SIGNAL DECODING IN ANALOG NETWORK CODING USING ASK AND FSK MODULATION SCHEMES

SIGNAL DECODING IN ANALOG NETWORK CODING USING ASK AND FSK MODULATION SCHEMES
Dept. ECE, BIT Page 1
CHAPTER 1
INTRODUCTION
Nowadays, wireless applications such as Wi-Fi, cellular phones and Bluetooth have
become an important part of daily life. But compared to the conventional wire line networks,
wireless networks can only provide very limited data rate because the underlying channel is
unreliable in nature. In practice, wireless channel is subject to fading, path loss, shadowing
and co-channel interference, and all these features would greatly degrade the quality of
transmitted signals.
Channel fading is one of the major downside to wireless communication. Channel
fading is caused by multipath propagation effect, which occurs when the reflectors
surrounding the transmitter/receiver happen to create multiple propagation paths for the
transmitted signals to traverse. Those multipath components may add constructively or
destructively at the receiver side, thus making the amplitude of the received signal fluctuate
randomly over time. When the channel is in deep fading, the wireless link may totally get
disconnected and no information can be delivered reliably.
Diversity techniques have been widely used to combat channel fading. Diversity is the
capability to send the same signal repeatedly through independent channels. As the receiver is
able to decode the source message as long as there exists at least one good channel, the
chance of link disconnection in cases of deep fading on all the channels could be reduced
significantly. Conventionally, there are three generic types of diversity: time diversity,
frequency diversity and spatial diversity. Time diversity is to send the same signal copy in
different time slots. To guarantee independent fading, the interval between adjacent
transmissions must be greater than the channel coherence time, which would incur large
processing delay especially when the channel is in slow fading. Frequency diversity is to send
the same signal copy in sufficiently separated frequency bands that experience independent
fading. However, frequency diversity is gained at a price of lower bandwidth efficiency,
which is costly since frequency resource is pretty scarce.
Spatial diversity is a relatively new technique to address the drawbacks of time
diversity and frequency diversity. Spatial diversity is achieved by deploying multiple
antennas at the transmitter/receiver, such that there exists one independent propagation path
between each pair of transmitter antenna and receiver antenna. Multiple antenna technique

has gained a lot of attention in recent years because it also provides an efficient way to
improve bandwidth efficiency.
Theoretically, the spatial diversity gain and multiplexing gain could be arbitrarily high
if it is possible to deploy infinitely many antennas at both the transmitter and receiver. But in
practice, since the user devices are usually of very limited size and the adjacent antennas
must be sufficiently separated to guarantee independency, it is pretty hard to equip too many
antennas on any single user device. Those hardware constraints lead to a new concept of
cooperative diversity.
1.1 Cooperative Diversity:
The main idea of cooperative diversity is to use distributed antennas instead of the co-
located physical antennas, where the distributed antennas could be any independent relaying
devices that may help to forward the source signals. As each relay link is able to provide one
additional diversity path, the available diversity gain could be quite remarkable in a dense
wireless network where there are abundant relaying devices between the transmitter and
receiver.
Motivating Example:
To illustrate the main concepts, consider the example wireless network in Fig.1.1, in
which terminals T1 and T2 transmit to terminals T3 and T4, respectively.
Figure.1.1: Illustration of radio signal paths in an example wireless network with
terminals T1 and T2 transmitting information to terminals T3 and T4, respectively.
This example might correspond to a snapshot of a wireless network in which a higher
level network protocol has allocated bandwidth to two terminals for transmission to their
intended destinations or next hops. For example, in the context of a cellular network, T1 and
T2 might correspond to handsets and “T3 = T4” might correspond to the base station. As
another example, in the context of a wireless local-area network (LAN), the case “T3 ≠ T4”
might correspond to an ad hoc configuration among the terminals, while the case “T3 = T4”
might correspond to an infrastructure configuration, with T3 serving as an access point. The

broadcast nature of the wireless medium is the key property that allows for cooperative
diversity among the transmitting terminals: transmitted signals can, in principle, be received
and processed by any of a number of terminals. Thus, instead of transmitting independently
to their intended destinations, T1 and T2 can listen to each other’s transmissions and jointly
communicate their information. Although these extra observations of the transmitted signals
are available for free (except, possibly, for the cost of additional receive hardware) wireless
network protocols often ignore or discard them.
At one extreme, corresponding to a wireless relay channel, the transmitting terminals
can focus all their resources on transmitting the information of T1; in this case, T1 acts as the
“source” of the information, and T2 serves as a “relay.” Such an approach might provide
diversity in a wireless setting because, even if the fading is severe between T1 and T3, the
information might be successfully transmitted through T2. Similarly, T1 and T2 can focus
their resources on transmitting the information of T2, corresponding to another wireless relay
channel.
Depending on the relay operations, all the cooperation protocols can be roughly
divided into two broad categories: analog relaying and digital relaying. In analog relaying
protocols, each relay simply forwards the received signals to the receiver after performing
some linear operations in the complex domain. As the additive noise is mixed with the signal
component, it is amplified and forwarded to the intended receiver too. By contrast, in digital
relaying protocols each relay needs to first decode the source message, re-encode it and then
forward it to the receiver. So the relay node always forwards a “clean” message, although the
message might be incorrect due to decoding errors. From an information theoretic view,
simple digital relaying cannot achieve cooperative diversity; however, if the relay can
somehow detect the decoding errors, then selectively forwarding the correct messages alone
could recover the diversity loss.

