Anticipative Energy and QoS Management: Systematically Improving the User Experience

Abstract

Energy efficiency remains a main design target for battery-powered wireless terminals. This chapter shows that significant energy savings can be achieved with smart(er) operation of the radio. Radios are destined to meet significant dynamics in application requirements, propagation conditions, and network load. Smart adaptation to these dynamics allows achieving the required performance with great (average) energy savings.

Specifically, a wireless local area network (IEEE 802.11a) is considered in which multiple users coexist, while meeting performance constraints and minimizing energy cost. Even for such an IEEE 802.11 network, a flexible and energy-scalable radio within a network of flexible radios can be managed smartly to improve the overall QoS or energy efficiency of the network, as illustrated in this chapter.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

6.1 Energy Efficiency for Smart Radios

6.1.1 Minimum Energy at Sufficient QoS

While the need for flexibility and intelligent control is well studied in the context of smart or cognitive radios for the sake of spectrum efficiency, it can used for optimizing the usage of other scarce resources such as energy. The design framework for smart radios of Chap. 3 is instantiated here to achieve smart, energy efficient software radios. More specifically, it is shown how it can be used to achieve smart, energy efficient IEEE 802.11a devices, provided their hardware is designed to be energy scalable. An energy scalable radio can be reconfigured or tuned at run-time in a way that energy consumption is impacted, so such a radio can benefit from a smart control strategy to save energy. Of course, this energy saving should not come at the expense of the user experience, so the objective of the smart control in this chapter is: how to adapt the radio so that the application performance is met at minimal possible energy consumption.

The focus of this chapter is on wireless networks where all users are in the same collision domain with an access point (AP) to arbitrate exclusive channel access (Fig. 6.2). An uplink real-time video streaming application is considered. The challenge in energy management for these systems is to determine how the system should sleep or scale and still meet per-packet QoS timing requirements. The instantiation takes advantage of the fact that the system will operate in dynamic environments where a single energy management solution is not sufficient. The main dynamics are encountered in the channel state and application load requirements. Furthermore, in a network of such systems, an efficient energy management algorithm should exploit the variations across users to minimize the overall network energy consumption.

Therefore the problem explored here could be stated as follows: How does one decide what system configurations to assign to each user at run-time to minimize the overall energy consumption while providing a sufficient level of QoS? This must be achieved for a network of users with bursty delay-sensitive data and over a slow fading channel.

We briefly recapitulate the following three observations that show that the proposed adaptation problem is not trivial and requires to streamline energy management approaches across layers.

• First, state-of-the-art wireless systems such as 802.11a devices are built to function at a fixed set of operating points assuming worst-case conditions. Irrespective of the link utilization, the highest feasible transmission rate is used and the power amplifier operates at maximum output power [21]. For non-scalable systems, the highest rate results in the smallest duty cycle and hence the lowest energy consumption. On the other hand, for scalable systems, this strategy results in excessive energy consumption for average channel conditions and link utilizations. Recent energy-efficient wireless system designs focus on VLSI implementations and adaptive physical layer algorithms where a lower transmission rate results in energy savings per bit [38, 71]. For these schemes to be practical, they should be aware of the hardware energy characteristics at various operating points.

• Second, to realize significant energy savings, systems need to shutdown the components when inactive. This is achieved only by tightly coupling the MAC communication to the power management strategy in order to communicate traffic requirements of each user for scheduling shutdown intervals.

• Finally, intrinsic trade-offs exist between schemes while satisfying the timeliness requirements across multiple users. As the channel is shared, lowering the rate of one user reduces the time left for the other delay-sensitive users. This forces them to increase their rate, at the cost of energy consumption or bit errors.

Our approach couples these tasks in a systematic manner to determine the optimal system-wide power management at run-time.

6.1.2 Smart Aspects and Energy Efficiency

We propose a two-phase run-time/design-time solution to efficiently solve the sleep-scaling trade-off across the physical, link and MAC layers for multiple users. It is an instantiation of the abstract design flow discussed in Chap. 3. At design-time the problem is resolved by searching for a set of close-to-optimal points in the solution space. This anticipates a set of possibly good system configurations. Starting from this configuration space, we can schedule the nodes at run-time to achieve near-optimal energy consumption with low overhead. The flow is illustrated in Fig. 6.1. It is clear that the set of possible points is fully characterized at design time. At run time, as function of the monitored scenario, the most energy efficient configuration can then be selected. In the next section, the design approach is detailed further. The research in this chapter has been performed in close collaboration with Rahul Mangharam at Carnegie Mellon University. This cooperation also leads to several shared papers [72–75].

