, where subcarrier and power allocation are done separately.

Proportional Rate Constraints Algorithm

A weakness of the Maximum Fairness algorithm is that the rate distribution among users is not flexible. Further, the total throughput is largely limited by the user with the worst SINR, as most of the resources are allocated to that user, which is clearly suboptimal. In a wireless broadband network, it is likely that different users require application-specific data rates that vary substantially. A generalization of the Maximum Fairness algorithm is the Proportional Rate Constraints (PRC) algorithm, whose objective is to maximize the sum throughput, with the additional constraint that each users data rate is proportional to a set of pre-determined system parameters

{wk}K_k=1.

This is the approach adopted in [9]. If yn

k is the data rate of the k-th user

on the n-th subcarrier, Cn _{is the capacity of the subchannel n, x}n

k has the

same meaning of γ_k,nin 1.3, Pmaxis the total power limitation and pn_k(y_kn) is

the power needed to transmit on subcarrier n at data rate y_kn, the objective function is: max PK k=1 w_k(PN n=1 yn k) s.t. PN n=1 K P k=1 pn k(ykn) ≤ Pmax (a) 0 ≤ yn k ≤ xnkCn (b) K P k=1 xn k ≤ 1 (c) xn k ∈ {0, 1} (d) (1.4)

Constraint (a) denotes that the total allocated power is not more than the total power limitation. Constraint (b) denotes that the allocated rate in a

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subcarrier should be between the lower bound 0 and upper bound Cn _of

the subcarrier. Constraints (c) and (d) ensure that the number of users allocated in a subcarrier is at most one in a scheduling period.

The PRC optimization problem is also generally very difficult to solve di-rectly, since it involves both continuous variables pn

k(ynk) and binary variables xn

k , and the feasible set is not convex. As for the Maximum Fairness case, a

prudent approach is to separate the subcarrier and power allocation proce-dure, and to settle for a near-optimal subcarrier and power allocation that can be achieved with manageable complexity. In fact, the method used to solve this algorithm in [9] is a suboptimal one, called Lagrangian Heuristic.

Proportional Fairness Scheduling

The algorithms discussed so far attempt to instantaneously achieve an ob-jective like the total sum throughput, equal data rates amongst all users, or pre-set proportional rates for each user. Alternatively, one could attempt to achieve such objectives over time, which provides significant additional flexibility to scheduling algorithms. In this case, in addition to throughput and fairness, a third element enters the trade-off, which is latency.

Let Rk(t) denotes the instantaneous data rate that user k can achieve at

time t, and T_k(t) be the average throughput for user k up to time slot t. The proportional fairness scheduler selects the user, denoted as k∗_{, with the}

highest R_k(t)/T_k(t) for transmission. In the long-term, this is equivalent to selecting the user with the highest instantaneous rate relative to its mean rate. The average throughput Tk(t) for all users is then updated according

to: T_k(t + 1) =    ³ 1 − 1 tc ´ T_k(t) + 1 tcRk(t) if k = k ∗ ³ 1 −_t1_c ´ Tk(t) if k 6= k∗ (1.5)

Parameter tc controls the latency of the system. If tc is large, then the

la-tency increases, with the benefit of higher sum throughput. If tcis small, the

latency decreases since the average throughout values change more quickly, at the expense of sum throughput.

Although the Proportional Fairness scheduler was originally designed for a single channel time-slotted system, it can be adapted to an OFDMA system

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by treating each subcarrier independently. In an OFDMA system, due to the multiple parallel subcarriers in the frequency domain, multiple users can transmit on different subcarriers simultaneously. Let Rk(t, n) be the

sup-portable data rate for user k in subcarrier n at time slot t. Then for each subcarrier, the user with the largest R_k(t, n)/T_k(t) is selected for transmis-sion. Let Ωk(t) denote the set of subcarriers in which user k is scheduled for

transmission at time slot t. Then the average user throughput is updated as: Tk(t + 1) = µ 1 − 1 tc ¶ Tk(t) +_t1 c X n∈Ωk Rk(t, n) (1.6)

for k = 1, ..., K. An implementation of PF for IEEE 802.16 networks is proposed in [9], where QoS is taken into account. This is realized assigning different values to the temporal window tc according to the QoS of each

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Chapter 2

System Overview

The goal of this thesis is to find a suitable scheduling strategy for the system described in [46]. Thus, prior to analyze the scheduling algorithm adopted, in the reminder of this chapter an overview of the above mentioned system is provided and an extent to the multiuser environment is proposed.

2.1 System Features

Recently, the use of wireless equipments and their standards for mobile com-munication has steadily increased worldwide. There are still new emerging applications and needs that demand high data rate. The so called fourth gen-eration (4G) aims at guarantee throughput rates of more than 100 MBit/s for outdoor traffic and 1 GBit/s for indoor traffic (see [10] for example). However, due to

• harsh multipath propagation conditions experienced at high data rates in both urban indoor and outdoor scenarios,

• lack of continuous large segments of spectrum,

an efficient use of the available bandwidth and a reliable transmission scheme become a crucial task for the design of next generation wireless systems. Therefore, the spectral efficiency of future communications is expected to increase significantly compared to the state of the art. The focus of next generation systems can be highlighted by the need of high spectral efficiency in combination with high flexibility for packet data traffic.

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In order to satisfy the aforementioned requirements, the recent stan-dardization bodies of WiMAX (Worldwide Interoperability for Microwave Access) and 3GPP/LTE (Long Term Evolution) include radio technology such as multicarrier (MC) modulation and multiple antenna based access scheme. In particular, MC modulation, in the form of Orthogonal Frequency Division Multiplexing (OFDM), efficiently uses the available spectrum and is very robust to typical mobile radio multipath environment.

