Table Of ContentOn the Use of Adaptive OFDM to Preserve Energy in Ad Hoc Wireless
Networks
Kamol Kaemarungsi and Prashant Krishnamurthy
Telecommunications Program,
School of Information Science, University of Pittsburgh
135 North Bellefield Avenue, Pittsburgh, Pennsylvania 15260.
Tel. 412-624-4099, Fax. 412-624-2788
{kakst112, prashk}@pitt.edu
Abstract - Orthogonal frequency division throughput, and routing efficiency are important
multiplexing (OFDM) is the physical layer in performance metrics. Energy efficiency is
emerging wireless local area networks that are especially important for mobile devices with
also being targeted for ad hoc networking. Mobile limited battery power. Cross-layer protocol design
devices in ad hoc networks need to conserve their and optimization can prolong the battery life of
energy because of the limited battery power. mobile devices [1]. Researchers have investigated
Adaptive OFDM is a technique that can improve making OFDM or discrete multitone (DMT)
the performance of OFDM in terms of increasing adaptive to maximize channel capacity by using
the capacity for a given transmit power by adaptive modulation and loading algorithms. Bits
exploiting the channel condition over a link. We and power loading algorithms control how the
believe that adaptive OFDM can be also exploited number of bits and power are allocated across all
in ad hoc networks to improve the energy subcarriers in OFDM such that the capacity over
performance of mobile devices. In this paper, we the link is maximized or the transmit power is
evaluate the improvement in performance of minimized. Several loading algorithms have been
adaptive OFDM over non-adaptive OFDM in ad proposed in the literature. For instance, the
hoc networks using simulations. algorithm of Fischer and Huber [2] is well known
1. INTRODUCTION for its simplicity and efficiency for discrete
Orthogonal frequency division multiplexing multitone loading. Campello in [3] also proved the
(OFDM) is important in wireless networks near optimality of the discrete greedy loading
because it can be used adaptively in a dynamically algorithm and suggested algorithms for efficient
changing channel. OFDM has also been selected loading with low complexity. However, it is not
as the standard physical layer for IEEE 802.11a clear how the ad hoc network performance
and IEEE 802.11g wireless local area networks constraints can impact making OFDM adaptive. In
(WLANs). At the same time, ad hoc networking ad hoc networking these measures may not be
using WLANs has received attention in recent sufficient to extend the battery life. This paper is a
years [1]. In ad hoc networks, energy efficiency, preliminary effort to understand whether adaptive
1
OFDM can impact the energy consumption in ad of the symbol, the inter-symbol interference (ISI)
hoc networks and how OFDM can be made caused by multipath fading can be further reduced.
adaptive. As a first step to understanding this Digital modulation schemes such as phase shift
problem, we compare the use of adaptive and non- keying (PSK) or quadrature amplitude modulation
adaptive OFDM in ad hoc networks in terms of (QAM) are usually used on each subcarrier;
energy consumption and bit error rates using however, the modulation technique does not have
simulations with QualNet. We only employ to be the same for all subcarriers.
