5.1 Introduction

The past decade has witnessed significant advances in the design of MTs and the offered communication services for mobile users. In particular, MTs are currently equipped with processing and display capabilities that enable them to support voice, video and data calls. In addition, MTs are capable of establishing simultaneous communications with BSs and APs of different networks, through multiple radio interfaces and using the multi-homing feature [154]. Utilizing multiple radio interfaces of an MT to support video or data transmission through multi-homing service can improve service quality in many aspects [155, 156]. Transmitting (data or video) packets over multiple networks (i) increases the amount of aggregate bandwidth available for the application, (ii) reduces the correlation between consecutive packet losses due to transmission errors or network congestion and (iii) allows for mobility support as it can reduce the probability of an outage when a communication link is lost with the current serving network as the user moves out of its coverage area [25].

Such an advancement in wireless services results, however, in high energy consumption for the MTs. It has been shown that there exists an exponential increase in the gap between the MT demand for energy and the offered battery capacity [24]. The operational time of an MT in between battery chargings is considered to be a significant factor in the user-perceived QoS [25, 157, 158]. Besides developing new battery technology with improved capacity, the operational period of an MT between battery chargings can be extended by managing its energy consumption [159]. Consequently, energy-efficient (green) communication techniques have been proposed as a promising solution to regulate the MT energy usage while satisfying the user-required QoS. In this context, the unique characteristics of the targetapplication should be accounted for while designing such green communication techniques.

In general, the key difference between video and data calls is the impact of the allocated resources on the call presence in the system [160]. For video calls, the amount of the allocated resources influences the perceived video quality experienced on the video terminal, while it does not affect the video call duration. On the contrary, the resource allocation to a data call affects its throughput and thus its duration. Consequently, for data calls, the objective is to maximize the achieved throughput at a reduced energy consumption for the MT. This is equivalent to maximizing the resulting energy efficiency as expressed by (1.28)–(1.32) while satisfying a target data rate for the MT. On the contrary, for video calls, maximizing throughput does not necessarily improve the resulting video quality. If video packets are not properly scheduled for transmission, they might miss their playback deadline, which consequently degrades the achieved video quality. As a result, for video calls, the main objective is to schedule video packets in a way that maximizes the resulting video quality while accounting for the MT battery energy limitation.

In this chapter, we present two radio resource allocation mechanisms that support green multi-homing data and video calls [54, 161]. The next section deals with developing green multi-homing radio resource allocation for data calls based on fractional programming [54] while Section 5.3 investigates developing a green multi-homing resource allocation mechanism for video calls based on a statistical quality guarantee [161].

5.2 Green Multi-homing Uplink Resource Allocation for Data Calls

The main limitation of the existing uplink multi-homing green radio resource allocation mechanisms for data calls in a heterogeneous wireless medium is that these solutions focus only on optimal power allocation to different radio interfaces of the MT, given an allocated bandwidth. Hence, the main focus so far is on exploiting the diversity in fading channels and propagation losses between the MT and different BSs/APs to enhance the uplink energy efficiency. However, further improvement can be achieved by exploiting the disparity in available radio resources at the BSs/APs of different networks. This calls for a joint optimization framework for bandwidth and power allocation to maximize uplink energy efficiency for a set of MTs with multi-homing capabilities. Furthermore, the existing resource aggregation schemes (e.g. carrier aggregation in LTE-advanced [134, 162, 163]) assume the scenario where all resources belong to the same service provider. Hence, centralized resource allocation schemes can be adopted. On the contrary, in a heterogeneous networking environment, the aggregated resources are operated by different service providers. Hence, novel decentralized mechanisms should be investigated to enable coordination among MTsand BSs/APs of different networks to satisfy the target QoS in an energy-efficient manner.

In this section, we present a QoS-based optimization framework for joint uplink bandwidth and power allocation to maximize energy efficiency for MTs in a heterogeneous wireless medium [54]. The heterogeneity of the wireless medium is captured in the problem formulation, in terms of different service areas, channel conditions, available radio resources at BSs/APs of different networks and different maximum transmit powers at the MTs. The energy-efficient uplink communication problem is formulated to jointly allocate uplink transmission bandwidth and power to a set of MTs, with minimum required QoS and multi-homing capabilities, from a set of BSs/APs with overlapped coverage. In dealing with a multi-user system, the objective is to maximize the performance of an MT that achieves the minimum energy efficiency.