To further increase the system robustness against the trouble arising from the wireless propagation channels, an efficient modulation scheme has to be combined, however, with a powerful and efficient channel coding tech-nique. This is the case of BICM, which was first proposed in 1992 by Zehavi as a pragmatic coding scheme for bandwidth-efficient communications [14] and, later, theoretically characterized by Caire, Taricco and Biglieri in [15]. BICM technique is based on the insertion of a bit-interleaver between the channel encoder and the modulator in order to increase the diversity order. The seminal works of and Tarokh [16], Foschini [17] and Telatar [18] proved that the spectral efficiency as well as the reliability of the wireless link can be dramatically improved by employing Multiple Input Multiple Output (MIMO) techniques. Signaling schemes exploiting the spatial domain to improve both reliability and throughput of wireless systems are commonly named space-time codes (STC) [16]. The STC performance improvement can be essentially accomplished by:

1. exploiting the diversity in space, for instance through space-time block

coding (STBC) or space-frequency multiplexing coding (SFMC), so as

to enhance link reliability against the variations in signal level induced by fading;

2. simultaneously transmitting parallel data streams, the so-called spatial

multiplexing (SM), in order to boost the data throughput and increase

spectral efficiency.

The above-mentioned concepts can also be successfully combined together leading to MIMO BIC-OFDM systems.

Finally, for a flexible and efficient use of the available bandwidth, besides the aforementioned modulation and coding techniques, MAC and PHY layer

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supporting flexible IP transmission are required. In order to guarantee a re-liable packet transmission, error handling and recovery policies such as chase combining (CC) or incremental redundancy (IR) HARQ must be supported.

2.1.1 Link Resource Adaptation

Link adaptation to varying radio channel conditions is nowadays one of the key technologies required for efficient use of the available spectrum. When a system does not adapt the transmission parameters to the actual channel conditions, the designer must consider a fixed link margin to maintain ac-ceptable performance also in the worst case channel condition. As apparent, this strategy leads to a very inefficient utilization of the channel. Of course, the basic premise is to estimate the channel at the receiver and feed back to the transmitter link quality information based on the estimate.

There are many parameters that can be varied at the transmitter according to the current channel status, such as

• data rate,

• coding rate/scheme,

• power distribution among the subchannels,

• space-time coding.

In order to further improve the link performance, all these adaptive tech-niques can be combined to design most powerful hybrid techtech-niques which jointly adapt multiple system parameters.

Adaptive Modulation Technique

In variable-rate modulation the data rate is varied relative to the channel gain. This can be done by fixing the symbol rate of the modulation and using multiple modulation schemes or constellation sizes. In this work we consider variable rate QAM transmission, where the number of QAM levels is varied according to the channel status and the quality criteria adopted [19].

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Adaptive Coding Technique

In adaptive coding different channel codes are used to provide different amounts of coding gain to the transmitted bits. For example a stronger error correction code may be used for harsh propagation conditions, while a weaker code may be used for favorable channel conditions. The imple-mentation used in this system for adaptive coding is called rate-compatible punctured convolutional (RCPC) codes [20], which consists of a family of convolutional codes at different code rates R. The basic premise of RCPC codes is to have a single encoder and decoder whose error correction capabil-ity can be modified by not transmitting certain coded bits (e.g. puncturing the code). Moreover, RCPC codes have a rate-compatibility constraint so that the coded bits associated with a high-rate (weaker) code are also used by all lower-rate (stronger) codes . Thus, to increase the error correction capability of the code, the coded bits of the weakest code are transmitted along with additional coded bits to achieve the desired level of error correc-tion. The rate compatibility makes it very easy to adapt the error protection of the code, since the same encoder and decoder are used for all codes in the RCPC family, with puncturing at the transmitter to achieve the desired error correction. Decoding is performed by a Viterbi algorithm operating on the trellis associated with the lowest rate code, with the puncturing in-corporated into the branch metrics.

Adaptive coding can also be combined with adaptive modulation as a hy-brid technique, which takes the name of Adaptive Modulation and Coding (AMC).

Adaptive Space-Time Coding Technique

Multiple antenna approach is a powerful way to improve the wireless system performance. Multiple antennas were traditionally used to combat fading impairments by exploiting multiple independent paths between transmitting and receiving antennas. Nevertheless, fading can be also viewed as a bene-ficial effect in a MIMO channel context; in fact, if the path gains between individual transmit-receive antenna pairs fade independently, multiple par-allel spatial channels are created from the channel matrix. By transmitting

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independent information streams in parallel through the spatial channels, the data rate can be increased at the price of poor error rate performance. This effect is called spatial multiplexing and it is suitable in the high SNR regime. In summary, MIMO systems can supply two types of gain: diversity

gain and spatial multiplexing gain. Every MIMO channel can provide both

gains simultaneously and hence, there is a fundamental tradeoff between how much of each type of gain can be extract by any coding scheme. In a block fading channel, an expression of optimum diversity gain as function of spatial multiplexing gain is provided in [21] as optimum tradeoff curve. This allows to create a series of intermediate space-time coding configu-rations limited by two extreme points: full diversity and full multiplexing gain respectively. Every configuration or MIMO option represents the best solution in a particular channel condition. Therefore, adaptive space/time coding technique change antenna use to trade off diversity and multiplexing based on channel conditions, [22], [23], [24]. Thus, an additional degree of freedom in AMC can be represented by the space dimension, i.e., the use of multiple antennas at the transmitter and receiver.

Hybrid Technique

Hybrid techniques can adapt multiple parameters of the transmission scheme, such as data rate, channel coding, and space time coding. In this case joint optimization of the different adaptive techniques is used to optimize a given objective function. Rate adaptation is often combined with adaptive cod-ing in the adaptive modulation and codcod-ing technique. In a wider sense, AMC can include also other techniques such as adaptive space time cod-ing and power allocation techniques. Adaptive modulation and codcod-ing has been widely investigated in the literature and is currently used in the many standards for data transmission in wireless networks, [25].

