1
Cooperative UWB Communication Using Range
Information
arXiv:1406.7756v1 [cs.IT] 30 Jun 2014
Vijaya Yajnanarayana, Rasmus Brandt, Satyam Dwivedi, Peter Händel
dAB
Abstract—In this work, we propose a strategy to utilize the
range information to create an interference free communication
through a common shared channel. The performance of this
scheme is compared with non-aided methods to quantify the
benefits of using the range information in the communication.
Proposed methods indicate that the throughput can be increased
by 60 percent for a network having random placement of 100
nodes with average distance of 10 m between them.
Index Terms—Sensor networks, ultra wideband, UWB communication, cooperative communication, position dependent communication.
A
B
dCA
dBC
C
Fig. 1. Peer to peer ad-hoc sensor network with 3 nodes. dAB , dBC and
dCA are the path lengths between nodes A, B and C.
I. I NTRODUCTION
Cooperative communication in resource constrained networks like many wireless sensor networks (WSN) is gaining popularity. Recently, cooperative scheduling across UWB
network has been discussed for positioning applications [1],
[2]. Methods to improve communication rate and reduce
interference with the help of shared range information through
cooperation is the topic of this paper. The proposed method
can be implemented in centralized or distributed fashion.
In networks, there are many situations where every node
need to transmit a message packet to every other node through
a shared broadcast channel. For example, in [3], [4] firefighters
share their position continuously through point to multi-point
communication where every firefighter broadcast their position
to all other firefighters. This enables every firefighter to know
where other firefighers are located. This kind of communication is also used in reporting health of the sensor node to all
other nodes in WSN as described in [5]. Another application
for this is in structural health monitoring using smart sensors
as discussed in [6]. In this paper we have proposed a methodology to utilize range information to aid communication in
similar communication scenarios. We use IR-UWB signals to
demonstrate the proposed techniques. Certain properties of IRUWB technology, such as, precise range measurement and
fine time resolution makes it a good candidate for the design
methodology considered in subsequent sections [7]. However,
techniques proposed in this paper can be extended to different
communication scenarios and other protocol technologies used
in WSN.
II. S YSTEM M ODEL
We consider 3 peer-to-peer line of sight (LOS) UWB
wireless sensor nodes which are connected to each other as
shown in the Fig. 1. A train of 10 UWB pulses are used as
message packets to be transmitted by each sensor. Concepts
proposed in this paper can be extended to modulated UWB
pulses as well. For example, message information can be
embedded by time-hopping or by altering the phase/amplitude
of pulse train without any change in the proposed methods [8].
The message packet is said to be correctly received if these
packets does not interfere, ie., there is no collision of packets
at the received node.
We assume that all the sensor clocks are synchronized to
same master clock. This can be accomplished using a message
passing techniques proposed in timing-sync (TSYNC) or reference broadcast synchronization (RBS) protocols [9], [10].
Time synchronization is done in commercial UWB systems
like Ubisense by connecting master nodes with Ethernet cables
[11]. Network synchronization ensures that all the nodes have
a same time scale in the network, which is essential for the
proposed technique to work.
III. O RTHOGONALIZATION WITH
TRANSMISSION .
SCHEDULED
In a network of N nodes, if we assume that the K = N2
range values are available, one approach to orthogonalize the
transmission is by creating a schedule where one message
packet (UWB pulse burst) is transmitted by a chosen node
in the duration of TD sec, where TD given by
TD =
D
,
c
(1)
where D is the maximum of the K range values. All nodes
are synchronized as described in Section II and in every TD
seconds one node will transmit. For the 3-node topology of
Fig. 1, TD is given by
TD =
dBC
max(dAB , dBC , dCA )
=
,
c
c
(2)
where c is the speed of light, dAB , dBC , and dCA denote the
distances between nodes. We define one report cycle, TR , as
the total duration required for the all the nodes in the sensor
network to transmit one message packet to all other nodes.