A geographical region is considered where a set of wireless networks is available, as shown in Figure 5.1. Different networks are operated in separate frequency bands by different service providers, and consequently, no interference exists among these networks. In particular, the set contains cellular networks with heterogeneous cell sizes (e.g. macro, pico and femto cells) and overlapped coverage areas. Each network has a set of BSs/APs in the geographical region. Interference management schemes (e.g. soft frequency reuse [138–141]) are implemented for interference mitigation among BSs/APs within the same network. Due to the overlapped coverage from BSs/APs of different networks, the geographical region is partitioned into a set of service areas. A unique subset of BSs/APs covers each service area. The total bandwidth available at network BS/AP is denoted by . A cooperative networking scenario is considered where different networks in cooperate in radio resource allocation through signalling exchange over a backbone [1].

A set of MTs perform uplink multi-homing data transmission in the geographical region. Let denote the subset of MTs which lie in the coverage area of network BS/AP . Using the multiple radio interfaces and through the multi-homing capability, each MT can communicate with multiple BSs/APs simultaneously. The bandwidth allocated on the uplink from network BS/AP to MT is denoted by , where for .¹ Let represent the transmission power allocated by MT to its radio interface that communicates with network BS/AP . Denote by the power amplifier efficiency. Hence, the MT transmission power consumption at each radio interface is given by [16]. The MT circuit power consumption for each radio interface consists of two components. The first component is a fixed circuit power consumption for each MT radio interface, and it captures the power consumption of the RF chain, that is, digital-to-analog converter, RF filter, local oscillator and mixer. The second component is a dynamic part that refers to the digital circuit power consumption and scales with the allocated transmission bandwidth (as bandwidth increases, more computations and baseband processing are required). The dynamic component is expressed as [53]

5.1

where denotes the reference digital circuit power consumption for a reference bandwidth and is a proportionality constant. For , . Denote by and by . Hence, the MT total power consumption for each radio interface is given by

5.2

Due to technology limitations, each MT radio interface has a maximum transmission power . The maximum power constraint at MT is given by . The MT target service quality can be obtained using the minimum data rate for MT .

The channel power gain between MT and network BS/AP is denoted by , and it captures both the wireless channel Rayleigh fading and path loss. Let denote the distance between MT and network BS/AP . The associated path loss is given by , where is the path-loss exponent. Let be a Rayleigh random variable associated with the link between MT and network BS/AP . The channel power gain between MT and network BS/AP is given by

5.3

The one-sided noise power spectral density is denoted by .

5.2.1 Optimal Green Uplink Radio Resource Allocation with QoS Guarantee

According to Shannon formula, the data rate achieved by MT using the radio interface communicating with network BS/AP is given by

5.4

The total achieved data rate by MT is , which should satisfy the required QoS, that is,

5.5

The total allocated bandwidth by network BS/AP should not be larger than the total available bandwidth, that is,

5.6

Given the technical limitation on the maximum transmission power for each radio interface, we have

5.7

The MT total power consumption includes both data transmission and circuit power consumption for all active radio interfaces, that is, for MT , . The total power consumption for MT , , should satisfy the MT maximum power constraint, that is,

5.8

Define the energy efficiency of MT , , as the ratio of the total achieved data rate to the total power consumption, that is, . The objective is to maximize the minimum achieved energy efficiency for . This is obtained through joint bandwidth and power allocation from all networks in to all MTs in , while satisfying the required minimum transmission rates and the total bandwidth and power constraints. Hence, the problem is formulated as

5.9

Problem (5.9) is classified as a max–min fractional program [164]. The optimization problem (5.9) is a concave–convex fractional program, since the numerator of , that is, , is concave, thedenominator is convex and the constraints constitute a convex set in and [54]. In order to solve (5.9), the following steps can be applied [54].