primitive cross-layering in that we preempt 2.1 The Channel State Information
transmission if there are insufficient power Adaptive OFDM takes advantage of the
resources at the transmitter based on channel independence of subcarriers by assigning higher
knowledge. In section 2 of this paper, we discuss energy and larger number of bits to subchannels
the notion of adaptive OFDM and bit loading that have better quality or higher SNR and
algorithms for adaptive OFDM. In Section 3, we assigning less energy and bits or none at all to the
provide a brief review of energy conservation poor quality subchannels. This technique is a well-
techniques in ad hoc networks. Section 4 discusses known result from information theory that states
the details of the simulation, the set up, and the that the channel capacity can be maximized by a
results. Section 5 considers approaches for future water-filling or water-pouring technique [3]. An
work. important assumption is that the transmitter has
2. ADAPTIVE OFDM the channel state information (CSI) in order to
OFDM is a sub-class of multicarrier perform power or bit allocation to achieve the
modulation (MCM) that combines parallel data maximum channel capacity. This may be difficult
transmission with frequency division multiplexing to achieve in practice, but it is possible that the
(FDM) technique and allows spectral overlap of estimated channel information can be obtained at
subchannels. The idea is to transmit single high- the transmitter using feedback from the receiver or
rate data stream over multiple parallel low-rate in the case of reciprocal channels. Note that the
data streams [4]. The low-rate data streams are CSI is only applicable between a given
modulated onto orthogonal subcarriers in order to communication pair and different CSI are required
avoid adjacent carrier interference and improve for different pairs of communicating nodes. The
spectrum efficiency. Due to the longer symbol channel state should also change slowly compared
period on each subcarrier, the OFDM signal is to the frame duration [5]. Otherwise, adaptive
more robust against large multipath delay spreads OFDM may perform worse than non-adaptive
that are normally encountered in wireless OFDM. In indoor wireless local area networks, it
environments. With a cyclic prefix or a repetition is likely that the channel changes very slowly
of part of OFDM symbol added at the beginning because the mobility of the node is limited. Both
2
adaptive and non-adaptive OFDM require channel inefficiency in greedy-like algorithms. The result
knowledge at the receiver in order to detect the is a slightly suboptimal allocation, but with a
correct transmit symbol on each subchannel. This dramatically reduced computational complexity
can be achieved by using known training symbols [3]. The authors predict that with advances in
or blind detection [6], [7]. All OFDM systems digital signal processing, the loading algorithms
require channel coding (such as convolutional will be able to perform in real time and be suitable
codes) to maintain low bit error rates [8]. for operations such as those envisaged in this
2.2 Loading Algorithms paper.
The water-filling power distribution is known An OFDM link can be modeled as a group of
to be the optimal solution for any spectrally parallel AWGN channels. The wideband radio
shaped channel [3]. The resulting bits or power channel is partitioned into discrete narrowband
allocation maximizes the information capacity and subchannels with channel bandwidth of ∆f Hz.
it is called the capacity-achieving distribution. A Each channel is free of inter-symbol interference
greedy algorithm can be used to find the optimal when ∆f is small and the channel response appears
solution for this problem. For a large number of to be flat for each channel. In the case of single
bits and subchannels on the order of 1000s, the carrier communications, the information capacity
greedy algorithm is inefficient due to operations for an ideal channel with AWGN follows
involving channel gain sorting and the number of Shannon's information capacity theorem. In
iterations [3]. However, in the case of small practical systems, a quantity called SNR gap is
number of bits and channels such as those in IEEE introduced and used to determine the efficiency of
802.11a, the number of bits is between 48 and 288 a modulation or encoding scheme compared to the
(to be loaded on 48 subchannels for data rates ideal scheme [3]. For a practical modulation or
between 6 Mbps and 54 Mbps) [9]. For instance, encoding scheme, the system can transmit at most
48 bits per one OFDM symbol with 4 µsec symbol R bits/transmission with the lowest acceptable
duration is needed to achieve a 6 Mbps data rate error rate. The SNR gap is defined as a ratio of
that includes a convolutional rate ½ code. ideal SNR at which the system can transmit at C
A number of loading algorithms have been bits/transmission over a practical SNR at which
proposed in the literature such as the algorithms by the system can transmit R bits/transmission. It is a
Fischer and Huber [2], and Campello [3]. They measure of how well the practical system
propose different approaches to solve the loading compares to an ideal modulation system. The
problem such as minimizing the bit-error-rate channel capacity in bits per transmission can be
(BER) (rather than maximizing the SNR or the calculated by [10].
capacity of the channel). Most algorithms try to α
C = log (1+SNR) (1)
avoid intense sorting and searching that causes 2 2
3
Note that α is the dimension of modulation optimization perspective [3]. First, a bit rate
scheme, i.e. α = 2 for M-QAM modulation maximization problem can be formulated by
scheme. Rearranging Equation 1 enables us to maximizing the total number bits across all OFDM
express the SNR as SNR = 22Cα−1. Using a subcarriers in Equation 3 subject to the constraint
that a fixed amount of power is available to the
similar expression for the SNR of practical
transmitter. This is similar to the classical water-
systems, the SNR gap, denoted by Γ, can be
filling formulation in [10]. Second, an energy
calculated as
minimization problem can be formulated by
22Cα−1 SNR
Γ = = . (2) minimizing the total amount of power on all
22Rα−1 22Rα−1
OFDM subcarriers in Equation 4 subject to the
The SNR for additive white Gaussian noise
constraint of a fixed amount of bits transmitted per
(AWGN) with noise variance of σ2 per dimension
OFDM symbol. Given an energy function ε(R )
n
can be defined asSNR = H2ε, where H is channel
α⋅σ2 for a particular modulation and coding technique
gain and ε is the transmit power per symbol. where R is the number of bits on subcarrier n,
n
Therefore, for a particular combination of R is the total number of bits per OFDM
Total
encoding scheme and modulation with 2- symbol, E is the fixed amount of power
Total
dimensional symbol constellation, the SNR gap available, and B is the fixed number of bits per
can be used to determine the data rate for symbol per second, the formulation of these
subchannel n in multicarrier communications [3] optimization problems are described below. Note
as that the resulting bit allocation should be a positive
integer.