Fig. 6.1

Focus of this chapter is on the run time control challenge for cognitive radio. Actions are taken based on a monitoring of the environment (channel and application state) and based on this information the optimal configuration point is selected based on a DT model

6.2 Anticipation Through Design Time Modeling

In this section, we follow the design steps considered in the design flow proposed in Chap. 3 to achieve the required performance at minimal QoS for the cognitive radios. Consider a wireless network as in Fig. 6.2 where multiple nodes are centrally controlled by an AP. Each node (such as a handheld video camera) desires to transmit or receive frames in real-time and it is the AP’s responsibility to assign channel-access grants. The resource allocation scheme within the AP specifies each user’s system configuration settings for the next transmission based on the feedback of the system state from the current transmission. It must ensure that the nodes meet their performance constraints by delivering their data in a timely manner while consuming minimal energy. The problem is first stated formally and a specific example is provided further in this chapter. The network consists of n flows {F ₁,F ₂,…,F _n } with periodic delay-sensitive frames or jobs. For notational simplicity, we assume a one-to-one mapping of flows to nodes, but the method is also applicable to more flows per node.

Fig. 6.2

Centrally controlled point-to-multipoint LAN topology with uplink and downlink communication

The design time steps, the focus of this chapter, are discussed in the next subsections. First, it is required to define the control dimensions or the available flexibility. Next, the system scenarios need to be determined or what scenarios the cognitive radio is expected to encounter. Then, the relevant cost, resource and quality dimensions need to be defined. They define what the cognitive radio should adapt for. These cost, quality and resource dimensions can be layered, to facilitate run-time information flow and ease of modeling. Finally, the mapping of the control dimensions impact on cost, quality and resource needs to be determined, for each of the system state scenarios. This means that for each possible scenario that the cognitive radio would encounter, it should be determined what the impact of a certain control know configuration would be on the cost, quality or resource dimensions. After these four design-time phases, the run-time phase can be carried out, as will be explained in Sect. 6.3.2.

6.2.1 Flexibility for Energy and QoS

Control Dimensions or Knobs (K _i,j ): For the considered 802.11a transceiver, we identify several control dimensions that trade-off performance for energy savings. Our system modeling is based on an 802.11a [76] direct conversion transceiver implementation with turbo coding [77] (Fig. 6.3). Four control dimensions have a significant impact on energy and performance for these OFDM transceivers: the modulation order (N _Mod ), the code rate (B _c ), the power amplifier transmit power (P _Tx ) and its linearity specified by the back-off (b).

Fig. 6.3

802.11a OFDM direct conversion transceiver

For the energy modeling, we focus on the power amplifier control knob as PA’s generally are the most power-hungry component in the transmitter consuming upwards of 600 mW [78]. The major drawback for 802.11a OFDM modulation is the large peak-to-average power ratio (PAPR) of the transmitted signal.¹ A high PAPR renders the implementation costly and inefficient since power-efficient PA designs require a reduced signal dynamic range [80]. However, reducing the PA’s linear power amplification range clips the transmitted signal and increases the signal distortion.

To combat this, new PA designs allow to adapt the gain compression characteristic independently of the output power. Adapting the PA gain compression characteristic allows to translate a transmit power or linearity reduction into an effective energy consumption gain. A back-off, b, can be used to steer the linearity of the amplification system versus the energy efficiency of the PA [21]. The back-off is defined as the ratio of the effective PA output power to the saturation output power corresponding to the 1 dB gain compression point (Fig. 6.4(b)). The saturation power and hence signal distortion for class A amplifiers (used with OFDM) are controlled by modifying the bias current of the amplifier, which directly influences its energy consumption (Fig. 6.4(a)). Since the linearity of the PA determines the distortion added to the signal, we can write the performance loss due to the PA as function of b: D _i (b). Consequently, we save energy from the increased PA efficiency, provided we ensure that the received signal to noise and distortion ratio (SINAD) is above the required sensitivity and do not need to retransmit the packet. For the system to be practical only discrete settings of the control dimensions are considered (listed in Table 6.1).

Fig. 6.4

Adapting the PA gain compression characteristic allows to translate a transmit power or linearity reduction into an effective energy consumption gain

Table 6.1 PHY parameters considered

We further consider the eight PHY rates supported by 802.11a based on four modulation and three code rates (Table 2.2). Given the above introduced N _Mod and B _c , the bitrate (B _bit ) achieved for each modulation-coding pair with N _c OFDM carriers and symbol rate B is given by:

$$ B_{\mathit{bit}}=N_c \times N_{\mathit{Mod}} \times B_c\times B . $$

(6.1)

Based on the bitrate, communication performance is determined by the Bit Error Rate (BER) at the receiver. When transmitter non-linearity is considered, the BER is expressed as a function of the above introduced SINAD. The SINAD is written as a function of the power amplifier back-off, given output power P _Tx and time and frequency varying channel attenuation A(t,f) as:

(6.2)

(6.3)

where the constants k, T, W and N _f are the Boltzmann constant, working temperature, channel bandwidth and noise figure of the receiver respectively. The relation between the power amplifier back-off b and the distortion has been characterized empirically for the Microsemi LX5506 [81] 802.11a PA in Fig. 6.4. The effective PA power consumption (P _PA ) can be expressed as the ratio of the transmit power (P _Tx ) to the PA efficiency (η _PA ) that is related to b by an empirical law fitted on measurements (Eq. 6.3).