2
Parameter
dAB
dBC
dCA
τ
With this approach, one report cycle is given by
TR = N TD
(3)
In UWB sensor networks, the flight time for the pulses to
reach other nodes is much larger compared to the duration
of the pulses themselves. We can reduce TR of network by
exploiting this fact. Consider a UWB sensor network in which
the path difference between any two nodes is greater than the
UWB pulse train width τ . Then, concurrent transmissions will
result in pulses arriving at different times at each node and
hence all transmissions are orthogonal. For example, consider
the 3 node network shown in Fig. 1. If |dAB − dCA | ≥ cτ ,
then the pulses transmitted simultaneously at B and C will
arrive at A at different times and hence A can correctly receive
them. Similarly |dAB − dBC | ≥ cτ and |dAC − dBC | ≥ cτ
will ensure correct message packet reception at B and C
nodes respectively. Thus all the three nodes can concurrently
transmit, and the report cycle can be completed in TD seconds
where TD is given by (2).
In general, for a N node network to ensure concurrent
orthogonal transmissions, network should follow the condition
|di,j − di,k | ≥ cτ
∀ i, j, k ∈ [1, 2...N ] | j, k 6= i and j 6= k,
(4)
where i, j and k denote the distinct nodes in the network
and di,j and di,k denotes the distance between the ith node
with j and k nodes. If the condition (4) is met then all the
nodes can concurrently transmit pulses, yet at each receive
node packets arrive at different times and will not interfere.
Thus, the report cycle TR is equal to the maximum path delay
TD in the network instead of N TD for scheduled transmission
as discussed before. However, the assumption that nodes are
arranged in a way that (4) is met is not always true, especially,
if the nodes are mobile. A methodology for reducing the TR
under this condition is discussed in next section.
IV. P ROBLEM F ORMULATION
AND
S IMULATION R ESULTS
When network having N nodes does not meet condition
(4), we can reduce TR by introducing delay ∆i to each node
i ∈ [1...N ]. The ∆i s are adjusted such that at every node,
the message packets arrive at different times. The ∆i can be
obtained by solving the following optimization problem.
minimize max (∆1 , ∆2 , . . . , ∆N )
{∆i }
subject to
(5)
J = J1 + J2 + ... + JN = 0,
where
di,j
di,k
Π pj t −
− ∆j pk t −
− ∆k dt
j,k
c
c
∀ i, j, k ∈ [1, 2...N ] | j, k 6= i and j 6= k.
Ji =
Z
Here p(t) is the UWB pulse train denoting the message
packet. The solution for the optimization problem (5) is
demonstrated using the configuration defined in Table I. To
illustrate the method, we use a train of 10 UWB pulses as a
message packet. In Table I, the path differences between nodes
Value
9.5 m
11 m
10.5 m
10 ns
TABLE I
3- NODE CONFIGURATION FOR TOPOLOGY IN F IG . 1. M ESSAGE PACKET
LENGTH OF τ CONSTITUTES 10 UWB PULSES .
do not meet the constraint defined in (4). That is, if all the
nodes transmit simultaneously they will interfere with each
other. For example, if at time t = 0, all the nodes A, B and
C concurrently transmit a UWB pulse train then the received
pulse at A, B and C are shown in the Fig. 2a.
To accomplish the short report cycle without interference,
the optimization (5) is solved using the grid search method. In
this method we set ∆A = 0, assuming that all the nodes are
synchronized to node A, J is computed by varying ∆B and
∆C over the interval [0, TD ], where TD is given by (2). The
solution for the optimization problem using the grid search
method yields ∆B = 8.4 ns and ∆C = 15 ns. With this delay
introduced in B and C, the pulses are not interfering as shown
in Fig. 2b.
Using the grid search method to solve (5) is costly, as the
algorithm complexity, O(M N ), exponentially increases with
the number of nodes in the network. Here M indicates the
quantization of ∆i s. Optimization of (4) cannot be posed as
a convex problem directly since the equality constraint is
not affine. However, this can be reformulated as a convex
optimization, under some assumptions. Consider the arrival
of messages at node i from node j and k as shown in Fig.