⎛ H 2ε ⎞ ⎛ G ε ⎞
R = log ⎜1+ n n ⎟ = log ⎜1+ n n ⎟, (3)
n 2⎜⎝ 2Γnσn2 ⎟⎠ 2⎜⎝ Γn ⎟⎠ Bit Rate Maximization or Water-filling Problem
N
where Gn = 2Hσn22 . If Tsym is the OFDM symbol Maximize ∑Rn(εn)= RTotal (5)
n n=1
duration, the data rate of OFDM over all N
Subject to ∑ε ≤ E and R ⊂ Z+(6)
subchannels is R = 1T ∑nN=1Rn . By n=1 n Total n
sym
Energy Minimization Problem
rearranging Equation 3 the energy function can be
N
written as a function of bits per subcarrier as Minimize ∑ε (R ) = E (7)
n n Total
n=1
2Γσ2 ( ) Γ ( )
ε = n n 2Rn −1 = n 2Rn −1 (4) N
n H 2 G Subject to ∑R = B and R ⊂ Z+ (8)
n n n n
n=1
2.3 Campello’s Algorithm
The solution to either one of the above
Campello suggests that the water-filling formulations can be found by forming a
problem can be formulated in two ways from the
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Lagrangian equation and taking the partial
derivative with respect to the multiple constraint
variables, i.e. ε for bit rate maximization and R
n n
for energy minimization [3]. For instance, the
Lagrangian equation for bit-rate maximization is
N ⎛ Gε ⎞ ⎛ N ⎞
J = ∑log ⎜1+ n n ⎟+λ⎜E −∑ε ⎟. (9)
n=1 2⎜⎝ Γn ⎟⎠ ⎝ Total n=1 n⎠
(a)
Assuming that the SNR gap is equal for every
subchannel, the solution to the problem consists of
a water-filling constant K. The subchannel energy
allocation can be calculated using this constant
and the SNR of the subchannel. The solution to the
optimization in Equation 5 is
1 ⎛ N 1 ⎞
K = ⎜E +Γ∑ ⎟ (10)
N ⎜ Total G ⎟
⎝ n=1 n ⎠ (b)
+
⎛ Γ ⎞
ε =⎜K − ⎟ , n =1,2,...,N (11)
n ⎜ G ⎟
⎝ ⎠
n
where (x)+ = x if x > 0, otherwise (x)+ = 0. Any
subchannel that has negative energy allocation will
be turned off by the transmitter. Note that the
amount of energy used is measured in joules =
watts×seconds. (c)
An example of the solution for energy
minimization is shown in Figure 1 for OFDM with
64 subcarriers. Figure 1a represents the channel
frequency response for a three equal-tap-gain
channel model. Figure 1b represents the
continuous bit loading result from the energy
minimization algorithm in [3]. Figure 1c
(d)
represents the discretized bit loading result and Figure 1. Example of Energy Minimization
Figure 1d represents the corresponding power Loading, (a) Channel Response, (b) Continuous
allocation. In this example, the noise variance is Bit Allocation, (c) Discrete Bit Allocation, (d)
assumed to be 1 for all subchannels. Power Allocation of Discrete Bit Allocation.