2.2 The Radio-mobile Channel Model

In a radio-mobile scenario, signals experience several paths due to reflec-tion, scattering and, in general, to the high number of obstructs between transmitter and receiver: this phenomenon is called multipath fading and is

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represented by multiple versions of the received signal with different atten-uation, phase and delays arrive.

Fading can be either a good or a bad effect:

• in a Line-of-Sight (LOS) context, it can be a disadvantage since the signal replies can cause a destructive interference to the direct signal;

• in Non Line-of-Sight (NLOS) condition, reflections are essential and exploited to correctly receive the signal.

The characterization of a radio-mobile channel can be given by some param-eters: the number of paths N (t) at time t, the amplitude αn(t), the delay τn(t) and the phase φn(t) of the n-th path at time t (these are modeled as

in-dependent random process), the transmission frequency fcand the possible

presence of a path in LOS. The channel is thus modeled as a time-variant linear system:

c(t, τ ) = N (t)_X n=0

αn(t)e−jφn(t)δ(τ − τn(t)) (2.1)

where τ represents the temporal interval between the applied impulse and the generic observation instant t.

An important parameter to take into account is the delay spread, which measure the temporal distance between the first arriving path and the ar-riving last. This delay indeed produces a extension of the signal transmitted that can cause intersymbolic interference. Moreover, due to Doppler effect, the channel cause a spread also in frequency: relying on the relative speed between transmitter and receiver, each tone is affected by frequency trans-lation, called Doppler bandwidth:

β_f = v

λcos α (2.2)

where v is the mobile speed, λ is the wavelength and α is the angle between the wave propagation and the terminal shift. We can now give a general expression for the transmitted signal s(t) and the received signal r(t), in absence of noise: r(t) = Re (" N (t)_P n=1 αn(t)u(t − τn(t)) # ej(2πfc(t−τn(t))+φ_Dn) ) = Re (" N (t)_P n=1 α_n(t)e−jφn(t)_{u(t − τ} n(t)) # e−j2πfct ) _(2.3)

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φDn is the phase shift due to Doppler effect and then the phase shift for

each path due to Doppler effect and delay τn(t) is:

φn(t) = 2πfcτn(t) − φDn (2.4)

All this events that affect a radio-mobile signal can cause fading. In fact the phases φn(t) of the multiple versions of the signal can produce constructive

or destructive interferences which are unpredictable. Fading can be classified as:

• Long-term fading: the signal amplitude fluctuates relatively slowly,

due to shadowing of the LOS path and obstructs, when the terminal movements are bigger than the wavelength λ;

• Short-term fading: due to multipath, the signal amplitude varies quickly

around is its mean value for shift on the order of the wavelength λ;

• Slow fading: the channel characteristics varies after several signaling

interval;

• Fast fading: the channel characteristics varies within a signaling

in-terval;

• Frequency flat fading: the channel delay spread is negligible respect to

the signaling interval;

• Frequency selective fading: the channel delay spread is not negligible

respect to the signaling interval.

2.2.1 Static Channel Model

If the channel characteristics do not vary quickly in time, the channel is not selective in time and the model results:

c(τ ) = N X n=1 αne−jφnδ(τ − τn) = N X n=1 αnδ(τ − τn) (2.5)

Let consider the channel frequency response:

C(f ) = N

X

n=1

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and the delay spread:

Tm = max

n |τn− ¯τ | (2.7)

with ¯τ the average delay. If all the delays were equal (τn = ¯τ ∀n), |C(f )|

would be constant: C(f ) = e−j2πf τ N X n=1 αn (2.8) |C(f )| = | N X n=1 α_n| (2.9)

Thus, we can define the coherence bandwith of the channel the maximum frequency interval in which |C(f )| does not vary significantly, and it is:

Bc∝ _T1 m

(2.10)

A signal transmitted on channel |C(f )| is distorted if bandwith B of the former is bigger than the coherence bandwith Bc of the latter. We can now

differentiate multipath channels in two classes:

1. Frequency selective: if B > Bc (T > Tm) and then the frequency

components will experience different magnitudes of fading;

2. Frequency flat: if B < Bc(T << Tm) and then the frequency

compo-nents will experience the same magnitude of fading. where T is the signaling interval.

The effect of the static channel can be represented by a complex coefficient:

a = ρejφ = e−j2πfcτ N

X

n=1

αn (2.11)

which means that the signal is affected by an attenuation and a phase shift but that it is not distorted, r(t) = Re{as(t)ej2πfct_}.

2.2.2 Time Varying Channel Model

In the previous section, we assumed a_n and τ_nstatic in time. This assump-tion though is not valid in a radio-mobile scenario in which attenuaassump-tion and delays change with the mobile position, becoming function of time.

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of path N and exploiting the central limit theorem. In this way, a(t) can be considered a gaussian process with spectral density depending on the mobile speed. Clarke model describes a(t) as a zero mean gaussian process with independent real and imaginary components. The spectral density results:

Sac(f ) = Sas(f ) =    σ2 2πfD 1 √ 1−(f /fD)2 for − fD 6 f 6 fD 0 otherwise (2.12)

Analyzing eqn. 2.12, the inverse of the Doppler frequency fD results to be

the coherence time of the channel, which is to say the time over which the frequency response of the channel do not vary significantly. Thus, if the signal has a signaling time T , the number of signals in the coherence time is 1/f_DT and the channel produces:

1. slow fading: if 1/fDT >> 1, or, the channel amplitude response does

not vary for several signaling interval;

2. fast fading: if 1/fDT << 1.

