AN IMPROVED CHANNEL MODEL FOR MOBILE AND AD HOC
NETWORK SIMULATIONS
Jeff McDougall
Electrical Engineering Dept.
Texas A&M University
College Station, TX 77843
[email protected]
Jeevan Joseph
Computer Science Dept.
Texas A&M University
College Station, TX 77843
[email protected]
ABSTRACT
In this paper we propose a low complexity fading channel
model for use in Mobile and Ad Hoc Network (MANET)
simulations. While numerous fading channel models
exist, our model provides accurate performance across a
wide range of signal to noise ratios (SNR) while requiring
minimal operational complexity and is applicable for
large, multi-node simulations. This work presents a
unique four-state Markov channel model for simulating
correlated channel errors and presents its statistical
accuracy and network performance.
KEY WORDS
Wireless Networks, Adhoc Networks, Fading Channels,
Cross-Layer Design
1. Introduction
The research area of mobile ad hoc networking has
enjoyed substantial popularity in recent years. Significant
strides have been taken in higher-layer protocol design,
specifically in the transport and networking layers.
However, there remains room for improvement in
simulating correlated physical (PHY) layer error
behaviour and its impact upon the media access control
(MAC) layer. One hindrance to progress in the crosslayer simulation of wireless links is the absence of a well
accepted fading channel model. While the need for
including correlated channel errors in wireless network
simulations has been well documented in the literature
[1], there have been relatively few researches employing
correlated channel errors for multi-node MANET
simulations.
The optimum channel model for observing MAC/PHY
interactions is one that simulates the physical layer with a
baseband equivalent channel. Most network simulations
involve the transmission and reception of millions of
packets with each containing thousands of bits. Due to
the computational complexity of simulating a wireless
link’s modulation, transmission, channel corruption and
demodulation, the optimum channel model proves
cumbersome.
When multi-node simulations are
Yu Yi
Electrical Engineering Dept.
Texas A&M University
College Station, TX 77843
[email protected]
Scott Miller
Electrical Engineering Dept.
Texas A&M University
College Station, TX 77843
[email protected]
attempted, the number of possible wireless links increases
exponentially with the number of network nodes, thus
making the optimum approach computationally
impractical for multi-node MANET simulations.
Many researchers desiring to incorporate correlated
channel errors within their network simulations have
employed one of two popular approaches, namely: the
Ricean Fading Model [2] and the two-state Markov
Model [3]. Most, however, have avoided simulating
correlated channel errors and instead opted for an energy
propagation model. In this paper, we propose an
improved fading channel model that overcomes the
disadvantages of previous models with only a negligible
increase in computational complexity. Performance gains
are achieved through a structured, sub-optimal
approximation of the distribution of channel-error
durations. Specifically, we offer a unique channel model
for accurately characterizing the distribution of short and
long run durations of a representative error trace.
Furthermore, network simulations are conducted to
quantize the gains in accuracy of our model as compared
to the popular 2-state Markov model.
As reviewed in Section II, several approaches are
possible for including correlated channel errors in
network simulations.
But these approaches have
shortcomings when applied to multi-node MANET
simulations. Section III presents the improved channel
model architecture and its statistical accuracy. Network
simulation results are presented and analysis provided in
Section IV with conclusions drawn in Section V.
2. Related Work
Fading channel models can be broadly categorized into
those that produce correlated channel statistics and those
that do not. The Ricean Fading Model and the 2-state
Markov model (2SMM) represent the two most advanced
and popular techniques for simulating correlated wireless
channel errors through the use of a fading process. The
Ricean model simulates channel integrity through
instantaneous signal-to-noise ratio (SNR) values derived
from a very thorough simulation of a fading process. The
2SMM takes a different approach by approximating a
representative error trace, or the ordered good/bad frame
integrity results obtained when operating across a fading
channel. While both techniques offer advantages for
specific network scenarios, they lack the overall accuracy
and/or simplicity necessary for multi-node MANET
simulations.
Punnoose et al. [2] propose a Ricean channel model
that produces very accurate instantaneous signal-to-noise
ratio (SNR) values for a single fading channel. The
drawback of this promising channel model is not the
accuracy of its fading channel statistics, but instead is the
process by which the frame integrity is derived. In fact,
frame integrity for this model is determined through a
threshold detector that compares the instantaneous SNR
value with a minimum receiver sensitivity value. Hence
all SNR values above the threshold yield uncorrupted
frames while all those below are received in error. While
offering a very simple implementation algorithm, this
approach is not representative of a true demodulation