3. We can treat the arrived pulses as boxes of width τ ,
and thus the pulses will not interfere if the corresponding
boxes do not overlap. If we have predetermined the order of
which the pulses should arrive at a particular node, we can
enforce that the corresponding boxes do not overlap using a
simple linear inequality. For example, in Fig. 3, this would
be ∆ij + ∆j + τ ≤ ∆ik + ∆k . Thus, we have isolated the
non-convexity of the optimization problem into selecting the
order in which the pulses should arrive at the different nodes.
Let αijk = 1 denote whether the pulse from node j to node
i should arrive before the pulse from node k to node i, and
αijk = 0 denote the reverse case. Then we can formulate the
following convex optimization problem:
minimize max (∆1 , ∆2 , . . . ∆N )
{∆i }
subject to
If αijk = 1:∆ij + ∆j + τ ≤ ∆ik + ∆k ,
If αijk = 0:∆ik + ∆k + τ ≤ ∆ij + ∆j ,
∆i ≥ 0,
∀ i, j, k ∈ [1, 2...N ] ,
j, k 6= i and j 6= k.
(6)
This is a convex optimization problem, as the objective
function is convex, and all the inequality constraints are
convex. Using CVX [12] to solve this for the configuration
defined in Table I, the arrived optimal delays are ∆A = 0,
∆B = 8.333 ns and ∆C = 15 ns. Within the grid search
tolerance, this is the same solution as from the grid search.
3
Messages from B and C received at A
Messages from B and C interfere at A
Message packets received at A
Message from B
Message from C
0.1
0.05
0
0
−0.05
−0.05
−0.1
Message packets
received at A
Message from B
Message from C
0.1
0.05
−0.1
0
10
20
30
40
50
60
70
80
90
100
0
10
Amplitude
Amplitude
Messages from A and C interfere at B
Message packets received at B
Message from A
Message from C
0.2
0.15
0.1
0.05
0
−0.05
−0.1
10
20
30
40
50
60
70
80
90
100
0
10
−0.1
30
40
50
60
70
80
20
30
40
50
60
70
90
100
80
90
100
90
Message packets
received at C
Message from A
Message from B
0.1
0
20
80
Message packets
received at B
Message from A
Message from C
0.05
−0.05
10
70
Messages from A and B received at C
0
0
60
0
−0.05
−0.1
50
−0.05
Message Packets received at C
Message from A
Message from B
0.05
40
0.1
Messages from A and B interfere at C
0.1
30
0.05
−0.1
0
20
Messages from A and C received at B
100
0
10
20
30
40
50
60
70
80
90
100
Time in ns
Time in ns
(a) Interfering message packets due to concurrent transmission.
(b) Arrival of packets without interference at A, B and C nodes after introducing
a delay of ∆B = 8.4 ns and ∆C = 15 ns in B and C nodes. respectively.
Fig. 2. Concurrent transmission on shared broadcast channel will result in Interference as shown in (a). If we solve the optimization problem defined in (5)
then the interference can be mitigated as shown in (b).
Message
(a)
(b)
dA
τ
= 9.
B
5
B
d AB
dAC
∆i,k + ∆k
A
= 10
dBC
.5
C
d∆CA = 2
C
= 11
C
d∆CA = 2
C
t
∆i,k + ∆k + τ
∆i,j + ∆j + τ
(d)
(c)
= 10
C
.5
1
D∆
A = 0
A
1
D∆
B = d∆BC = 2.5
dA
Fig. 3.
5
B
A
∆i,j + ∆j
= 9.
Messages from j and k arriving at i
C
dBC
1
D∆
C = d∆CA = 2
= 11
B
d∆BC = 2.5
The following selection rule was used: αijk = 1 if ∆ij ≤ ∆ik .
Even though the formulated problem is convex, the problem
still remains of selecting the αijk . For the N -node scenario,
this is in itself a combinatorial optimization problem. Instead,
we propose an alternative where we adjust the path difference
between nodes di,j and di,k to satisfy (4) in an iterative way.
Adjusting the path difference is same as introducing delays
at nodes j and k, so that the pulses from j and k do not
interfere at node i. The algorithm is described below in steps
followed by an example of a 3-node network scenario defined
in Table I.