Next, at MAC layer, we can add the number of retransmissions as control knob. These knobs are practical and sufficient to illustrate the potential of the proposed methods.

6.2.2 The Varying Context

System State (S _i,m ): In a wireless environment, with e.g. VBR video traffic, the system state scenarios used in this design case are the current channel state and application frame size. We study the impact of both constant bitrate (CBR) and variable bitrate (VBR) traffic. For VBR traffic we employ MPEG-4 encoded video traces [82, 83] with peak-to-mean frame sizes ranging from 3 to 20. All fragmentation is done at the link layer and we use UDP over IP. As the maximum frame size is assumed to be within the practical limit of 50 fragments, we construct Cost-Resource-Quality curves for 1, 2, 3, 4, 5, 10, 20, 30, 40, 50 fragments/frame and interpolate for intermediate values. The application layer frame size is translated to lower layer Queue Size and fragment size to facilitate state monitoring and calibration. As a result, no additional measurements are needed to model traffic requirements, which can be fully captured in the mapping.

The indoor wireless channel suffers from frequency-selective fading that is time-varying due to movements of the users or obstacles in its environment. This varying fading results in varying PER as function of the current transceiver settings. We use a frequency selective and time varying channel model to compute this PER for all transceiver settings. An indoor channel model based on HIPERLAN/2 [84] was used for a terminal moving uniformly at speeds between 0 to 5.2 km/h (walking speed). Experiments for indoor environments [83] have found the Doppler spread to be approximately 6 Hz at 5.25 GHz center frequency and 3 Hz at the 2.4 GHz center frequency. This corresponds to a coherence time of 166 ms for 802.11a networks. A set of 1000 channel frequency response realizations (sampled every 2 ms over one minute) were generated and normalized in power. Data was encoded using a turbo coder model [77] and the bit stream was modulated using 802.11a OFDM specifications. For a given back-off b and transmit power P _Tx , the SINAD at the receiver antenna was computed for the channel realization A(t,f) by Eq. 6.2.

We assume an average path-loss A of 80 dB at a distance of 10 m, which consists both of the transmit antenna gain G _t , receive antenna gain G _r and the propagation loss. This path-loss is from an empirical model developed at IMEC (Fig. 6.5). It is representative for indoor channels and results in pathlosses in between the Free space model and Two ray ground model, which is commonly used for outdoor applications.

Fig. 6.5

Typical indoor pathloss model

From the channel realization database, a one-to-one mapping of SINAD to receive block error rate was determined for each modulation and code rate. The channel is then classified into 8 classes, determined by a 2 dB difference in the receive SINAD that is measured for a turbo code BlER of 10⁻³ (Fig. 6.6(a)). We use a similar 2 dB discrete step for the PA knobs (Table 6.1). In order to derive a time-varying link-layer error model, we associate each channel class to a Markov state, each with a probability of occurrence based on the channel realizations database (Fig. 6.6(b)). Given this eight-state error model, we are able to model the PER, expressing the performance per MAC layer packet L _frag , for different configurations. The PER is obtained in Eq. 6.4 by assuming the block errors are uncorrelated for a packet size of L _frag bits and a block size of 288 bits:

$$ P_e = \bigl[1-(1-\mbox{BlER})^{\frac{L_{\mathit{frag}}}{288}}\bigr]. $$

(6.4)

Fig. 6.6

Markov channel model used for indoor 802.11a wireless communication (a) BlER versus SINAD and (b) histogram for steady state Markov state probabilities

This calibration is not a fundamentally new characterization of the hardware. This BlER-SINAD information just has to be combined with a set of channel states that are extracted on-line. The combination of this run-time channel with hardware properties into metrics for higher layer metrics of the database is a key enabler.

6.2.3 Objectives for Efficient Energy and QoS Management

We determine the set of quality, energy cost and resource dimensions that are relevant to the considered scenario where users transmit video data towards a central AP (Fig. 6.2).

• 1. Cost Function (C _i ): The optimization objective considered in the design case in this chapter is to minimize the total energy consumption of all users in terms of Joules/Job. For example, in a video context, a job is the timely delivery of the current frame of the video application.

• 2. QoS Constraint (Q _i ): The optimization has to be carried out taking into account a minimum performance or QoS in order to satisfy the user. As delivery of real-time traffic is of interest, we describe the QoS in terms of a single QoS metric which is in this design case defined to be the job failure rate (JFR) [85]. JFR is defined as the ratio of the number of frames not successfully delivered before the deadline to the number of frames issued by the application over the lifetime of the flow. In this specific delay-sensitive video context, the QoS constraint is hence specified at run-time by user i as a target $\mathit{JFR}_{i}^{*}$. This QoS definition could be extended to a broader range of quality targets. We note again that, next to this explicit QoS constraint that can be adapted or configured at run-time, application bitrate constraints are implicit constraints given through by the use of scenarios.