5.2.1.1 Transform (5.9) into a Convex Optimization Problem

This can be done following the parametric approach using a given parameter [164]. The optimal value of , which results in the optimal bandwidth and power allocation for (5.9), can be obtained through an iterative algorithm. For a non-negative parameter , (5.9) can be transformed into

5.10

The optimal solution of (5.9) can be determined by finding a root of equation , which can be obtained using a Dinkelbach-type algorithm, as given in Algorithm 5.2.4 [165].

Algorithm 5.2.4 converges to the optimal solution of (5.9) in a finite number of iterations [165].

5.2.1.2 Finding the Optimal QoS-Aware Joint Power and Bandwidth Allocation for a Given

This is done by solving (5.10) which constitutes an important step in Algorithm 5.2.4. Letting , (5.10) can be re-written as

5.11

Since (5.11) has a linear objective function and convex constraints, it is a convex optimization problem [142]. Following the decomposition theory and using the same steps as those adopted in Chapter 4, the Lagrangian function for (5.11) can be defined as , where and are resource allocation matrices with and and is a Lagrangian multiplier vector for the first constraint in (5.11), , , and are Lagrangian multiplier vectors and matrices for constraints (5.5)–(5.8), respectively. Applying the KKT conditions on the Lagrangian function and using the same steps as those in Chapter 4, we find (i) the optimal power allocation at the MT as a function of the Lagrangian multipliers , , and and (ii) the optimal bandwidth allocation at each BS/AP as a function of the Lagrangian multipliers , , and [54]. The optimal values of the Lagrangian multipliers can be obtained by solving the dual problem using a gradient descent method as described in Chapter 4 [54]. In the following, are sufficiently small step sizes, , , and . Algorithm 5.2.5 finds the optimal power allocation for a given allocated bandwidth and .

Given the allocated power from Algorithm 5.2.5, the optimal bandwidth can be allocated using Algorithm 5.2.6.

Using the optimal power and bandwidth allocated in Algorithms 5.2.5 and 5.2.6, the objective now is to find the jointly allocated resources that satisfy the target data rate and maximize the resulting energy efficiency for a given . Define . Algorithm 5.2.7 gives the optimal solution of (5.11) for a given value of by iterating over and until convergence to find the optimal joint bandwidth and power allocation solution that maximizes the minimum energy efficiency for a given in the region and satisfies the required QoS by all MTs.

The framework described in Algorithms 5.2.4–5.2.7 is illustrated in Figure 5.2. Using Algorithms 5.2.4–5.2.7, the decentralized uplink energy-efficient radio resource allocation framework is summarized in the following 10 steps:

1. Step 1. The BSs/APs start with initial bandwidth allocation to all MTs in service and initialize the value for every MT. The MTs allocate initial powers to their different radio interfaces. Every MT calculates its initial value and broadcasts it together with an initial value to the serving BSs/APs.
2. Step 2. The BSs/APs exchange their information to find the value , as shown in Algorithm 5.2.4.
3. Step 3. The BSs/APs check a termination condition (as shown in Algorithm 5.2.4): ? If the condition is true, the framework is terminated; otherwise, go to Step 4.
4. Step 4. Every MT broadcasts to its serving BSs/APs its and values. All BSs/APs exchange their information regarding their minimum and determine , as shown in Algorithm 5.2.7.
5. Step 5. The BSs/APs check a termination condition (as shown in Algorithm 5.2.7): with and with ? If the condition is true, go to Step 9; otherwise, all BSs/APs update the values, as shown in Algorithm 5.2.7. Also, all BSs/APs exchange their information to find and broadcast this value to all MTs.
6. Step 6. All BSs/APs allocate their radio resources (e.g. bandwidth) to all MTs in service using Algorithm 5.2.6.
7. Step 7. All MTs perform power allocation at their radio interfaces using Algorithm 5.2.5.
8. Step 8. Go to Step 4.
9. Step 9. Every MT checks its total achieved data rate . If does not converge, the MTs update their value and broadcast it to all serving BSs/APs, as shown in Algorithm 5.2.7. Go to Step 4.
10. Step 10. If converges, every MT transmits its value to all serving BSs/APs. Go to Step 2.