2.2.3 Block Fading Channel Model

In packet transmission simulations, a slow fading channel model is usually assumed; we can suppose a constant a(t) for several signaling intervals or for all the entire packet transmission. It is equivalent to approximate a(t) with a step function and, in each step, a can be modeled as in eqn. 2.11, where ρ and φ are two random variables.

• ρ is a Rayleigh random variable if there is no LOS, otherwise it is

modeled as a Ricean random variable.

• φ is supposed to be uniformly distributed in [0,2π].

The channel assumed in this thesis is indeed the block fading one described above. The received signal can thus be expressed by:

r(t) = N

X

n=1

ans(t − nT ) (2.13)

where T is the signaling interval of the transmitted signal s(t), nT is the de-lay with whom the ray reach the receiver and anare the channel coefficients

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described in eqn. 2.11. This model is also referred as Tapped-delay-line

model.

Usually, the channel profile is given providing the number of the path N , the delay and the variance σ2

n ∆

= E|an|2 of the distortion coefficients on each

path. These profile are standard and refer to typical environments as Typi-cal Urban (TU), Hilly Terrain (HT), Rural Area (RA), etc.

In all the simulations conducted in this work, the channel power profile adopted is the TU reported in tab. 2.1 and represented in fig. 2.1.

σr 2 [dB] 0 -2 -4 -6 -8

Testcase - Channel Profile

Figure 2.1: Testcase - Channel Profile.

Path # Delay (µs) Relative Power (dB)

1 0 -3.3 2 50 0 3 100 -0.99 4 200 -1.5 5 250 -3 6 600 -9.40

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2.3 Overall Radio Access Processing

This section summarizes the radio access processing scheme adopted in this work, which is suitable for next generation wireless systems.

First of all, it is worth noting to point out that the packet-centric

vi-sion proposed in [10] is adopted. In this vivi-sion, the key design guideline is

the optimization toward the transport of packet defined as the fundamental piece of information to be communicated over the radio interface.

In order to satisfy the packet centric paradigm, the packet should be kept as an integral unit as far down in the protocol stack as possible. Conse-quently, as proposed in [10], we assume a one-to-one mapping of packets to retransmission units of the RLC protocol (RLC-PDU). Each RLC-PDU is characterized by a sequence number, the corresponding payload and the cyclic redundancy check (CRC). The next step in the packet-centric design is to map one RLC-PDU to exactly one FEC block. This peculiar structure allows an LRA strategy aimed at optimizing the delivery of packets since we are interested in the entire packet and not in the reception of a part of it. The main motivation for the packet centric process lies in its simpli-fied structure and its potential for an efficient cross-layer design by keeping packets as integral units.

In this context, in order to control the transmission errors to deliver error-free data to the users, ARQ (Automatic Repeat Request) [11] error handling and recovery policies are implemented. The advantage of obtaining high reli-ability in ARQ systems can be coupled with the advantage of Forward Error Correction (FEC) systems in order to provide a good throughput even in poor channel conditions. Such a system, called Hybrid ARQ (HARQ), is essentially a combination of Forward Error Correction (FEC) with ARQ, in an optimal manner. HARQ algorithms have now become an integral part of packet communication systems and a comprehensive understanding of how HARQ acts upon the system performance is crucial in designing an efficient LRA algorithm.

Furthermore, considering a multiuser environment, an adaptive system allocates (schedules) time, frequency and antenna resources based on channel

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quality and user requirements [12]. It enables efficient resource utilization and multiuser scheduling gains, when channels to different terminals fade independently. In systems based on time division multiple access/adaptive OFDM (TDMA/OFDMA), time-frequency resources, called chunks, are al-located to the individual users and link adaptation is performed individually in each chunk. The chunk size is chosen such that the channel is essentially flat in time and frequency. This provides a flexible small-scale granularity of the resources for multiuser scheduling and link adaptation, which makes it possible to obtain large multiuser diversity gains.

In the proposed system, each terminal predicts the signal-to-interference-and-noise ratio (SINR) over a major part of the total bandwidth. All active terminals report source coded SINR values or source coded suggested mod-ulation formats over a shared uplink control channel. A resource scheduler, located close to one or several radio access points, allocates finally the down-link resources in order to optimize the overall goodput (defined in sec.??) and satisfy the QoS requirements of each user as described further in this work.

2.3.1 Basic Resource Unit: Chunk

The basic time-frequency resource unit, chunk, consists of a rectangular time-frequency area that comprises a number of subsequent OFDM symbols and a number of adjacent subcarriers, and is allocated exclusively to one user data flow. Considering the system parameters listed in table 2.2 and the block fading channel described in §2.2.3, the dimension of a chunk is calculated as follows.

Centre Frequency 1.9 GHz

Number of Subcarriers 1024

Bandwith 20 MHz

OFDM Symbol Length (ex. CP) 51, 2µs

Cyclic Prefix 6, 4µs

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In order to find the number of subcarriers in a chunk, we have to com-pute the coherence bandwith of the channel, that is the frequency interval in which the frequency response of the channel is supposed constant. The channel profile adopted is the one listed in 2.1: Pn is the ray power and τ_n the relative delay with whom the ray is received. From these parame-ters, recalling the analysis developed in §2.2.3, we can calculate the channel attenuation coefficients an:

an=

p

Pn, (2.14)

the path weights:

w_n= a2n Np P n=1 a2 n (2.15)

and the average delay as

¯ τ = Np X n=1 wnτn. (2.16)

Finally, the delay standard deviation is computed as:

στ = v u u tXNp n=1 wn(τn− ¯τ )2 (2.17)

and the coherence bandwith is

B_c= 0.02/σ_τ. (2.18)

Thus, for the model assumed, Bc= 170KHz. Since the bandwith of a single

subcarrier is f_sp = 20·106

1024 = 19, 5KHz, the number of adjacent subcarriers

composing a chunk is:

N_sub= 170KHz

19, 5KHz = 8, 7 → 8 (2.19) Let now investigate the number of adjacent OFDM symbols that com-pose a chunk. Until the channel does not vary in time, the transmitter does not have to perform a new resources allocation. The coherence time of the channel is computed as:

Tc= 0.1_{v · f}c

0, (2.20)

where c = 3 · 108_{m/s is the speed of light, v is the mobile speed and f} 0

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v = 20m/s, which correspond to a vehicular speed, the coherence time is Tc= 750µs. Since the OFDM symbol length with CP is 57, 6µs, the number

of OFDM symbol transmitted in a chunk is:

Nsym= _SymbLengthTc = 12. (2.21)

In fig. 2.2 the structure of the chunk adopted in [12] is illustrated. A chunk contains payload symbols and pilot symbols. The feedback loops for the FDD system is designed to be as fast as possible, under realistic con-straints imposed by computation times and signaling delays, see [13] for more details. However, channel prediction is needed for scheduling and link adaptation, since extrapolating the present channel estimate would lead to large performance losses for vehicular users. Thus, in addition to channel estimation in coherent reception, the pilots are used for channel prediction for resource allocation and link adaptation. The chunks may also contain control symbols to minimize feedback delays, i.e. in-chunk control signaling. Anyway, in the simulation performed in this thesis, a chunk is supposed to be composed only by payload symbols.

Figure 2.2: Chunk Model

Based on channel measurements up to chunk time i, all active terminals predict the channel quality in all chunks within a sub-band of interest at the future chunk time i + 2. These reports are source-coded and transmitted

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on uplink control symbols within the uplink chunks at time i + 1. The appropriate MCS that could be used by each terminal in each chunk is then determined. The adaptive resource scheduler at the base station allocates each chunk at time i + 2 exclusively to one of the flows. The allocation is reported by control symbols placed within the allocated downlink chunks at time i + 2. The control symbols are all located on the same sub-carriers as the pilots to simplify use of them for decision-directed channel estimation.

2.3.2 MAC Architecture

The Radio Link Control (RLC), Medium Access Control (MAC) and Phys-ical (PHY) layer interactions are depicted in figure 2.3 where the overall radio access processing has been split into two main steps.

• Packet Processing: after attachment of CRC, each RLC-PDU is FEC encoded with an outer code, bit-interleaved and punctured to produce incremental redundancy for the later use by a Hybrid ARQ scheme. The encoded segments are queued per flow in the resource schedul-ing buffer. These queues are then drained with bit-level granularity. For each buffer, there is one resource scheduler that determines which queues are to be drained, and to what extent. The resource scheduler works on the time-scale of the chunk duration and try to perform an allocation that optimize the objective function described in §3.

• Frame Processing: the scheduled bits are mapped by adaptive cod-ing and modulation with bit-interleavcod-ing onto the physical channel resource units.

2.4 Single User SISO System Model

To better understand the OFDMA case, the system is first analyzed consid-ering only a single user. With reference to the block diagram depicted in fig. 2.4 and according to the radio access process outlined in §2.3, each RLC-PDU of N_b”information bits” (actually including also RLC-PDU overhead) is transmitted through L consecutive OFDM symbols, denoted in the sequel

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Figure 2.3: Simplified Model of the Overall Radio Access Processing

as frame. The information bits are first encoded by a convolutional coder, then punctured to obtain a certain code rate r. This process generates, for each RLC-PDU encoded, N_c= N∆ _b/r coded binary symbols (cbs), b_k, which are subsequently randomly interleaved. The bit-level interleaver randomly maps the generic coded binary symbol b_k into one of the label bits carried by the symbols of the OFDM subcarriers according to the notation shown below

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Figure 2.4: Single User SISO System Model

where Π(k)= {l∆ k, nk, ik} is the interleaver operation that maps the index k

of the cbs into a set of three coordinates:

1. lk, the position of the OFDM symbol within the frame; 2. n_k, the OFDM subcarrier number;

3. ik, the position of the cbs within the label of the QAM symbol on a

certain subcarrier.

The interleaver is assumed to be fully random so that the probability of mapping the generic coded binary symbol b_k (taken out of the available Nc)

into the ith label bit of the QAM symbol transmitted on the subcarrier n, into the lth OFDM block, denoted as c_l,n,i, with l = 1, . . . , L, n = 1, . . . , N and i = 1, . . . , m(n), is

Pr {bk→ cl,n,i}=∆ _N1

c, (2.23)

where m(n)_{denotes the number of cbs allocated on the subcarrier n.}

With reference to fig. 2.4, the cbs coming out of the interleaver are well or-dered by the Subcarrier Parser and ready to be Gray mapped onto M-QAM

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symbols, with M = 2∆ m _{and m ∈ {0, 2, 4, 6}. The 0 means no transmission.}

The M(n)_{-QAM signal set used in the n-th subcarrier, with M}(n) ∆

= 2m(n)

, is defined as χ(n) ∆

= {ξ(n)₁ , · · · , ξ_M(n)(n)} and it is determined by the bit loading

algorithm described in 3.3.2.

The symbols are suitably normalized such that:

¯ ξ2=∆ M_P(n) v=1 |ξ(n)v |2 M(n) = 1 (2.24)

The generic QAM data-bearing symbol xn

l ∈ χ(n) is sent on the n-th

sub-carrier during the l-th OFDM block and Exn l{|x

n

l|2} = ¯ξ2 = 1.