process. Furthermore the Ricean model simulates only
one fading process that is common to all links within the
network simulation. Therefore all inter-nodal wireless
links experience the same fading process and all links
with a common average power will experience a truly
unrealistic event: identical channel errors. The Ricean
model can also utilize significant storage space as all
channel statistics are computed before the simulation
begins. While the Ricean model offers an adequate
approach for a single link simulation, when disregarding
the frame integrity concerns, it does not offer an
appropriate solution for multi-node MANET simulations.
Zorzi et al. [3] present a formal procedure for utilizing
a 2SMM to approximate a link’s frame error process for a
Rayleigh fading channel.
The procedure defines
transition parameters for a two-state Markov process with
a ‘good’ state representing a successful frame
transmission and a ‘bad’ state representing channel error.
While requiring very little computational complexity to
operate, the 2SMM has been shown to produce significant
throughput errors at low to moderate SNR [4],[5],[6].
Due to the inability of the 2SMM to operate across all
SNR values of interest, it should be used selectively for
those MANET simulates with a guaranteed high SNR.
Konrad et al. [4] offer a unique variant of the
traditional 2SMM called the Markov-based Trace
Analysis (MTA) channel model. In their approach, a
representative error trace is divided into stationary subtraces that are each modeled independently.
The
transition probabilities between sub-trace models are
solved through observations of the length distributions of
each sub-trace. Due to the model’s use of exponential
trace lengths one could model each sub-trace with a
2SMM. Therefore, the MTA channel model can be
summarized as a 2SMM with time-varying parameters.
The MTA approach offers a somewhat general purpose
algorithm for channel modeling. However, the MTA
algorithm, as proposed in [4], suggests an ad-hoc
approach for parameter estimation and thus introduces the
risk of user error while hindering repeatability.
Compared to the above channel models, our approach
utilizes a mixture of geometric distributions to
approximate the distribution of ‘good’ and ‘bad’ channel
state durations. Similar to the 2SMM, our approach
involves a representative error trace. However instead of
attempting to approximate low-order parameters of the
error trace, our approach attempts to model the actual
distribution of ‘good’ and ‘bad’ run durations.
3. Model Architecture
A significant challenge facing low complexity channel
model development is identifying the statistical accuracy
required to generate representative network performance
results. Compounding the challenge of channel model
analysis is the lack of an optimum ‘simulated’ channel by
which to benchmark performance of sub-optimal
approaches, resulting in an open loop design process.
Upon identifying this deficiency, we constructed a
baseband equivalent physical layer simulation (BEPL)
within ns2 that employs CCK modulation (802.11b)
operating across a flat Rayleigh fading channel [5]. This
tool offers a closed loop comparison of network
performance for various channel models.
Often, channel models will attempt to simulate the
statistics of a representative error process. The results of
a transmission across a wireless link can be quantified as
belonging to the discrete space E = {0,1} where 1 denotes
a corrupted frame and 0 denotes a successful reception. A
representative error trace is generated by sending
sequential, common-length frames across a channel of
interest and classifying the results according to E.
Assuming the error trace to be a stationary random
process {Xn | n ≥ 0 }, one can attempt to fashion a discrete
channel model that approximates the statistics of Xn. It is
often helpful to approach this problem through observing
the duration of consecutive ones (bad run) and
consecutive zeros (good run) produced by Xn.
Following the approach of [4], we define two random
processes with a discrete space E = {0, 1, 2, …}:
 The bad run duration process {Bn | n ≥ 0},
represents the number of consecutive ones
occurring at the nth bad run.
 The good run duration process {Gn | n ≥ 0},
represents the number of consecutive zeros
occurring at the nth good run.
According to [3], the 2SMM parameters can be solved
using the frame error rate ‘e’ and average burst error
length ‘mb’ of a representative error process. In terms of
our definitions, we can solve for these quantities as
shown:
e
1
,
E Gn 
1
E Bn 
(1)
mb  EBn .
(2)
While the 2SMM parameters can be set with only first
order statistics of Gn and Bn, it has been shown to produce
significant throughput errors when compared to the BEPL
results [6] at low to moderate signal to noise ratios (SNR).
Good
State
Bad
State
Ĝ
B̂
3.1 The Run Length Model
We propose that accurate network performance can be
achieved through a channel model capable of
approximating the distributions of Gn and Bn. An optimal
approximation will attempt to simulate the joint statistics
of Gn and Bn, however due to the extreme complexity of
this approach, we propose the structured, sub-optimal
method of independently modeling Gn and Bn through a
run length model (RLM). The RLM contains two states
(Fig 1) representing good runs and bad runs. Each state
produces a consecutive run of common frame results with
the durations defined by random variables as shown:

RLM bad state duration { B̂ }, is a random
variable representing the number of consecutive
ones occurring when the ‘bad’ state is entered.

RLM good state duration { Ĝ }, is a random
variable representing the number of consecutive
zeros occurring when the ‘good’ state is entered.
An example realization is provided for the RLM process,










x1 ,..., x g1  0 , x g11 ,.., x g1b1  1,...


 

 


 

xn   x N 1  ,..., x N 1 
 0 ,  , (4)

2

2
  
 

g i  bi  1
g i  bi   g N




 
  i 1

 i 1
 2



 
 

 
 

 

,..., x N
 1 
 x N2



 2

 

   gi bi 1b N
g i  bi 






 
i

1
i

1
2
 






 

that begins in the ‘Good State’ and has N-1 state
transitions. As shown, the process alternates between the
two RLM states with each state producing a run of
consecutive zeros (gi) or ones (bi). The expected number
of realizations produced by the RLM in this example is
E n | N states  
    
N
E Gˆ  E Bˆ .
2
(3)
Fig 1. Run Length Model (RLM)
If the realizations of the representative run duration
processes Gn and Bn are assumed to be independent,
identically distributed (i.i.d.), one can make the following
assignments for the RLM state duration random variables,




P Bˆ n  i  PBn  i  n, i ,
P Gˆ n  i  PGn  i  n, i .
(5)
(6)
Finally, we can approximate the discrete probabilities of
the (assumed) i.i.d. parameters Gn and Bn through
observing the relative frequency of (G=i) and (B=i) in the
representative error trace.
We have found that some network simulations
employing the RLM channel produce throughput results
nearly identical to those obtained from employing the full
BEPL channel. While the results were encouraging, the
approach was problematic as it required a very long
representative error trace to obtain good estimates of the
run duration processes Bn and Gn. Producing the
extensive representative error traces required prolonged
physical layer simulations, and the resulting random
variables B̂ and Ĝ were challenging to implement. The
RLM, while not ideal, provided a ‘sanity check’ for the
validity of using run duration processes as the bases for
developing low complexity channel models.
3.2 The Four State Markov Model
The RLM is designed to exactly match the
distributions of the, assumed i.i.d, processes Gn and Bn.
While producing good networking results, the RLM
requires a non-trivial setup time for each environment to
be simulated.
The drawbacks associated with
implementing the RLM impelled us to produce a
simplified realization of the RLM random variables
B̂ and Ĝ to approximate the distributions of Gn and Bn.
As an alternative to matching Gn and Bn explicitly, we
notice in Fig. 2 that short and long duration runs of both
Gn and Bn follow a somewhat exponential behaviour.
PMD of B(n) Comparison for SNR=10dB
0
10
Sample Rep.
Error Trace
Matched 4-state MM
Matched 2-state MM
-1
10
PMD
-2
10
-3
10
-4
10
-5
10
0
50
100
Run Duration
200
PMD of G(n) Comparison for SNR=10dB
0
10
Sample Rep.
Error Trace
Matched 4-state MM
Matched 2-state MM
-1
10
-2
PMD
150
10
-3
10
-4
10
-5
10
0
100
200
300
Run Duration
400
500
Fig 2. Run Duration Distributions Bn & Gn
Comparisons
In an attempt to reduce implementation complexity, we