• 3. Shared Resource (R _i ): In this dissertation, we consider the particular case where access to the channel is only divided in time. The fraction of resource consumed by node i is denoted by R _i .

To summarize, each flow F _i is associated with a set of possible system states S _i,m , which affects the mapping of the control dimensions K _i to the Cost (K _i ,S _i,m →C _i ), Resource (K _i ,S _i,m →R _i ) and Quality (K _i ,S _i,m →Q _i ) that will be specified in the next section. It is essential to note that for each user, depending on the current state, the relative energy gains possible by rate scaling or sleeping are different and should hence be exploited differently. Each user experiences different channel and application dynamics, resulting in different system states over time, which may or may not be correlated with other users. This is a very important characteristic which makes it possible to exploit multi-user diversity for energy efficiency.

As the system performance requirements are specified at the application layer and the energy consumption is at the lower (hardware) layers, it is essential to: (a) translate the application layer requirements to relevant metrics at each intermediate layer and (b) to define clean interfaces between layers for an Energy-Performance feedback mechanism (see Fig. 6.7). This is to allow for a local calibration of the hardware which makes implementation more feasible, still enabling translation of to application specific quality metrics. For delay-sensitive traffic, the QoS metric of interest is the target JFR ^∗.

Fig. 6.7

A smart radio design approach spans multiple layers with corresponding performance metrics. The case study demonstrates the energy management methodology in the 802.11a WLAN setting

At the link-layer, each application frame is fragmented into one or more fixed-sized fragments. An application frame size or rate requirements are hence translated into a local Queue Size. Next, as shown in Fig. 6.7, the JFR ^∗ is translated at the link layer to a PER constraint, which corresponds to a maximum Block Error Rate (BlER) as a function of the physical layer low-level knobs. The BlER is a result of the receive SINAD for given PHY parameters. Each target JFR may be satisfied by one or more control dimension configurations, K _i , each associated with the energy consumed (cost) and time required (resource) to complete the frame transmission in the current system state. The state is defined by a discrete channel state and traffic requirement (i.e. current frame size), which can easily be monitored as the Queue Size. Channel classification and monitoring is typically a more difficult problem. At run-time, based on a node’s current system state and JFR ^∗, the corresponding Cost-Resource set of points are fetched from memory. From each curve, configuration settings are then chosen using the fast greedy algorithm such that the total transmission time for all nodes is less than the deadline. We first discuss the control dimension mapping to obtain those Pareto-optimal trade-off sets.

6.2.4 Anticipating the Performance

The key aspects of the method for design of an energy efficient cognitive radio are the mapping of the control dimensions to cost, resource and quality profiles respectively, and the generality of this mapping. A resource (respectively cost, quality) profile describes a list of potential resource (respectively cost, quality) allocation schemes resulting from each configuration point. These profiles are then combined to give a Cost-Resource-Quality trade-off, which is essential for solving the resource allocation problem (Fig. 6.8). The Cost-Resource-Quality trade-off function represents the behavior of a specific system for one user in a given system state.

• Cost profile properties

  • The finite set of discrete control dimension configurations can be ordered by their increasing cost.

  • The overall system cost, C _net , is defined as the weighted sum of costs of all flows, where each flow can be assigned a certain weight depending on its relative importance or to improve fairness [86]. Users may be assigned higher weights for example when their battery capacity is low or when they downscale their transmission rate by decreasing the video quality and get rewarded for reducing the network congestion. Users with a higher weight will typically be allowed to save more energy compared to other users: $C_{\mathit{net}} = \sum_{i=1}^{n} \omega_{i} C_{i}$.

• Resource profile properties

  • The finite set of discrete control dimension configurations can be ordered according to minimal resource requirement.

  • The system resource requirement, R, is defined as the sum of the per flow requirements: $R = \sum_{i=1}^{N} R_{i}$.

• Quality profile properties

  • The finite set of discrete control dimension configurations can be ordered with quality.

  • The system quality, Q, is met when each individual user’s constraint is met: $\mathit{JFR}_{i}\leq \mathit{JFR}_{i}^{*}$, 1≤i≤n.

Fig. 6.8

At design-time, a Cost, Resource and Quality profile is determined for each set of control dimensions based on the system state. The optimal Cost-Resource-Quality trade-off is derived from this mapping to give operating points used at run-time

The finite set of discrete control dimensions can be ordered, describing a range of possible costs, resources and quality for the system in each system state. For each additional unit of resource allocated, we only need to consider the configuration that satisfies the quality constraint and achieves the minimal cost for that resource unit. For each system state (e.g., channel and application loads), a subset of points is determined by pruning the Cost-Resource-Quality set of points to yield only the minimum cost configurations, which will be denoted by C _i (R _i ,Q _i ).