The average transmit power allocated the generic n-th subcarrier is P(n) ∆

=

p(n)S, where p(n) is a normalized power coefficient, 0 ≤ p(n) ≤ 1, and S is

the maximum average power value that can be allocated on each subcarrier. The average power per subcarrier is thus

¯ P = N P n=1 P(n) N ≤ S. (2.25)

Replacing the expression of P(n) _{in 2.25, we obtain the following constraint}

on the normalized power:

N

X

n=1

p(n)≤ N. (2.26)

The data-bearing QAM symbols are frequency mapped into the N available subcarriers using an Inverse Discrete Fourier Transform (IDFT) unit, which provides a sample every Ts seconds. A conventional cyclic prefix (CP) of

length Ncp samples is inserted at the beginning of each IDFT output block

to maintain the orthogonality between subcarriers and avoid interference between successive symbols. The resulting OFDM signal experiences a fre-quency selective fading channel which will be assumed stationary during the whole frame duration.

At the receiver side, the signal will go through the whole inverse OFDM processing in order to be coherently demodulated subchannel per subchan-nel, exploiting the channel estimation, which will be assumed perfect. From this channel estimation, the post-processing SNRs are derived, and

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besides the BICM metric evaluation and the Viterbi decoding, they are also used for making Link Adaptation at the next packet transmission.

Finally, the soft-demodulated metrics are deinterlived and the Log-Likelihood Ratios (LLRs) will feed a Viterbi decoder in order to obtain a ML estimation of the information bits, ˆuk, composing the RLC-PDU.

2.4.1 Post-processing SNRs Computation

In this section, we take advantage of the fact that the OFDM system can be represented as a set of parallel gaussian subchannels to state an analysis of it, which will be helpful for a further definition of a comprehensive Link Quality Metric (LQM). So, the post-processing SNRs for each subchannels are computed.

Let us now focus on the transmission of the generic coded binary symbol

bk. According to the notation outlined above, it is included into the label of

the QAM symbol xn

l ∈ χ(n). The expression of the sample relevant to the n_k-th subcarrier in the l_k-th OFDM block at the output of the DFT unit of the receiver is:

zn_l_k = A(n)xn_l + wn_l (2.27)

with

A(n)=pP(n)_H(n)₌

q

p(n)_SH(n)_. _(2.28)

H(n)_{is the complex-valued channel gain experienced on the n-th subcarrier}

and wn

l is a zero-mean unit-variance gaussian RV, representing the channel

noise contribution on the n-th subcarrier.

The instantaneous post-processing SNR relevant to the generic nth subchan-nel is then defined as:

γ(n) ∆= Ã ¯ ¯A(n)¯¯ σw(n) !₂ (2.29)

and we will refer at the set of all the post-processing SNRs as the vector:

γ =

n

γ(n)

o_N

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2.4.2 Adaptive BICM Paradigm and Bit Loading

When bit loading is not adopted by an adaptive GMC transmission scheme, the same modulation have to be transmitted over all the subcarriers, with the same power allocation as well. Anyway, for each packet transmission, based on the channel feedback, it can be possible to select a different modulation (e.g. M-QAM ) and a different code rate r. The combination of this two parameters is called Modulation and Coding scheme (MCS), or mode for short. The modes considered in our example are summarized in Table 2.3.

Mode Modulation Code Rate

1 4-QAM 1/2 2 4-QAM 2/3 3 4-QAM 3/4 4 4-QAM 5/6 5 16-QAM 1/2 6 16-QAM 2/3 7 16-QAM 3/4 8 16-QAM 5/6 9 64-QAM 1/2 10 64-QAM 2/3 11 64-QAM 3/4 12 64-QAM 5/6

Table 2.3: Supported MCS without bit loading.

With reference to fig. 2.5, the FEC block can be concatenated with a single M-QAM mapper, through a bit-level interleaver, being the modula-tion constrained to be the same for each subcarrier. Nonetheless, the more general scheme depicted in fig. 2.4 is still valid. M-QAM modulation with Gray mapping is used in order to minimize the number of bit errors in every channel symbol error event.

The considered system operates with a feedforward, punctured, 64-state convolutional encoder, with mother code rate r = 1/2 and df ree = 10, whose

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Figure 2.5: Adaptive BICM Paradigm - Mode selection.

polynomial generators are:

g1 = 1338 = 1011011

g2 = 1718 = 1111001 (2.31)

Different code rates have been obtained from the mother convolutional code, by making use of the puncturing patterns shown in Table 2.4.

For the termination of convolutional code, there are three possibilities:

• Truncation: encoding is terminated with the last bit of the message

and the encoder terminates in a state which is not known at the re-ceiver side. This option provides a bad protection of the last bits of the message, leading to an error floor, and should therefore be avoided.

• Zero-termination: after encoding of the message, some tails bits are

appended which drive the encoder state to zero. Here, we have the same protection for all the bits of the message, but, some extra bits, for driving the encoder state to zero, are required.

• Tail-biting: the initial state is chosen such that it coincides with the

final state. This is the chosen solution, because it combines the ad-vantage of the two previous methods, that is, all the bits are protected equally and the code rate is been maintained.

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Code rate Puncturing matrix df ree 1/2 P = " 1 1 # 10 2/3 P = " 1 1 1 0 # 6 3/4 P = " 1 1 0 1 0 1 # 5 5/6 P = " 1 1 0 1 0 1 0 1 0 1 # 4

Table 2.4: Puncturing matrices.

5 4 3 2 1 0 GP (bits/subcarrier) 40 30 20 10 0 Es/N0 (dB) 'Mode 1' 'Mode 2' 'Mode 3' 'Mode 4' 'Mode 5' 'Mode 6' 'Mode 7' 'Mode 8' 'Mode 9' 'Mode 10' 'Mode 11' 'Mode 12'

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In fig. 2.6, the average goodput per subcarrier, which will be exactly defined in ??, is shown for the MCS described above.

The main system parameters adopted in the simulation are displayed on Table 2.5.

Testcase

System Channel Bandwidth (MHz) 20 Number of used subcarrier 64 Subcarrier spacing (MHz) 312.5 Cyclic prefix (µs) 0.8 OFDM Symbol duration (µs) 4

Table 2.5: Main Parameters of the OFDM system simulated.