propose to approximate the desired distributions through
random variables with a mixture of geometric
distributions,
f n  p1    n  1  p 1    n ,
(7)
where α, β, and p are parameters suitably chosen to
approximate the desired run duration. One set of
parameters {αb, βb, pb} is chosen for the bad run durations
fB(n) and another set {αg, βg, pg} for the good run
durations fG(n). The resulting 2-state RLM is illustrated
in Figure 3.
Since the distributions of the random variables B̂ and Ĝ
are approximated using a mixture of geometric
distributions, the resulting RLM can be realized with a
simple 4-state Markov Model as illustrated in Fig. 4.
Both the good and bad states have been split into two substates, one which tends to produce short runs and one
which tends to produce long runs. In this model, any
transition ending in one of the good states produces a
correct sub-frame while any transition ending in one of
the bad states leads to a sub-frame error. The parameters
αb and pb are chose to fit the slope of the ‘head’ (short run
durations) of Bn’s probability mass distribution (PMD),
while βb is chosen to fit the slope of the ‘tail’ (long run
durations). In the same way, {αg, βg, pg} are chosen to
match the PMD of Gn.
As shown, the 4SMM offers an elegant implementation
for the approximated RLM in Fig. 3 and thus overcomes
one of the major drawbacks of the more general RLM
presented in Fig. 2. The parameters of the 4SMM (as
stated) are still based upon knowledge of a representative
PMD, and thus the 4SMM does not improve upon the
need for long physical layer simulations. We are
currently formalizing an approach to analytically set the
4SMM parameters, {αg, βg, pg} and {αb, βb, pb}, from
knowledge of E[Gn] and E[Bn] for a Rayleigh fading
channel. This approach will alleviate the 4SMM’s
dependence upon PMD ‘head’ and ‘tail’ slopes. In the
next section we present performance results for network
simulations employing channel approximations and
compare the results against those obtained when
employing a BEPL channel.
4. Network Performance of Channel Models
In this section, we present results of network
simulations employing our improved channel model
(4SMM) and compare them against the performance
obtained with both the 2-state Markov model and a BEPL
channel. In this section, we help to quantify the network
impact of the assumptions made in Section III.
4.1 Channel Model Integration
Ns2 is a complex, open-source network simulator that
has a noteworthy following in the MANET field. One
significant drawback to ns2 is the complexity associated
with network simulations. In an effort to increase the
repeatability of our work, we present a brief description of
our ns2 configuration. In all cases, a unique channel
model is placed within the wireless_phy.cc module. The
channel models require knowledge of the simulator time,
the sending and receiving nodes, frame length of the
transmitted packet and the total number of nodes being
simulated. All simulations were performed with a
constant average power to ensure a proper comparison
αg
Good State
(Short)
βg
π2
π4
Good State
(Long)
π1
Good State
Bad State
fĜ(n);{αg, βg, pg}
f B̂ (n);{αb, βb, pb}