5
The dual formulations of water-filling solution output power during the transmitting and receiving
can be applied at the physical layer to either state add additional energy consumption to that of
maximize the data rate or minimize the energy on the idle state [11]. In the literature three separately
each frame transmission. These two alternatives energy preservation approaches are suggested at
are investigated in the next section for their impact different layers for ad hoc wireless networks [12].
on the energy consumption of an ad hoc wireless For instance, power saving protocols and power
node. The question that this paper would like to control protocols are suggested at the MAC layer
answer is how much of energy can be preserved and a maximum lifetime routing protocol is
by employing adaptive OFDM on the physical suggested at the network layer. These approaches
layer. Another question regarding the cross-layer only focus on the protocols at the medium access
protocol design is how the channel information control layer and above. They try to minimize the
gain from the loading algorithm will help improve energy consumption in different parts of ad hoc
the energy preservation of ad hoc wireless systems by maximizing the idle state, minimizing
network. the transmit power, and using routing knowledge
3. TECHNIQUES FOR REDUCING to extend the network lifetime.
ENERGY IN AD HOC NETWORKS 3.1 Energy preservation at the MAC layer
Due to the emergence of small mobile devices Power saving protocols and power control
with limited battery capacity, energy-aware protocols are categorized as energy efficient
protocols are key to the success of this technology. techniques at the MAC layer. The power saving
It is suggested that the energy optimization should protocol puts most of the ad hoc nodes into sleep
be done across all protocol layers in a cross-layer mode as often as possible. It is more suitable for
approach [1]. Each cross-layer protocol stack networks with a centralized control that is needed
should adapt its operations to the network load, the to maintain the connectivity of all adjacent nodes
energy budget, and link characteristics. The that go into sleep mode. To implement this
cooperation and exchange of necessary approach in a peer-to-peer ad hoc network will be
information between layers must be allowed for quite complex due to the scheduling of the sleep
any cross-layer protocol to adapt to global system time. It also limits the capacity of ad hoc networks
constraints and characteristics. Energy on ad hoc because these nodes cannot forward frames during
wireless devices is consumed differently during their sleeping period. It is a tradeoff between
the transmitting state, the receiving state, and the network capacity and energy preservation [13].
idle state. It has been shown from early There is also significant cost of changing the node
measurement results that the power used during state from sleep to idle and vice versa that may
the idle state of a mobile node dominates the outweigh the power saving technique [14]. On the
overall (total) energy consumption, while the other hand, power control protocols reduce the
6
transmit power to levels that can just maintain the temporal fluctuations of the channel in frequency
connectivity between adjacent ad hoc nodes. This selective fading media. The service requested by
approach can minimize the energy consumption the MAC layer can be supported by this smarter
due to transmission and additionally improve the physical layer equipped with a bit loading
network capacity by minimizing the interference algorithm.
between transmissions [13]. In our work, using adaptive OFDM, an extra
3.2 Energy preservation at the routing layer channel capacity is gained during a short period
Instead of focusing on power consumption at when the channel is considered good for
each mobile node, an energy conserving routing transmission. During this time, the physical layer
approach tries to create energy aware routing can transmit a MAC frame faster using the same
mechanisms for ad hoc wireless networks. For transmit power level as it could without adaptive
example, in the maximum lifetime routing OFDM. This benefit can be converted into the
protocol, a selection is made from different routing saving of energy consumed for transmission. The
metrics such as minimum energy routing, max- loading algorithm based on bit rate maximization
min routing, and minimum cost routing to preserve [3] is selected as our choice of study. The idea
the energy in forwarding packets [12]. The ad hoc here is to push as many bits across the channel as
network routing protocol should consider both the possible while the transmitter has the opportunity
cost of transmitting each packet and the residual to do so thereby reducing the channel holding time
energy of nodes that will be used to further on average. We assume that advances in digital
forward packets. All three approaches discussed so signal processing techniques allow the radio
far focus mainly on specific layer of the protocol channel to be estimated fast enough in a slowly
stack and do not consider any cooperation between changing wireless environment.