Each of the 12 curves is obtained by transmitting 10000 packets, made of N_b = 1024 payload bits and N_h = 32 header bits, with the respective MCS. Each multipath channel realization is modeled as a 6-taps independent Rayleigh RVs and will be assumed stationary for the whole frame duration. The channel power profile is the one described in §2.2.3.

The transmitter hence will choose the MCS which, for the particular channel realization experienced, will optimize the expected goodput. The information on the channel state rely on some feedback information, ad-dressed as LQM in figure 2.4. The particular LQM exploited will be exposed in the ??.

An improvement if the BICM paradigm is an AMC scheme which does not assign the same modulation over all the subcarriers but rather try to optimize the expected goodput assigning to the subcarriers also different modulations. Thus, for each subcarrier n, it is possible to transmit a deter-mined number of bits, m(n)_{, belonging to a finite set M . In the this system}

three possible constellations are considered: 4-QAM, 16-QAM, 64-QAM to-gether with the no transmission (0), that is:

M = {0, 2, 4, 6} (2.32)

Though, when bit loading is adopted, a single LQM value will not be enough to obtain a full adaptation, so the entire post-processing SNR vector might

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be sent at the transmitter.

The improvements, adopting a bit loading algorithm, are shown in fig. 2.7

4 3 2 1 0 GP(bit/subcarrier) 40 30 20 10 0 Es/N0 (dB) Static Modes

Bit Loading Algorithm

Figure 2.7: Bit loading vs. 12 static modes: goodput performance.

2.4.3 Hybrid Automatic Repeat Request (HARQ)

A significant issue in the design of wireless communication systems support-ing reliable data transmission is how to control the transmission errors in order to deliver error-free data to the users. To this respect, error handling and recovery policies are implemented by resorting to a joint use of powerful error correcting and/or detection schemes with retransmission of corrupted data, which is commonly referred to as ARQ (Automatic Repeat Request) [11].

Before showing the advanced ARQ techniques employed in the system an-alyzed in this work, the three basic types of ARQ schemes are here briefly described:

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for an acknowledgment for that frame before transmitting again. If a negative acknowledgment (NAK) is received, the same frame is sent again. If positive acknowledgment (ACK) is received, the next frame is sent.

• Go-back-N. The transmitter sends frames continuously: N frames are

sent during a round-trip time, which is defined as the time interval between the transmission of a frame and the reception of an acknowl-edgment for that frame. When a NAK is received for a frame, the transmitter sends that frame again as well as the N − 1 succeeding frames. At the receiver side, when a frame is detected in error, the receiver sends a NAK to the transmitter, and discards that frame as well as the subsequently N − 1 received frames.

• Selective-repeat. The frames are also transmitted continuously.

How-ever, the transmitter only retransmits the frame for which a NAK was received. A sufficiently large buffer must be provided at the receiver side to deliver the frames in correct order to the user.

ARQ systems are simple, easy to implement, and provide high system reliability. However they suffer from a severe decrease in throughput when the channel error rate increases. The advantage of obtaining high reliability in ARQ systems can be coupled with the advantage of Forward Error Cor-rection (FEC) systems in order to provide a good throughput even in poor channel conditions. Such a system is called Hybrid ARQ (HARQ).

When HARQ is used, each erroneously received packet, instead of being discarded, is stored at the receivers, and then combined with retransmit-ted copies. Two well-known types of HARQ are Chase Combining (CC, also known as Type I) [26] and Incremental Redundancy (IR, also known as Type II) [27]. In literature a variant of the latter HARQ scheme is presented—the Partial IR, also known as Type III [26].

Chase Combining HARQ

In Type-I HARQ scheme, a coded packet is transmitted initially and if the packet is found to be affected by errors, usually through the use of

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Cyclic Redundancy Check (CRC), a retransmission request in the form of no-acknowledgment (NACK) is fed-back to the transmitter. Upon reception of this NACK, the transmitter sends the same coded packet again. If the receiver is capable of buffering previously received signals, the optimal so-lution is to combine these multiple signals according to the maximal ratio combining (MRC) principle, which was first discussed by Chase [28]. Incremental Redundancy HARQ

In the Type-II HARQ scheme, when a NACK is received, instead of sending the same coded packets, the transmitter tries to construct and send only additional coded parities.

Partial Incremental Redundancy HARQ

For IR scheme, instead of multiple-transmission of the initial codeword, also new and not-yet-used coded symbol are transmitted when an decoding error occurs, decreasing the coding rate. In type-III HARQ scheme, or variant IR, self-decodability is imposed for each retransmission. Generally speaking, the not-yet-used coded symbols add redundancy while the already sent symbols increase the itself likelihood metric, in fact the retransmitted packet can be Chase-combined with the previous packets to increase the diversity gain. The selection of different coded version of the same packet is accomplished by a using different puncturing pattern, as shown in figure 2.8.

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2.5 Single User MIMO System Model

As described in sec. 2.1.1 MIMO technology is a key breakthrough in wireless communication, enhancing link reliability and/or data rate without requir-ing additional frequency bandwidth.

The MIMO BIC-OFDM system is depicted in fig. 2.9 and the new devices are described below.

Figure 2.9: Single User MIMO System Model

The encoder, interleaver and mapper perform the same operations than the SISO case, save that now one more coordinate must be considered, or, the spatial stream. In fact, in eqn. 2.22, Π(k) = {l∆ _k, n_k, q_k, i_k} where q_k

is the spatial stream relevant to the selected subcarrier. From now on, we refer as subchannel the pair of subcarrier and spatial stream (n, q).