5.2.3 Performance Evaluation

Consider a geographical region that is covered by a micro BS (indexed as 1) and two femto-cell APs (indexed as 2 and 3, respectively). Due to the overlapped coverage among the BS and the two APs, three service areas can be distinguished. In the first and second areas, MTs can get service from both the micro BS and one femto AP. In the third service area, MTs can get service only from the micro BS. The simulation parameters are given in Table 5.1, and are adopted from [16, 45, 53, 166] and [167]. The performance of the optimal and suboptimal approaches is compared with a benchmark based on [31] that investigates only power allocation in a heterogeneous wireless medium for energy efficiency. Hence, given some bandwidth allocation from different networks, every MT independently allocates transmission power to its radio interfaces to maximize its own energy efficiency [54].

Parameter	Value
	10 MHz
	5 MHz
	dBm/Hz
	501.2 mW
	100 mW
	Uniformly distributed in Mbps
	4
	0.35
	W/Hz

Two simulation cases are considered. In the first case, each service area has 5 MTs, and we show the performance of the optimal and suboptimal approaches (using Algorithms 5.2.4–5.2.6 and the two phases in Section 5.2.2, respectively) as compared with the benchmark. In the second case, each service area has 10 MTs. In this case, we show the results of the suboptimal framework as compared with the benchmark. In each of the conducted simulations, we vary the total power consumption at MTs, , which is displayed across the -axis. The total available power is used in both data transmission and circuit power consumption. Over the range , we aim to investigate the performance of the proposed optimal and suboptimal approaches with respect to the benchmark in two situations. The first situation () presents comparable transmission and circuit power consumption values (due to the low total available power). The second situation () presents a large available transmission power than the circuit power consumption (due to the high total available power). Simulation results are averaged over 100 runs.

Figure 5.3a and b show the plots of minimum and average achieved energy efficiencies against , respectively. Given the simulation settings, energy efficiency is improved with , as the MTs can enhance the achieved throughput at a slight increase in power consumption. With low total available power, lower energy efficiency is achieved due to the comparable values of transmission power consumption (which translates into a useful term, i.e. throughput) and circuit power consumption (which does not contribute to the achieved throughput). With more total available power, more power can be consumed for data transmission, which translates into a higher throughput and enhanced efficiency. As shown in the figures, the proposed optimal and suboptimal approaches outperform the benchmark. This is mainly due to two reasons. First, the proposed approaches jointly optimize bandwidth among MTs and power allocation at each MT to maximize energy efficiency unlike the benchmark, which optimizes only power allocation. Hence, in the new approaches, bandwidth and power allocations are performed according to the channel conditions at different radio interfaces of different MTs and the available energy at each MT. This results in the improved performance in Figure 5.3a and b. Second, the proposed approaches aim to maximize the minimum energy efficiency in the geographical region, unlike the benchmark where every MT aims to maximize its own energy efficiency independent of other MTs. This results in the improved performance of the proposed approaches in Figure 5.3. The optimal approach exhibits improved performance over the suboptimal approach due to the fact that the optimal approach calculates its dual variables at every time slot using the actual CSI, whereas the suboptimal approach is based on the average CSI. However, overall the suboptimal approach has an improved performance over the benchmark with a reduced signalling overhead and computational complexity. Furthermore, as the number of MTs increases in the system, lower energy efficiency is achieved. This is mainly due to the increased competition over the radio resources at the BS and APs, which leads to reduced bandwidth allocation per user, and hence, a lower energy efficiency is achieved.

Figure 5.4 shows the average satisfaction index of MTs versus . The satisfaction index captures the ability of the radio resource allocation approaches to satisfy the QoS requirements of the MTs. In particular, the satisfaction index is defined as [83]

5.15

where if is satisfied, and 0 otherwise. As shown in Figure 5.4, the optimal approach always achieves a satisfaction index of 1. Overall, the suboptimal approach has an improved satisfaction index over the benchmark. This is mainly due to the improved achieved throughput of the suboptimal approach as compared with the benchmark. While the suboptimal approach and benchmark satisfy the minimum required data rates of the MTs, the suboptimal approach achieves a much higher throughput than the benchmark due to the CSI-based bandwidth allocation, which leads to a higher satisfaction index.