π3
π5
π7
Bad State
(Short)
αb
π6
π8
Bad State
(Long)
π1 = (1-αg)Pb
π2 = (1-αg)(1-Pb)
π3 = (1-βg)(1-Pb)
π4 = (1-βg)Pb
π5 = (1-αb)Pg
π6 = (1-αb)(1-Pg)
π7 = (1-βb)(1-Pg)
π8 = (1-βb)Pg
βb
Fig 3. Approximated RLM
Fig 4. Four State Markov Model (4SMM)
4.2 Network Performance of Channel Models
A simple two-node network was constructed to
observe the performance of a single duplex, wireless link.
Each node was assigned a constant bit-rate load of 512B
packets equalling 20% of the channel rate, for a total of
40% load offered to the network. Simulations were
conducted for the following network setup: constant SNR
of between 5 and 15dB, 802.11 MAC protocol with point
coordination function and queue length of 50 packets and
user datagram protocol (UDP). The model parameters
used in these simulations are presented (or can be
obtained from) Table 1.
Both the 4SMM and the 2SMM parameters employed
in the simulations were obtained from representative error
traces of a CCK modulation (802.11b) format operating
across a Rayleigh fading channel with a maximum
Doppler frequency of ~9Hz equating to an effective
mobile speed of around 1.1m/s. The error traces, as
defined in Section III, present a picture of the availability
of the channel with respect to time.
αg
βg
pg
αb
βb
pb
5
0.4966
0.9835
0.8522
0.4966
0.9937
0.9339
7
0.4966
0.9896
0.8509
0.4966
0.9908
0.9208
8
0.4966
0.9917
0.8457
0.4966
0.9892
0.9105
SNR
9
0.4966
0.9934
0.8559
0.4966
0.9875
0.9042
10
0.4966
0.9948
0.8516
0.4966
0.9859
0.8972
11
0.4966
0.9958
0.8514
0.4966
0.9841
0.8903
12
0.4966
0.9967
0.8585
0.4966
0.9824
0.8831
13
0.4966
0.9974
0.8470
0.4966
0.9806
0.8609
14
0.4966
0.9979
0.8523
0.4966
0.9788
0.8596
15
0.4966
0.9983
0.8388
0.4966
0.9770
0.8399
Link Success Ratio (LSR) vs. Signal to Noise Ratio
1
0.9
0.8
LSR
between models; however a MANET simulation would
want to pass the average receiver power – obtained
through a propagation module. All simulations were
based upon the ns 2.27 build and complied with gcc 3.3.3.
The channel models return a frame integrity flag that is
then interpreted by the wireless_phy.cc module such that
a return of 0 indicates a channel failure while a 1 indicates
channel success. Failures are interpreted by ns2 as though
the packet was received at a power below both the
receiver threshold (RXthresh_) and the carrier sense
threshold (CSThresh_). Thus, all channel failures are
treated as un-observed transmissions. While this was
initially a point of concern, simulations showed that our
observations of the network performance were almost
identical regardless of which thresholds defined a failure.
The channel models are integrated into a ‘drop-in’
replacement for the wireless_phy.cc module and thus
offer a graceful option for simulating correlated channel
errors in a MANET simulation.
0.7
0.6
BEPL - Simulated fading
4SMM
2SMM
0.5
0.4
7
8
9
10
12
13
14
15
Fig 5. Link-Layer Performance Comparison
As such, care was taken to account for time between
transmissions, as described in [7].
The 2SMM parameters can be obtained from the error
traces as shown in (1) & (2), or approximated using the
first order statistics of B̂ and Ĝ as shown,
b