We define a calibration function p _i , that is computed for every state S _i,m

and defines a mapping between the Resource, Cost and the Quality of a node in a system state, S _i,m , as shown in Fig. 6.8. {K _i } is the set of configuration vectors for node i. Given the points after calibration in the Cost-Resource-Quality space, we are only interested in the ones that represent optimally the trade-off between energy, resource and quality for our system. Although the discrete settings and non-linear interactions in real systems do not lead to a convex trade-off, it can be well approximated as follows.

We calculate the convex minorant [87] of these pruned curves along the Cost, Resource and Quality dimensions, and consider the intersection of the results. We call this set the optimal Cost-Resource-Quality trade-off in the remainder. The optimal Cost-Resource-Quality trade-off is plotted in the dimensions TXOP-JFR-Energy/frame in Fig. 6.9(a) for the considered 802.11a WLAN design case. We will show later that the maximum segment size of the convex minorant determines the solution’s deviation from the optimum.² Configurations on segments that are small compared to the largest segment size can be pruned away without affecting the bounds of the solution. As a result, we can typically expect less than 30 configurations per state. At run-time, the resource allocation scheme in the AP adapts to the system state by fetching the correct configurations from memory. This operation is cheap compared to the cost of calibration that only has to be carried out once. In the next subsection we detail how this information can be combined efficiently into a global set representing the network trade-off. Profiling each user separately and combining the information at run-time is optimal for independent users or when the correlation is unknown. When correlation is present and known, the number of system states to calibrate and the run-time combination could be further reduced.

Fig. 6.9

Control dimension mapping

6.3 Managing the User Experience

We first formally state the energy efficient cognitive radio resource allocation problem to be solved at run-time. Then we propose a very efficient algorithm to achieve the network-wide optimal configuration.

6.3.1 Smart Resource Allocation Problem Statement

We recall that our goal is to assign transmission grants via the AP, resulting in an optimal setting of the control dimensions to each flow and node such that the per-flow QoS constraint for multiple users are optimally met with minimal energy consumption. For a given set of resources, control dimensions and QoS constraints, the scheduling objective can be formally stated as:

$$ \min_{C_{\mathit{net}}} \sum_{i=1}^n \omega_i C_i, \quad 1\leq m \leq s$$

(6.5)

s.t.

(6.6)

(6.7)

(6.8)

(6.9)

(6.10)

The solution of the optimization problem yields a set of feasible operating points, $\bar{\mathbf{K}}=\{\mathbf{K}_{i},\ 1 \leq i \leq n\}$, for the network which fulfill the QoS target, maintain the shared resource constraint and minimize the system cost. While the profile mapping and pruning is done during a one-time calibration step, we now propose how the optimal configuration $\bar{\mathbf{K}}$ is determined efficiently at run-time using those profiles.

6.3.2 Greedy Resource Allocation

As the current system state of all the nodes and flows is only known at run-time, a light-weight scheme is necessary to assign the best system configurations for each user, while meeting the QoS requirements. We therefore employ a greedy algorithm to determine the per-flow resource usage R _i for each flow to minimize the total cost C _net while meeting the system constraints. The algorithm first constructs the optimal local Cost-Resource trade-off curve C _i (R _i ) by taking the optimal points in both dimensions that meet the run-time average quality constraint JFR ^∗. Next, the scheduler traverses all flows’ two-dimensional Cost-Resource curves and at every step consumes resources corresponding to the maximum negative slope across all flows (taking into account user preference or weight if appropriate). This ensures that for every additional unit of resources consumed, the additional cost saving is the maximum across all flows taking into account the agreements made at admission time. We assume that the current channel states and application demands are known. The exchange of state information and operating points between nodes and the AP is obtained by coupling the MAC protocol with the resource manager as explained in the next section.

We determine the optimal additional allocation to each flow, R _i >0, 1≤i≤n, subject to $\sum_{i=1}^{n}R_{i} \leq R$. Our greedy algorithm is based on Kuhn–Tucker [87]:

• 1. Allocate to each flow the smallest resource for the given state, R _min . By assumption, all flows are schedulable under worst-case conditions, i.e., $\sum_{i=1}^{n}R_{\mathit{min}}\leq R$.

• 2. Let the current normalized allocation of the resource to flow F _i be R _i , 1≤i≤n. Let the unallocated quantity of the available resource be R _avl .

• 3. Identify the flow with the maximum negative slope, $|C_{i}'(R_{i})|$, representing the maximum decrease in cost per resource unit (i.e. moving right and downward the C _i (R _i ) convex minorant in Fig. 6.10). If there is more than one, pick one randomly. If the value of the minimum slope is 0, then stop. No further allocation will decrease the system cost further.

  Fig. 6.10

  

  Bounded deviation from the optimal in discrete Cost-Resource curves

• 4. Increase R _i by the amount till the slope changes for the ith flow. Decrement R _avl by the additional allocated resource and increment the cost C by the consequent additional cost. Return to step 3 until all resources have been optimally allocated or when R _avl is 0.