5.3 Green Multi-homing Uplink Resource Allocation for Video Calls

Consider now an uplink multi-homing video transmission from an MT [168]. In the absence of an appropriate energy management strategy, the MT can use up all its available energy, and hence, might drain its battery before call completion. As a result, an energy management strategy is required to ensure a sustainable video transmission, over different radio interfaces, for the call duration. However, this problem has been overlooked, so far, in the literature. A simple energy management sub-system can equally distribute the MT available energy over different time slots of the video call duration. Given the time-varying bandwidth availability and channel conditions over different time slots, using this uniform energy distribution will lead to inconsistent temporal fluctuations in the video quality. An appropriate energy management sub-system should use the MT energy in a way such that it can support a consistent video quality in the call duration over time varying bandwidth and channel conditions.

In this section, an energy management sub-system is presented for MTs to support a sustainable multi-homing video transmission in a fading channel over a target call duration in a heterogeneous wireless access medium [161]. The energy management sub-system is based on a two-stage approach. In the first stage, through video quality statistical guarantee, the MT can determine a target video quality lower bound that can be supported for a target call duration with a small outage probability. In the second stage, the MT adapts its energy consumptionduring the call, following a three-step framework to achieve at least the target video quality lower bound.

The video sequence is encoded into a bit stream using a layered/scalable video encoder. The layered representation of the video sequence is composed of a base layer and several enhancement layers [169]. Each video layer is periodically encoded using a group-of-picture (GoP) structure. Time is partitioned into time slots, , of equal duration , where and denotes the call duration, which is a random variable. At every time slot, the MT has a new GoP, from different layers, ready for transmission. The time slot duration is determined based on the source encoding rate in frames per second (fps). Each time slot has frames from different layers, , and each frame can be of I, P or B type. I frames are compressed versions of raw frames independent of other frames. P frames only refer to preceding I/P frames, while B frames can refer to both preceding and succeeding frames. The data within one time slot are encoded inter-dependently through motion estimation, while data belonging to different time slots are encoded independently [170]. A video frame has the following characteristics [170]:

• Size—Each frame is encoded into packets and each packet contains data relative to at most one frame [171]. Frame is fragmented into packets, , where denotes the maximum allowable size for frame at each GoP. The frame size (in numbers of video packets, ) is represented by an independent identically distributed (i.i.d.) random variable that follows a probability mass function (PMF) [170]. The frame size across different GoPs follows the same PMF given the frame type (I, P or B). The PMF, , can be calculated for different video contents and frame types as in [172]. The frame size, , for frames of I, P or B type is constant within one time slot and varies from one time slot to another. The packet size (in bits) for frame is denoted by .
• Distortion Impact—Each frame, , has a distortion impact value per packet, . It represents the amount by which video distortion is reduced if this packet is received on time at the decoder side. The packet distortion impact value, , for different video contents and frame types can be calculated as in [173].
• Delay Deadline—It represents the time by which the frame should be decoded at the destination, which is also known as the decoding time stamp [168]. Packets that belong to the same frame have the same delay deadline, which is denoted by . Since videos are encoded using a fixed number of fps within the same layer, the difference in the delay deadline between any two consecutive frames within the layer is constant [168].The delay difference is given by . The transmission deadlines of all packets within a given GoP expire within .
• Dependence—Within each time slot, since some frames are encoded based on the prediction of other frames, there are dependencies among these frames. Hence, packet decoding of one frame depends on the successful decoding of packets from other frames. These dependencies among packets of different frames, within one time slot, are expressed using a directed acyclic graph (DAG) [170], as shown in Figure 5.5. Hence, each video packet is said to have ancestors . Packets which belong to have higher distortion impact and smaller delay deadline than packet .

Consider an uplink live video transmission from an MT [168]. The MT is equipped with multiple radio interfaces and presents multi-homing capabilities. As a result, the MT can establish communications with multiple wireless networks simultaneously and employ them for video packet transmission. Let denote the utilized radio interfaces and assume .

The uplink bandwidth allocated to the MT for radio interface is denoted by [4–6]. The offered bandwidth to the MT varies according to call arrivals and departures. Call arrivals follow a Poisson process, the channel holding time follows a general distribution and all calls are served without queueing. Hence, an model can be used to capture the statistics of the number of calls that are simultaneously in service [5 6]. Hence, using the statistics of the number of calls in service and the resource allocation mechanism, the probability that bandwidths are offered to radio interfaces , , can be derived based on a Poisson distribution [5 6, 161].