the techniques [12]. To solve the problem of channel state
3.3 Adaptive vs. Non-adaptive OFDM information at the transmitter, we add extra
information in the MAC header of the IEEE
This paper suggests an adaptive protocol layer
802.11 protocol within the request-to-send (RTS)
that fits into cross-layer design criteria at the
and clear-to-send (CTS) packets and the details are
physical layer with a primitive cooperation
discussed in the next section. Since the maximum
between the physical layer and MAC layer. A
allowable data rate in fading channels can be
potential stronger cooperation is possible with the
higher or lower than the MAC layer’s minimum
bit rate and power budget parameters as the
request rate, the MAC protocol in this paper
information exchanged between the physical and
decides on allowing the communication over the
MAC layer. Given that the radio channel
link by choosing to reply or not reply with a CTS
characteristics can be estimated at the receiver, an
frame. By this, the MAC layer avoids a longer
adaptive OFDM physical layer can exploit the
7
transmit time with smaller data rate that could The Rayleigh multipath fading is modeled
consume more energy. with three tap gains according to the JTC indoor
4. SIMULATION AND RESULTS office areas Channel A, although this not strictly
The performance of an ad hoc wireless for a 5 GHz frequency band [18]. The tap
network using adaptive OFDM is evaluated with parameters are shown in Table 1. Each tap is a
the QualNet packet level simulator. Below we random process generated before the actual
describe the parameters and scenario used in our simulation using Jakes’ method [19]. During the
simulations at various layers of the protocol stack. simulation, a set of tap gains is randomly selected
4.1 Radio channel model from a pool to simulate the Rayleigh fading
between each pair of nodes.
A two-ray path loss model is assumed with a
shadow fading sigma of 12 dB which is suitable Table 2. JTC Indoor Office Areas Channel A
for indoor environments [16]. The thermal noise Tap Relative Delay Average Power
No. (nsec) (dB)
floor is calculated from the Boltzmann constant k
1 0 0
= 1.379×10-23 W/(Hz⋅K°) at T = 290 K°, noise 2 50 -3.6
3 100 -7.2
factor F = 10, and an effective noise bandwidth in
BW Hz using the following equation W = The maximum Doppler shift frequency of the
F⋅k⋅T⋅BW = BW⋅3.9991×10-20 Watt. model is set to f = 30 Hz for slow time-varying
d
The simulator has a radio model with capture channels which corresponds to the maximum
capability that can receive the strong radio signal mobile speed of v = 1.73 m/s at f = 5.2 GHz. Each
c
among interferering signals [17]. Packet error is OFDM symbol has symbol duration T = 4 µsec.
sym
based on the SNR threshold – i.e., a packet is Assuming a maximum data frame length of 4096
assumed to be in error if the SNR is below a bytes and each OFDM symbol can support 24 un-
threshold of 10 dB above the noise level. The coded bits, the frame duration is approximately
physical and MAC parameters follow the IEEE T = (4096×8×4µsec)/(24) ≈ 5.461 msec. The
frame
802.11a specifications [9] and are summarized in
normalized maximum Doppler rate is f ×T ≈
d frame
Table 1. However, the rate fall back feature is not
0.1638 which is close to the reasonable values for
used.
the rate adaptive physical layer system in [20].
Table 1. IEEE 802.11a Specifications 4.2 Physical layer model
Physical Layer A continuous bit loading algorithm based on
Center Frequency 5.2 GHz
Campello’s bit rate maximization algorithm [3] is
Channel Bandwidth 20 MHz
Minimum Data Rate 6 Mbps
implemented in the simulation for both transmitter
Receiver Threshold -82 dBm
Antenna height 1.5 m and receiver. It is possible to find the maximum
number of bits per OFDM symbol. The digital
8
modulation scheme on each subchannel is transmission duration, which depends on the
assumed to scale the constellation from 1 bit to instantaneous data rate and frame size for a given
higher bits per symbol using BPSK and M-QAM transmit power. The transmit energy is calculated
modulations. The SNR gap is assumed to be 8.8 by multiplying the transmit power consumption of
dB for un-coded QAM bits with error rate P of 1412 mW by the duration of the frame. The energy
e
10-6 as given in [7]. The resulting bit rate is based consumption rates for both transmit, receive, and
on a continuous bit distribution and needs to be idle states are assumed to be constant over time.