1 For a topology having N nodes, labeled [1....N ], select
node i, i ∈ [1...N ], add additional path lengths d∆ji and
d∆ki , ∀j, k ∈ [1...N ], j, k 6= i to nodes j and k to satisfy
(4).
2 Repeat Step 1, by selecting one by one all nodes [1...N ]
in the network. Each time carry over additional path
lengths added di,j + d∆ji and di,k + d∆ki . Total path
length at the end of iteration n is given by
X
n−1
n
(7)
d∆ij .
D∆i
= D∆i
+
j
B
Fig. 4. Iteration 1 for 3-node network shown in Fig. 1 with configuration
defined in Table I.
3 Repeat Step 1 and Step 2 until additional path lengths
for each nodes do not change across iteration, that is
following condition holds for all i ∈ [1...N ].
n−1
n
D∆i
= D∆i
(8)
This indicates that the (4) is met for all nodes
simultaneously.
The proposed method is illustrated with the 3-node network
shown in Fig. 1 with configuration defined in Table I. Figure
4 (a) shows that the addition of additional path length of
2 = (3 − (dAC − dAB )) is required at node C to meet the
constraints in (4) so that pulses from B and C do not collide
at A. Similarly Fig. 4 (b) and Fig. 4 (c) adds additional path
lengths to the previous topology to avoid collisions at nodes
B and C respectively. At the end of the 1st iteration the total
path length for each of the nodes are given in Fig. 4 (d).
4
(a)
(b)
B
= 9.5
B
dA
B
1
D∆
B = 2.5
d AB
A
dAC
= 9.5
A
= 11
C
B
= 10
.5
C
1
D∆
C = 2
dBC
C
d∆CA = 2.5
(c)
C
1
D∆
C = 2
C
d∆CA = 2.5
C
(d)
= 10
C
.5
2
D∆
A = 0
A
dA
2
1
D∆
B = D∆B = 2.5
C
dBC
= 11
1
2
D∆
C = D∆C + d∆CA = 4.5
B
1
D∆
B = 2.5
B
Fig. 5. Iteration 2 for 3-node network shown in Fig. 1 with configuration
defined in Table I.
100. The topology consisted of random placement 100 sensor
nodes in a two dimensional plane with average distance of
10 m. For grid search method, algorithmic complexity for
solving (5) increases exponentially, O(M N ), as the number of
nodes N increases. Due to the computing resource constraints
for large N , grid search method cannot be practically solved.
However, the earlier discussed methods, convex relaxation of
(5) to (6) and proposed iterative algorithm can be solved. For
N = 100, convex method with allocation strategy αijk = 1 :
if j < k, and the proposed iterative method, on an average
results in the reduction of report cycle by 60%.
VI. C ONCLUSION
The Second iteration is illustrated in Fig. 5. Notice that we
carried the new topology with added path lengths from previ1
1
1
ous iteration (D∆A
, D∆B
D∆C
) to iteration 2 and at the end of
2
2
2
iteration 2 , total path lengths added are (D∆A
, D∆B
, D∆C
)=
(0, 2.5, 4.5). Now the iteration is stopped as it meets the
conditions defined in Step 3.
Translating the path lengths into path delays by dividing by
speed of light c results in (∆A , ∆B , ∆C ) ≈ (0, 8.3 ns, 15 ns).
This is same result from the grid search and convex methods. The proposed algorithm requires far less computation
compared to grid search method. Also note that the proposed
solution does not always solve (5), however for most practical
purposes the results are fairly close to solution of (5) as long
as added path lengths are diversified uniformly across all the
nodes. The performance of the proposed methods for large
network topology is discussed in the next section.
V. R ESULTS
In the beginning of Section III, we mentioned that we
can orthogonalize the message packets by allowing only one
packet to be transmitted for maximum path delay in the
network. For the configuration in Table I the report cycle TR
can be computed as below.