The interleaver is assumed to be fully random so that the probability of mapping the generic coded binary symbol bk (taken out of the available Nc)

into the ith label bit of the symbol transmitted on the subchannel (n, q), into the lth OFDM block, denoted as cl,n,q,i, with l = 1, . . . , L, n = 1, . . . , N ,

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q = 1, . . . , Ns, and i = 1, . . . , m(n,q), is

Pr {bk→ cl,n,q,i}=∆ _N1

c, (2.33)

where m(n,q) _{denotes the number of bits transmitted on the subchannel}

(n, q).

On the subchannel (n, q), m(n,q) _{interleaved bits are Gray mapped into a} M(n,q)_{-QAM signal set denoted with χ}(n,q)_.

The symbol vector x(n)_l = [x∆ (n,1)_l , x(n,2)_l , · · · , x(n,Ns)

l ] is space/time encoded

according to the particular MIMO scheme and transmitted on the nth sub-carrier, where x(n,q)_l ∈ χ(n,q)_{. The available RF bandwidth of the MIMO}

sys-tem is split into N subcarriers where the input/output (I/O) relationship is described by the complex matrix H ∈ CNt×Nr_{, being N}

tand Nr the number

of transmit and receive antennas, respectively. The transmit power matrix allocated to the generic nth subcarrier is P(n)= S D∆ ¡p(n,1)_{, p}(n,2)_{, · · · , p}(n,Ns)¢_,

where p(n,q) _{is a power coefficient such that}

P =∆ P_N n=1Tr ³ P(n) ´ N Nt ≤ S, (2.34)

and S is the maximum value of the average power.

The data-bearing QAM symbols are frequency mapped into the N available subcarriers using an Inverse Discrete Fourier Transform (IDFT) unit, and a cyclic prefix of length N_cp is inserted. The resulting OFDM signal experi-ences a frequency selective fading channel which will be assumed stationary during the whole frame duration.

For a given multiple antenna setting, various transmission scheme can be considered. The system considered here encompasses a full-range of MIMO technology, including:

• Space-Time Block Code (STBC). Transmit diversity, such as Alam-outi code [35] is supported to provide spatial diversity and increase robustness.

• Spatial Multiplexing (SM). SM is supported to take advantage of higher peak rates and increased throughput.

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• SVD precoding/decoding. Assuming CSI available at both the trans-mitter and the receiver side, it is possible to separate the MIMO chan-nel into parallel subchanchan-nels through singular value decomposition (SVD) [36]. This techniques, which is also called multiple beamform-ing (MB) when combined together with BICM [37], can be easily as-sociated with OFDM thanks to the equivalent parallel channel model. With SVD precoding/decoding, diversity and spatial multiplexing gain can be trading off by exploiting only the largest Ns eigenvalues of the

channel matrix.

At the receiver side, the samples are collected into blocks of size N +Ncp.

After CP removal, they are transformed by a DFT unit of size N . The channel estimation now computes the MIMO CSI which can be used to predict the performance of the next packet transmission whereas the STF decoder uses the MIMO CSI to separate different source signals. These signals are then soft demodulated, deinterleaved and decoded.

Post-processing SNRs computation

MIMO-OFDM system can be represented as a set of parallel gaussian sub-channels where per-channel SNRs depend on the particular STC considered. In order to provide a unified analysis which could help in the definition of a comprehensive link performance model, per-channel post processing SNRs for each considered MIMO scheme are computed.

According to the notations outlined above, after interleaving and modula-tion mapping, the binary coded symbol is included into the label of the QAM symbol x(nk,qk)

lk . We can thus express the sample relevant to the

sub-channel (nk, qk) in the lkth OFDM block at the output of the DFT unit of

the receiver as z(nk,qk) lk = A (nk,qk)_x(nk,qk) lk + w (nk,qk) lk , (2.35)

where A(nk,qk) _{is the post-processing channel gain experienced on the}

sub-channel (n_k, q_k), which depends on the particular MIMO scheme selected, and w(nk,qk)

lk is a Gaussian RV with variance σ

(nk,qk) w

2

representing, in general, the noise plus interstream interference contribution on the (n_k, q_k) subchan-nel.

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The istantaneous post processing SNR values relevant to the generic sub-channel (n, q) is then defined as

γ(n,q)=∆ Ã |A(n,q)_| σw(n,q) !₂ (2.36)

Resorting to a vectorial notation, the I/O relationship relevant to the n_kth subcarrier of the lkth MIMO-OFDM block can be expressed as

z(nk) lk = A (nk)_x(nk) lk + w (nk) lk (2.37)

where A is a complex diagonal matrix defined as A(nk) _{= D(A}∆ (nk,1)_{, · · · , A}(nk,Ns)_),

while the noise vector is w(nk) lk ∆ = [w(nk,1) lk , · · · , w (nk,Ns) lk ] T_.

2.6 Multiuser System Model

In a multiuser scenario u RLC-PDU, with u = 1, ..., U , can be transmitted per frame. Each RLC-PDU of Nb information bits is encoded with a code

rate Ru(according to the link adaptation strategy) and bit-level interleaved,

as described in 2.3. The scheduler then assigns to the u users the chunks on which they can transmit, according to the scheduling strategy outlined in chapter ??.

Let define au the on/off vector composed by Nc elements, where Nc is the

total number of chunks available in a scheduling period. The element au(n)

is set to 1 if the scheduler allows the u-th user to transmit on the chunk n, 0 otherwise. Each chunk is assigned to only one user every scheduling period, so that:

U

X

u=1

D(au) = I[NcxNc] (2.38)

Thus, considering a single antenna system and a chunk composed by only one subcarrier (Nc= N where N is the total number of subcarriers) in order

to simplify the notation, each user transmits his QAM symbols on the sub-carriers assigned and the QAM scheduled symbol vector can be expressed by xs l,u ∆ = n au(n)xn_l,u o_N n=1where x n

l,uis the QAM symbol on the n-th subcarrier