The average transmission power allocated to radio interface is denoted by . Let denote the received signal-to-noise ratio (SNR) at the BS/AP communicating with radio interface . It is assumed that the channel conditions do not change much during one time slot. Hence, the received SNR value, , , is constant within one time slot and varies independently from one time slot to another [168, 170, 174].

Each radio interface, , can support a discrete set of data rates , with . Radio interface can support data rate if the received SNR value, , for this radio interface exceeds some threshold . The set of thresholds , , can be calculated using Shannon formula as

5.16

and is assumed to be .

For each time slot, let denote a video packet scheduling decision, where if packet of frame is assigned to radio interface , otherwise . Variable denotes the instantaneous transmission power allocation to radio interface . The circuit power required to keep radio interface active is denoted by . The MT available energy at the beginning of the call is denoted by .

5.3.1 Energy Management Sub-system Design

The energy management sub-system consists of two stages. The first stage takes place during call set-up and aims to determine an optimal QoS lower bound that can be supported over the call duration, given the MT available energy, target callduration and video and radio interface characteristics. The second stage takes place during the call where the MT adapts its energy consumption to satisfy at least the target video quality lower bound calculated in the call set-up.

5.3.1.1 Statistical QoS Guarantee for Wireless Multi-homing Video Transmission

Let denote the video quality metric which is defined as the distortion impact ratio of the transmitted packets to the total available packets in time slot . Due to channel fading and time-varying radio access bandwidth (and hence, time-varying data rates at different radio interfaces) and packet encoding statistics, the video quality metric is a discrete random variable. For a stationary and ergodic process underlying the system dynamics (in terms of channel fading, offered bandwidth and packet encoding), the time subscript of can be omitted. Hence, is expressed as

5.17

We aim to find the video quality cumulative distribution function (CDF), , given the MT available energy, the time varying offered bandwidth and channel conditions at different radio interfaces, the target call duration and the video packet characteristics in terms of distortion impact, delay deadlines and packet encoding statistics. Using the video quality CDF, we can find the video quality lower bound, , that can be supported by the MT for the target call duration such that , with . This is achieved following a three-step framework:

1. 1. Calculating the probability of employing a given set of data rates at different radio interfaces: In a Rayleigh fading channel, the probability that data rates are used at radio interfaces can be calculated as [161]
   5.18
2. where denote the set of offered bandwidths to the MT, represents the average received SNR for radio interface , denotes the average channel power gain for radio interface and denotes the one-sided noise power spectral density.
3. 2. Calculating the video quality CDF given the frame size and data rate statistics: Next, we aim to find the video quality that can be achieved given the MT data rates at different radio interfaces and frame size , where can be of I, P or B type. Using the data rate and packet encoding statistics, we find the video quality CDF, .

Since video packets that belong to the same frame have the same delay deadline of the frame, the required rate to transmit a packet , , is given by [168]. The scheduled packets to a given radio interface, , should satisfy

5.19

Video packet scheduling should capture the dependence relationship among different video packets within the same time slot. The packets with unscheduled ancestors should not be transmitted since they will not be successfully decoded at the destination, and thus, they waste the MT and network resources. This requirement can be expressed by a precedence constraint

5.20

Finally, a video packet should be assigned to one and only one radio interface

5.21

Hence, multi-homing video packet scheduling, given the available data rates , , at different radio interfaces and frame size with belonging to I, P or B type, should satisfy

5.22

The optimization problem (5.22) is a binary program. Problem (5.22) can be mapped to a new variant of the knapsack problem, referred to as precedence-constrained multiple knapsack problem (PC-MKP) [25]. The available items are the video packets, , , the item weights are the required data rates, and the profit associated with each item is the packet distortion impact value, . As we have multiple radio interfaces, the problem has multiple knapsacks each with capacity . Due to the dependencies among different video packets within the time slot, MKP admits the precedence constraint (5.20). Since the knapsack problems are NP-hard [175], PC-MKP is also NP-hard. We present a greedy algorithm that can solve the PC-MKP of (5.22) in polynomial time based on [176]. Video packets are first classified into root and leaf items. In general, root items have higher precedence order than leaf items. For a video packet transmission, root items (packets of I and P frames) have higher distortion impact than leaf items (packets of B frames) [170]. Consider the following variables -the set of unassigned packets, -the current used capacity at radio interface (the remaining capacity is ), -the set of assigned packets to radio interface () and -the index of the radio interface where packet is currently assigned to. The multi-homing video packet scheduling algorithm is described in Algorithm 5.3.8.