TD
=
TR
=
max(dAB , dBC , dCA )
= 36.66 ns
c
N · TD = 3 · 36.66 = 110 ns
(9)
(10)
However, if the path difference in the network topology
satisfy (4) then all the nodes can concurrently transmit, thus
one report cycle can be completed in time duration equal
to maximum path delay in the network, that is 36.66 ns.
More often (4) is not met, under these circumstances, we
can minimize the time required by solving (5). We also
modified the problem so that it can be cast as an convex
optimization problem and solved it using Matlab with convex
solver CVX. For the configuration in Table I, we showed that,
(∆A = 0 ns, ∆B = 8.33 ns, ∆C = 15 ns) solves (6), therefore
as per the solution, B will transmit last after a delay of 15 ns
and complete the report cycle. So one report cycle for the
configuration in Table I is
TR = TD + 15 ns = 36.66 + 15 = 51.66 ns
(11)
Notice the report cycle is reduced from 110 ns to 51.66 ns.
The algorithms was used for a practical example with N =
In this paper, we proposed a methodology utilizing the range
information to aid communication between sensor nodes in
peer-to peer network. An optimization problem is formulated.
Solution of the optimization problem is found which results
in reduction in report cycle compared to conservative way
of sending one message packet for a duration of maximum
path delay in network. We have proposed practical algorithms
which have less complexity compared to grid search.
R EFERENCES
[1] S. Dwivedi, D. Zachariah, A. De Angelis, and P. Händel, “Cooperative decentralized localization using scheduled wireless transmissions,”
Communications Letters, IEEE, vol. 17, no. 6, pp. 1240–1243, June
2013.
[2] G.E. Garcia, L.S. Muppirisetty, and H. Wymeersch, “On the tradeoff between accuracy and delay in uwb navigation,” Communications
Letters, IEEE, vol. 17, no. 1, pp. 39–42, January 2013.
[3] Isaac Skog John-Olof Nilsson, Dave Zachariah and Peter Händel, “Cooperative localization by dual foot-mounted inertial sensors and interagent ranging,” EURASIP Journal on Advances in Signal Processing
2013, vol. December 2013, pp. 164, 2013.
[4] J. Rantakokko, J. Rydell, P. Stromback, P. Händel, J. Callmer, D. Tornqvist, F. Gustafsson, M. Jobs, and M. Gruden, “Accurate and reliable
soldier and first responder indoor positioning: multisensor systems and
cooperative localization,” Wireless Communications, IEEE, vol. 18, no.
2, pp. 10–18, April 2011.
[5] A. Bharathidasan and V. Anand, “Sensor networks: An overview,” Tech.
Rep., Dept. of Computer Science, University of California at Davis,
2002.
[6] T. Nagayama and B.F. Spencer Jr., “Structural health monitoring using
smart sensors,” Tech. Rep., NSEL Report, Series 001, 2007, [online]
Available : http://hdl.handle.net/2142/3521.
[7] A. De Angelis, S. Dwivedi, and P. Händel, “Characterization of a
Flexible UWB Sensor for Indoor Localization,” Instrumentation and
Measurement, IEEE Transactions on, vol. 62, no. 5, pp. 905–913, 2013.
[8] M.Z. Win and R.A. Scholtz, “Impulse radio: how it works,” Communications Letters, IEEE, vol. 2, no. 2, pp. 36 –38, feb. 1998.
[9] Saurabh Ganeriwal, Ram Kumar, and Mani B. Srivastava, “Timing-sync
protocol for sensor networks,” in Proceedings of the 1st International
Conference on Embedded Networked Sensor Systems, New York, NY,
USA, 2003, SenSys ’03, pp. 138–149, ACM.
[10] Jeremy Elson, Lewis Girod, and Deborah Estrin, “Fine-grained network
time synchronization using reference broadcasts,” SIGOPS Oper. Syst.
Rev., vol. 36, no. SI, pp. 147–163, Dec. 2002.
[11] “Ubisense Company,” http://www.ubisense.net/.
[12] Michael Grant and Stephen Boyd, “CVX: Matlab software for disciplined convex programming, version 2.0 beta,” Sept. 2013.