In our implementation, we sort the configuration points at design-time in the decreasing order of the negative slope between two adjacent points. The complexity of the run-time algorithm is O(Lnlog (n)) for n nodes (∼20) and L configuration points per curve. Further in this chapter, we demonstrate that for a practical system in each possible system state (i.e., channel and frame size), the number of configuration points to be considered at run-time is relatively small (∼30). Taking into account that the relation C _i (R _i ) is convex, we now prove that the greedy algorithm leads to the optimal solution for continuous resource allocation. Following that, we extend the proof for systems with discrete working points to show that the solution is within a bound from the optimal.

Theorem 4.1

For a continuous resource allocation to be optimal, a necessary condition is ∀i, 1≤i≤n, R _i =0, or for any flows {i,j} with R _i >0 and R _j >0, the cost slopes $C_{i}'(R_{i}) =C_{j}'(R_{j})$.

Proof

For a continuous differentiable function, the Kuhn–Tucker [87] theorem proves such a greedy scheme is optimal. Suppose for some i≠j, let the optimal resources be R _i >0, R _j >0, and $|C_{i}'(R_{i})| > |C_{j}'(R_{j})|$. As the savings in cost per resource for F _i is larger, we can subtract an infinitesimal amount of resource from F _j and add it to F _i . Total system cost is reduced, contradicting the assumed optimality. □

In a real system, however, the settings for different control dimensions such as modulation or transmit power are discrete. This results in a deviation, Δ, from the optimal resource assignment. We now show this worst-case deviation Δ from the optimal strategy is bounded and small.

Theorem 4.2

∃0≤Δ<∞, such that C _OPT ≤C _MEERA ≤C _OPT +Δ, where C _OPT is the optimal cost (energy consumed by all users) and C _MEERA is the cost in the discrete case.

Proof

For all flows, {F ₁,F ₂,…,F _n }, the aggregate system resources consumed are stored in the decreasing order of their negative slope across all per-flow Cost-Resource C _i (R _i ) curves. Based on this ordering, the aggregate system C(R) trade-off is constructed, consisting of segments resulting from individual flows. The greedy algorithm traverses the aggregate system C(R) curve, consisting of successive additional resource consumptions (at maximum cost decrease), until the first segment, s, is found that requires more resources than the residual resource R _avl (Fig. 6.10).

Let the two end points of the final segment s be (r _s ,c _s ) and (r _s+1,c _s+1) in C(R). Let (r _c ,c _c ) be the optimal resource allocation in the optimal combined Cost-Resource curve.

We observe that c _s −c _s+1≤Δ, therefore C _MEERA −C _OPT <Δ. Moreover, we note that with more dimensions (K _i,j ) considered, a better approximation can be obtained. □

6.4 IEEE 802.11a Design Case

To demonstrate the usability of the proposed control scheme we apply it to control a flexible OFDM 802.11a modem. The target application is the delivery of delay-sensitive traffic over a slow fading channel with multiple users. We associate the system Cost to energy, the Resource to the time over the shared medium and the Quality is the JFR.

We briefly consider the trade-offs present across the physical circuits, digital communication settings and link layer in our system. Increasing the modulation constellation size decreases the transmission time but results in a higher PER for the same channel conditions and PA settings. The energy savings due to decreased transmission time must offset the increased expected cost of re-transmissions. Also, increasing the transmit power increases the signal distortion due to the PA nonlinearity [81]. On the other hand, decreasing the transmission power also decreases the efficiency of the PA. Considering the trade-off between sleeping and scaling, a longer transmission at a lower and more robust modulation rate needs to compensate for the opportunity cost of not sleeping earlier. Finally, as all users share a common channel, lowering the rate of one user reduces the time left for other delay-sensitive users. This compels other users to increase their rate and consume more energy or experience errors.

6.4.1 Energy-Performance Anticipation

Four control dimensions for the physical layer have been introduced to steer energy and performance of these OFDM transceivers. As function of these control dimensions, the energy E _Tx (K _i ) needed to send and the energy E _Rx (K _i ) needed to receive a unit of L _frag bytes need to be characterized.

We realistically assume that the energy consumption of the digital baseband is a linear function of the number of symbols to decode ($E^{R}_{\mathit{DSP}}$ and $E^{T}_{\mathit{DSP}}$ in energy/symbol). For the turbo coder, the energy cost depends on the number of bits to decode ($E_{\mathit{DSP}}^{R}$ in energy/bit) at the receiver [77]. The block size used for the turbo coding is 288 bits. Based on current implementations [78], the frequency synthesizer, Analog-to-Digital Converter (ADC), Digital-to-Analog Converter (DAC), Low-Noise Amplifier (LNA) and filters are assumed to have a fixed front-end power consumption P _FE as given in Table 6.1. The time needed to wake-up the system (stabilization time for the Phase-Locked Loop (PLL) in the frequency synthesizer) is assumed to be 100 μs, which is optimistic but can be achieved when designing frequency generators for this purpose. Application layer frames are fragmented at the link layer into L _frag -sized fragments. We obtain the following expressions for the energy needed to send or receive a fragment of length L _frag , as a function of the current knob settings:

(6.11)

(6.12)

Finally, to complete the model, we introduce a term P _idle that denotes the power consumption when the transceiver is idle (Table 6.1).