Algorithm 5.3.8 consists of two parts. The first part (A1) aims to find a feasible solution for the problem by assigning items (video packets) with the highest profit (distortion impact) to different knapsacks (radio interfaces) while considering their precedence constraints. The second part (A2) aims to improve the feasible solution of (A1). This is achieved by considering all pairs of packed items (video packets) and, if possible, interchanges them whenever doing so allows the insertion of an additional item (video packet) from the remaining ones, if all its ancestors are packed, into one of the knapsacks (radio interfaces). In (A2) of Algorithm 5.3.8, and are updated whenever some is updated. If the total number of available video packets in a given time slot is , then the complexity of Algorithm 5.3.8 is , that is, has polynomial time complexity in terms of the number of radio interfaces and video packets.

Using Algorithm 5.3.8, the video quality that can be achieved using data rates , at radio interfaces and frame size with belonging to I, B or P type can be calculated. The set of different data rates and packet encoding combinations that result in the same video quality is denoted by . We can map the data rate and frame size statistics into a video quality PMF given by

5.23

where denotes the joint PMF of video packet encoding for I, B and P frames and it is obtained through the multiplication of the PMFs of I, B and P frames assuming an i.i.d. frame size statistics [170]. Consequently, the video quality CDF, , can be calculated.

3) Finding the maximum video quality lower bound that can be supported for the target call duration: From (5.18), the probability that data rates are used at different radio interfaces depends on the average received SNR values , . Therefore, the video quality CDF is a function of the average transmission power at different radio interfaces. Hence, the distribution of the average transmission power, , among different radio interfaces, that is, , affects the resulting video quality CDF.

Since is a random variable, we aim to guarantee that the MT available energy can support a target call duration, . Hence, we first find that satisfies , . Assuming an ergodic process for system dynamics, in order to find the maximum video quality lower bound that can be supported for the target call duration with some statistical guarantee , we need to solve

5.24

The first constraint in (5.24) represents an inequality (instead of an equality) condition since the supported data rates at different radio interfaces form a discrete set, and hence, the achieved video quality is also discrete. Consequently, an equality in the first constraint of (5.24) cannot always be satisfied, unlike the inequality. In (5.24), is a design parameter that can be chosen to strike a balance between the desired performance (in terms of the video quality and energy consumption) and success probability of the call delivery. This issue is further investigated in the performance evaluation subsection. The second constraint stands for the average power consumption of the MT, which is based on the total available energy and the target call duration. In the proposed energy management sub-system, the MT cannot assume an average energy consumption greater than that value.

Heuristic optimization techniques, for example, the genetic algorithm (GA) [177], can be used to solve the optimization problem (5.24). The GA can be easily implemented in smart phones as it consists of simple iterations. In addition, using the GA in solving (5.24) is fast due to the small number of variables (the number of radio interfaces ranges from 2 to 4).

Following (5.24), the MT can support a multi-homing video quality at least equal to for the call duration with an outage probability , given by

5.25

5.3.1.2 Energy-Efficient QoS Provision for Wireless Multi-homing Video Transmission

During the call, the MT adapts its energy consumption to satisfy at least the maximum video quality lower bound calculated in the call set-up. In good channel and/or network conditions, the MT achieves a video quality better than the lower bound. However, in bad conditions, the MT satisfies a quality not less than the lower bound. This strategy is performed in three steps:

1. Step 1: The MT determines the total required data rate, at the current time slot, to satisfy at least , given the current time slot video packet encoding. Let denote the resulting video quality that can be achieved at time slot by scheduling a set of video packets for transmission. The total required data rate, , can be calculated using Algorithm 5.3.9.
2. Step 2: The MT determines the minimum power required at each radio interface, and hence, the required data rate at each radio interface, to satisfy the total required data rate calculated in Step 1, given the current time slot channel fading and offered bandwidth. Let denote the MT available energy at the beginning of time slot . The transmission power allocation problem can be formulated as
   5.26

   Similar to (5.24), (5.26) can be solved using the GA. Hence, during every time slot with duration , the MT updates its transmission power allocation at each radio interface to satisfy its target video quality.