E Bˆ  pb
 1  pb  b ,
1b
1 b

(8)
g
g
E Gˆ  p g
 1  p g 
.
1g
1 g

(9)
The simulated network environment was designed such
that the MAC interactions across the fading channel had
significant impact upon the chosen observations of link
throughput and queue length.
Figure 5 presents link
throughput results in the form of a link success ratio
(LSR). The LSR is defined as the ratio of all successfully
received data to all offered data,
 
l n, i 


LSR 
 
  l n, i 
N 1
K n
n 0
N 1
i 1
J n
rx
n 0
i 1
tx
(10)
where lrx(n,i) represents the frame length of the ith packet
successfully received at node n and ltx(n,i) represents the
frame length of the ith packet sent from node n.
Furthermore, N represents the total number of nodes and
the quantities J(n) and K(n) respectively represent the
total number of (not necessarily unique) packets sent from
and successfully received at node n.
Another important observation point for link-layer
analysis is the physical layer interface queue. In an effort
to observe the impact of the fading channels, we charted
the ratio of packets dropped at the interface-queue relative
to the number of transmitted packets. The interfacequeue drop ratio (IQDR) is defined as,
n
TX n 
n 0

IQDR 

N 1
Table 1. 4-State Markov Model Parameters
11
SNR in dB
D
n 0 IFQ
N 1
(11)
Interface-Queue Drop Ratio (IQDR) vs. Signal to Noise Ratio
5. Conclusions
0.35
BEPL - Simultated fading
4SMM
2SMM
0.3
IQDR
0.25
0.2
0.15
0.1
0.05
0
7
8
9
10
11
12
13
14
15
SNR in dB
Fig 6. Interface-Queue Drop Ratio Comparison
where DIFQ(n) represents the number of packets dropped
at the interface queue of node n due to retransmissions
and TX(n) represents the number of total frames
transmitted from node n. The IQDR results are presented
in Figure 6.
All the channel models were designed to have the same
amount of available and un-available time, the differences
between the models are found in the correlation between
un-available times. To the casual observer, it might seem
that LSR should be constant for all distributions having a
common frame error rate and that higher order statistical
variations in run durations would not affect this metric.
In fact, the LSR would be common across the channel
models if data was randomly offered to the channel;
however network protocols attempt to gauge the channel
status before offering data to the link. The LSR results
presented in Fig. 5 show the effects of the 802.11 point
coordination function (PCF) on links with correlated
channel errors defined by the different channel models.
Poor performance by the 2SMM indicates that even a
protocol as simple as a request-to-send (RTS), clear-tosend (CTS) protocol, such as PCF, can be sensitive to the
higher order statistics of an error process.
The second comparison was made on the interfacequeue of the MAC layer. Packets are dropped from the
MAC queue if the number of retransmissions for a
specific packet exceeds a threshold (default of 7 in ns2).
The results presented in Fig. 6 show that the 2SMM
channel drops packets from the MAC queue at a ratio of
up to 4 times greater than the optimum/simulated BEPL
channel. In comparison, the 4SMM more conservatively
models the IQDR, which appears to be a direct function
of the 4SMM’s ability to approximate the distributions of
Gn and Bn.
In this paper we propose an improved channel model
designed to independently approximate the distributions
of Gn and Bn for a representative error trace. Our 4SMM
channel provides an elegant implementation option for
approximating correlated channel errors when simulating
Rayleigh fading. Network simulations presented in this
paper quantify the improvement of the 4SMM over the
traditional 2-state Markov model as presented by [zorzi].
The advantages of our innovative channel model include:
accurate link throughput and queue performance across
low to high SNR links, ability to simulate multiple
wireless links without significant memory requirements
and ease of implementation. The current disadvantages of
the 4SMM can be summarized by it’s time consuming
parameter estimation routine, which we are currently
working towards resolving with an analytical method for
parameter estimation.
The 4SMM channel provides a graceful option for the
MANET researching community by providing a low
complexity channel model for accurately simulating
correlated channel errors in multi-node environments.
References:
[1] R.R. Rao, Perspectives on the Impact of Fading on
Protocols for Wireless Networks, Proc. IEEE
International Conf. on Personal Wireless Comm.,
Mumbai, India, 1997, 489-493.
[2] R.J. Punnoose, P.V. Nikitin, D.D. Sancil, Efficient
Simulation of Ricean Fading within a Packet Simulator,
Proc. 52nd IEEE Vehicular Technology Conf., Boston,
MS, 2000, 764-767.
[3] M. Zorzi, R.R. Rao and L.B. Milstein, Error Statistics
in Data Transmission over Fading Channels, IEEE Trans.
Comm., 46(11), 1998, 1468-1477.
[4] A. Konrad, B.Y. Zhao, A.D. Joseph, R. Ludwig, A
Markov-based channel model algorithm for wireless
networks, Wireless Networks, 9(3), 2003, 189-199.
[5] J. McDougall, S. Miller, Sensitivity of Wireless
Network Simulations to a Two-State Markov Model
Channel Approximation, Proc. Globecom 2003 – IEEE
Global Telecommunications Conference, San Francisco,
2003, 697-701.
[6] J. McDougall, S. Miller, A Statistical Approach to
Developing Channel Models for Network Simulations, to
appear in Proc. WCNC 2004 – IEEE Wireless
Communications and Networking Conf, Atlanta, 2004.
[7] D.B. Johnson and D.A. Maltz, Adaptive link layer
strategies for energy efficient wireless networking,
Wireless Networks, 5(5), 1999, 339-355.