discretized by rounding down to the nearest 4.3 MAC layer model
integer. Campello [3] suggests an Energy Tighten The IEEE 802.11 MAC layer is based on
Algorithm to reallocate the left-over energy from Carrier Sense Multiple Access with Collision
the rounding bit to guarantee an optimal solution. Avoidance (CSMA/CA). The simulation operates
Assuming the loading calculation can be done in only in the distributed coordination function
real time due to the small number of bits and (DCF) mode. It also has the request-to-send (RTS)
subcarriers (as discussed previously) we ignore the and clear-to-send (CTS) control signaling to avoid
energy spent on this calculation as not significant. the hidden terminal problem and to carry extra
The bit loading can only be done on a data frame information for channel estimation procedures as
since the transmitter can gain the channel in [20]. The overhead information is the SNR level
information only after the CTS frame has arrived. and channel impulse response estimated at the
Therefore, all signaling (control) frames – the RTS receiver. Figure 2 illustrates an adaptive OFDM
and CTS are not adaptive. Due to the multiple transmission procedure.
receiver possibility, the MAC broadcast frames are
RTS Channel
also non-adaptive. Both control and broadcast tim T R BEistt iLmoaatdioinng a fnodr
e MAC’s decision
frames are sent at a rate of 6 Mbps.
CTS w/ CSI
The power consumption is based on the Channel
T R is good.
Perform
estimated values given in Agere’s product
Bit
Loading
specification 2003 [21]. The estimated active Adaptive DATA
T R
receive and transmit power consumption of an
802.11a standard device is given as 951 mW and
ACK
1412 mW respectively. The idle state power T R
consumption is assumed to be equal to power Figure 2: Procedure of DATA frame transmission
consumption in receive mode although this is an
over-estimate. We use per packet energy The network allocation vector (NAV) duration
consumption in this paper. The energy consumed for each data frame is calculated from the smallest
by each frame is linearly dependent on its data rate of 6 Mbps. We do not vary it according
9
to the variable duration of the adaptive OFDM adaptive OFDM when the received SNR is
frame. This causes a longer waiting time due to the changed due to the distance. The simulation
NAV in neighboring nodes, but it does not cause duration is 120 sec. Each experiment has 10
any problems to the transmission. The data frame repetitions and we calculate the 95% confidence
duration will be guaranteed to have at least 6 interval of the mean value of the energy
Mbps of bandwidth in our modification to the consumed. We assume that nodes in the network
MAC protocol in the case of adaptive OFDM. We always have packets for transmission. Each node
note that this study does not attempt to maximize has a constant bit rate (CBR) packet generator
capacity, but only evaluate the energy savings which generates a 2020-byte packet every 90 msec
from adaptive OFDM. or a data rate of 179.556 kbps. The traffic is only
4.4 Network layer model one hop from the origin node and only 4 CBR
The network layer is the internet protocol (IP) streams from node 1 to node 2, node 2 to node 3,
and the transport layer is UDP. The routing node 3 to node 4, and node 4 to node 1 are present.
protocol is ad hoc on demand distance vector Each node cannot transmit and receive at the same
(AODV) in unicast mode [22]. This protocol time.
discovers a route whenever there is a request by 4.6 Results
issuing a Route Request (RREQ) message. The The simulation results of the average transmit
routing table on each node is filled by both RREQ energy consumed per node is shown in Figure 3.
message and the reply information on the unicast
hr 95% Upper C. I. 95% Lower C. I. Mean
W
Route Reply (RREP) message from the
n m 3.5
neighboring nodes. The old route in the table is on i 3
pti
eliminated based on the sequence number and its um 2.5
s
n
activity. In this study, we do not modify this ergy coer node1.52
np
protocol to learn of the change from the physical mit e 1
s
layer. The routing protocol parameters are set an 0.5
ge tr 0
4ac.5co Nrdeitnwg otor kth teo vpaoluloesg yin [22]. Avera a-25m n-25m a-50m n-50m a-100m n-100m a-150m n-150m a-200m n-200m
Four ad hoc nodes are placed in a simple Figure 3. Comparison of transmit energy
consumption
rectangular topology. The nodes are assumed to be
stationary which is the case for most indoor
Here adaptive and non-adaptive nodes in each
operations of today. The distance between two
experiment are denoted with letter a and n
closest nodes is varied from 25 meters to 200
following by the distance, respectively. At each
meters. The simulation study compares the energy
distance point, the adaptive OFDM physical layer
reduction achieved by adaptive OFDM over non-
consumes less energy. This is because on average
10