3. Step 3: The MT performs video packet scheduling given the data rate at each radio interface, calculated in Step 2. Using the data rates that can be supported through the transmission power allocation calculated in (5.26), Algorithm 5.3.8 is used to schedule the current time slot available video packets for transmission. The resulting video quality satisfies the lower bound , calculated in (5.24), over the entire call duration with a success probability .

The energy management sub-system procedure for supporting a sustainable video transmission over the call duration with consistent video quality is summarized in Figure 5.6.

5.3.2 Performance Evaluation

The performance of the energy management sub-system, which is referred to as statistical guarantee framework (SGF), is compared with two benchmarks. The first benchmark, which is referred to as total energy framework (TEF), aims to maximize the resulting video quality subject to the MT battery energy limitation [161]. The second benchmark, which is referred to as the equal-energy framework (EEF), satisfies an energy budget per time slot for energy management. A uniform energy budget per time slot is considered, where the MT available energy at time slot is uniformly distributed over the remaining time slots [161].

Video sequences are compressed at an encoding rate of 30 fps [171]. The GoP structure consists of 13 frames with one layer (base layer) and one B frame between P frames. As a result, the time slot duration is 433 ms. The PMFs of the I, B and P frame sizes are given in [161]. The decoder time stamp difference between two successive frames, , is 40 ms [168]. Each video packet requires a transmission data rate of 2 Kbps. The video packet distortion impact values are for I frames, for P frames and for B frames [171]. Two radio interfaces are used for video transmission (). The circuit power for each radio interface is 10 mW. The offered bandwidth statistics on the two radio interfaces is given in [161]. The set of data rates that can be supported on each radio interface is Mbps. Each radio interface is subject to a Rayleigh fading channel with average channel power gain and . For comparison, a video call is established using the three set-ups SGF, TEF and EEF. The available energy at the beginning of the call for the three set-ups is 3 kJ. For the SGF, the video quality lower bound is calculated in the call set-up, and it is equal to , while and .

Figure 5.7 plots the achieved video quality over the call duration using EEF, SGF and TEF. The TEF uses all the MT available energy, and hence it drains its battery before call completion. This is because the main objective of TEF is to maximize the video quality in the current time slot, without considering the impact of the consumed energy on the video quality in the remaining time slots. The EEF takes into consideration the target call duration by equally distributing the MT available energy over the remaining time slots. However, due to the time-varying video packet encoding, offered bandwidths and channel conditions at the different radio interfaces, using the uniform energy budgets leads to inconsistent temporal fluctuations in the video quality. The resulting video quality for some time slots can be as shown in Figure 5.7. On the contrary, the SGF can adapt the MT consumed energy at every time slot according to the packet encoding, offered bandwidth and channel conditions at the two radio interfaces. Consequently, the SGF can support a consistent video quality over different time slots, which is at least equal to the target lower bound ().

Figure 5.8 plots the MT residual energy over the call duration. The MT residual energy using the TEF near the middle of the call is insufficient to support a video transmission. Since the EEF uses a uniform energy budget for different time slots regardless of the channel fading, the slope of the consumed energy is almost constant over the first two-thirds of the call period. For the SGF, the MT consumed energy does not have an equal slope as the MT adapts its energy consumption based on the video packet encoding and channel conditions at the different radio interfaces over the time slot.

The advantages of SGF over the two benchmarks can be summarized as follows: (i) SGF guarantees a sustainable multi-homing video transmission over the target call duration, unlike TEF and (ii) SGF supports a consistent video quality over different time slots by adapting its energy consumptionaccording to the video packet encoding and channel conditions at different radio interfaces, and consequently, SGF can control the QoS lower bound violation probability.