Obtaining the actual values for energy consumption for each of the configurations only depends on the fragment size, and the analog and digital baseband power consumption values as function of the configuration settings. In practice, this information is obtained very fast by transmitting a L _frag packet once (requiring 0.1 to 1.3 ms depending on the configuration) using e.g. 1000 configurations (hence 1.3×10⁻³×1000=1.3 s for a complete system profile). It is acceptable to spend this time since this calibration only needs to be carried out once over the system lifetime and gives us sufficient information to fully characterizes the device’s energy and performance as function of the control dimensions considered.

We now have expressions for the gross transmission rate (Eq. 6.1) and for the energy consumption to send L _frag bits. However, to obtain the complete energy and performance models, we have to also take into account all overheads and compute the total energy and resource cost for each scenarios.

For each combination of feasible control dimensions of node i, K _i (which we will simplify to K), we compute the total expected energy consumption, total transmission time and resulting JFR while using the properties of a sleep-enabled 802.11e MAC. We assume that during each communication instance, all transmissions use the same configuration to eliminate reconfiguration costs. All transmissions employ the contention-free mode with transmit opportunity (TXOP) grants of 802.11e HCCA [88]. Let E _H , E _ACK and T _H , T _ACK be the pre-determined energy and time needed to transmit a header and acknowledgment. The energy and time needed for a successful E _good and failed³ E _bad transmission is then determined following Fig. 6.11 and using parameters listed in Table 6.1:

(6.13)

(6.14)

(6.15)

(6.16)

We now include the MAC layer retransmissions. Each fragment is transmitted with configuration K, for which we can determine the Packet Error Rate P _e , based on Eq. 6.4. The probability that the frame is delivered with exactly (m+p) attempts (including p retransmissions), is given by the recursion:

(6.17)

(6.18)

in which $\binom{m }{ i}$ denotes the number of combinations to select i fragments out of m. The resulting probability to deliver a frame (JFR) is:

$$ 1-\mathit{JFR}^m_p(\mathbf{K}) = \sum_{j=0}^p D^m_j(P_e,\mathbf{K}). $$

(6.19)

Time and energy requirements are respectively given by:

(6.20)

(6.21)

The expected energy for a given configuration is the sum of the probabilities that the transmission will succeed after m good and j bad transmissions multiplied by the energy needed for good and bad transmissions. A second term $Z^{m}_{p}(\mathbf{K})$ should be added to denote the energy consumption for a failed job, hence when there are less than m good transmissions, and (p+1) bad ones:

(6.22)

The third term H(K) denotes the cost that has to be added once every scheduling period. We will show later that this cost corresponds to a wake-up cost only and no reconfiguration cost should be taken into account, where we assume that the cost for each configuration K is constant.

Fig. 6.11

Timing of successful and failed uplink frame transmission with 802.11e HCF

We determine the Energy-Time-JFR trade-off as a function of the system state and number of retransmissions for each K. This specifies the full profile for the system, and is determined only once during design or calibration time. These can then be combined into the 3D profiles of the system (Fig. 6.9(a)). This cost, resource and quality profile information is stored in each node’s driver. We further prune the 3D profile to obtain per-flow Energy-TXOP curves. Configuration points that do not meet the target JFR ^∗ are pruned. Next, the convex minorant is computed in both Energy and TXOP dimensions. The resulting two-dimensional Pareto-optimal trade-off curves are shown in Fig. 6.12 for the considered channel and frame size scenarios.

Fig. 6.12

The resulting Energy-TXOP Pareto-optimal trade-off curves to be combined at run-time to achieve the network optimum

6.4.2 Anticipative Control in the 802.11 MAC Protocol

Based on the Energy and TXOP curves for each node, the scheduler in the AP can efficiently derive a near-optimal resource allocation at run-time using the greedy scheme described in Sect. 6.3.2. The scheduler requires feedback on the state of each user and then communicates the decisions to the users. In order to instruct a node to sleep for a particular duration, the AP needs to know when to schedule the next packet. Waking a node earlier than the schedule instance will waste energy. Buffering just two frames informs the AP of the current and also the next traffic demand, allowing a timely scheduling and communication of the next period TXOP. In the ACK, the AP instructs the node to sleep until the time of the next TXOP meanwhile also communicates the required configuration. The AP now communicates with each node only at scheduling instances (Fig. 6.13). As the real-time packets are periodic, we eliminate by doing so all idle time between transmission instances. When a node joins a network, it sends its cost, resource and quality curves (stored in its driver) to the AP during the association phase. The AP then stores this and refers to it during each scheduling instance. By adding just three bytes in the MAC header for the current channel state and the two buffered frame sizes, each node updates the AP of its current requirement in every transmission. Protocols such as 802.11e provide support for this communication and therefore require only minor modifications. The AP then fetches the predetermined set for the current state from memory. In the case study, this corresponds to less than 3000 bits per state. A software-based QoS Module within the AP’s network management layer maintains the list segments of all associated nodes and processes the current state of each node. At the beginning of each period, it executes the run-time phase of the control method and determines the configuration for each node during that period. The scheduling period requirement is determined by the rate at which the system state varies. Channel measurements show coherence times of 166 ms for stationary objects and moving scatterers [37]. Given a video frame rate of 30 ms, it is clear that this requires a scheduling period less than 30 ms. Since this timing requirement is rather low, a software module is sufficient. Alternatively, the QoS module can be integrated in a light-weight RTOS present in most embedded devices (as done in [89]). We expect the performance of the control method be lower for mobile networks with faster state dynamics, when it is difficult to feedback the system state timely. Faster adaptation schemes will be needed that integrate the adaptation module in hardware close to the physical layer [90].

Fig. 6.13

MAC with two-frame buffering in the Scheduler Buffer to remove data dependencies and maximize sleep durations. By the third period of the single flow shown, frames 1 and 2 are buffered and frame 1 begins service. As the transmission duration of frame 2 is known at this time, the sleep duration between completion of frame 1 until the start of service of frame 2 is appended in the MAC header

6.5 Adapting to the Dynamic Context

We now show how a cognitive radio can save energy by optimally adapting to the varying context. More specifically, the smart radio knows how to adapt its flexibility across many layers to achieve the best configuration in terms of QoS, energy or resource use. The focus is on real-time streaming media applications with a reasonable target JFR ^∗ set to 10⁻³. In order to evaluate the relative performance of the cognitive control method, we consider four comparative transmission strategies:

• 1. Smart: This is the optimal scheme considering the energy trade-off between sleep and scaling, exploiting multi-user diversity. The node configurations are based on the profiles of Sect. 6.4.1.

• 2. PHY-layer: This scheme considers only physical layer scaling knobs. The Energy-TXOP profiles are set to scale maximally as no sleep mode is available.

• 3. MAC-layer: In this scheme only sleeping is possible by the energy-aware MAC-layer. The physical layer is fixed to the largest constellation and code rate, with maximum transmit power. This approach is used by commercial 802.11 devices [8]. However, the 2-frame buffering makes the proposed implementation more efficient as it eliminates all idle time between transmissions.

• 4. Fixed: Similar to MAC-layer scheme but the transceiver remains in idle after transmission. A basic scheme with no energy management and hence no dynamic range is exploited here.

The Energy-TXOP profiles are computed for the control dimensions considered in each scheme and used by the scheduling scheme implemented in the Network Simulator ns-2 [91]. This simulator has been extended with transceiver energy and performance models, and a slow fading channel model. Our simulation model implements the functions of the 802.11e with beaconing, polling, TXOP assignment, uplink, and downlink frame exchange, fragmentation, retransmission and variable super-frame sizing. In all results, the total energy consumed by a node is averaged over a long duration to statistically capture the dynamics present in the scenario.

Consider the scenario where a single user has to deliver a unit frame every scheduling period. In Fig. 6.14, the energy consumption (normalized by the maximum energy consumed by Fixed) is plotted for the four schemes over different channel states. The anticipative adaptation method outperforms the other techniques in each state, since it takes advantage of the energy that can be saved by both sleeping and scaling. The energy needed to transmit a data fragment increases from best to worst channel state due to a combination of (a) the lower constellation needed to meet the PER (hence smaller sleep duration), (b) a higher required output power to account for the channel and (c) the increased cost of retransmissions. We observe, for example, that in the best channel state, the energy consumption is low for both the fixed and global approaches, and energy gains primarily result from sleeping. However, in the bad channel state the transmission energy is more important and scaling becomes more effective. The ratio of fixed to scalable energy varies as transceivers are designed differently. The take this into account during the calibration of system profiles. For a given platform, as users demand different levels of QoS, the proposed method jointly leverages the MAC and PHY to maximize the energy savings. A smart radio with control flexibility along many protocol layers, should know how to adapt to ensure an optimal user experience, energy use or resource use.

Fig. 6.14

Energy consumption across different channel states for 1 fragment

6.6 Conclusions

In this chapter it was shown how a flexible radio can be designed to meet the target QoS at minimal energy consumption for a set of anticipated scenarios. Flexible radios often have many different control knobs that can be tuned to save energy or boost performance. When many different knobs exist across many different layers, it becomes hard to anticipate the optimal configuration at design time. It was shown in this chapter how to achieve this for a 802.11a flexible radio. In the next section, it will be shown how a cognitive radio can be designed when the optimal configuration cannot be known perfectly at design time.