CHAPTER 2
WIRELESS NETWORK CODING
For cooperative diversity, the relays need to first acquire the source message before
forwarding it to the receiver. However, practical devices are usually subject to half-duplex
constraint, i.e., they cannot transmit and receive signals at the same time. As a result, the
whole end-to-end data relaying is completed in two phases: data acquiring phase and data
forwarding phase. Since an independent channel is required for each phase and only one
message could be delivered across those two phases, it incurs a pre-log factor 1/2 on the
spectral efficiency. For multi-relay systems, such rate loss is even larger if the intermediate
relays operate on orthogonal channels.
To save channel use for data forwarding phase, the relay can choose to combine
different source messages via network coding and forward a single mixed message rather
than forward the individual messages separately. Broadly speaking, network coding refers to
arbitrary coding (i.e., mapping from input to output) at intermediate nodes. But some
pioneering literatures in this area focus only on wire-line applications, where the physical
channel is assumed to be error free and the contents of source messages are combined beyond
the physical layer. With these simplifications, it has been proved that network coding could
achieve the min-cut max-flow throughput bound for multicast networks.
For mobile networks, it is very hard to connect the transmitter/receiver to the relay
station by cable directly. So all the inter-node communications go through wireless links, and
the underlying channel features play an important role in the design and analysis of network
coding. As wireless channels suffer severe random fading that may result in serious
transmission errors, and multiple transmitters would also cause co-channel interference.
Consequently, the existing analytical results on wire-line networks no longer hold for
wireless applications, and new findings may rely on information theory and communication
theory from a physical-layer view.
For wireless transmissions, the transmitted signal consists of the modulated symbols
instead of the raw information bits. Depending on the way for mixing source messages, it
gives rise to two different types of wireless network coding schemes. On one hand, the relay
could choose to decode different source messages and then combine the bit-streams in the
finite field. This is called digital network coding (DNC) and it is a legacy network coding
scheme previously developed for wire-line networks. Alternatively, the source signals could

be combined symbol-wise in the complex field directly to simplify relay operations, since the
decoding could be omitted. This is a unique analog network coding (ANC) scheme dedicated
for wireless applications, as the wireless devices usually have the capability of interference
cancelation and multi-user detection. In practice, DNC and ANC are suitable for digital
relaying and analog relaying, respectively.

CHAPTER 3
ANC: ANALOG NETWORK CODING
Wireless interference is considered harmful. Interference creates collisions, prevents
reception, and wastes scarce bandwidth. Wireless networks strive to prevent senders from
interfering. Analog Network Coding (ANC), instead of avoiding interference, exploits the
interference of strategically picked senders to increase network throughput. When multiple
senders transmit simultaneously, the packets collide. But looking deeper at the signal level,
collision of two packets means that the channel adds their physical signals after applying
attenuations and time shifts. Thus, if the receiver knows the content of the packet that
interfered with the packet it wants, it can cancel the signal corresponding to the known packet
after correcting for channel effects. The receiver is left with the signal of the packet it wants,
which it decodes using standard methods. In a wireless network, packets traverse multiple
hops. When packets collide, nodes often know one of the colliding packets by virtue of
having forwarded it earlier or having overheard it. Thus, this approach encourages two
senders to transmit simultaneously if their receivers can leverage network-layer information
to reconstruct the interfering signal, and disentangle it from the packet they want.
Note the analogy between analog network coding and its digital counterpart. In
traditional digital network coding, senders transmit sequentially, the routers mix the content
of the packets and broadcast the mixed version. In analog network coding, senders transmit
simultaneously. The wireless channel naturally mixes these signals. Instead of forwarding
mixed packets, routers forward mixed signals. Since it allows multiple transmissions to occur
simultaneously yet still be received correctly, analog network coding increases network
capacity. We show via analysis and implementation on software radios that our approach
achieves higher throughput than both traditional wireless design and digital network coding.
Consider the canonical example for wireless network coding in which Alice and Bob
want to send a message to each other as shown in Fig. 3.1(a).
(a) Alice-Bob topology

(b) Traditional Approach
(c) Digital Network Coding (DNC)
(d) Analog Network Coding (ANC)
Figure 3.1: Alice-Bob Topology: Flows Intersecting at a Router. With analog network
coding, Alice and Bob transmit simultaneously to the router; the router relays the
interfered signal to Alice and Bob, who decode each other’s packets. This reduces the
number of time slots from 4 to 2, doubling the throughput.

The radio range does not allow them to communicate without a router, as shown in
Fig. 3.1(b). In the traditional approach, Alice sends her packet to the router, which forwards it
to Bob, and Bob sends his packet to the router, which forwards it to Alice. Thus, to exchange
two packets, the current approach needs 4 time slots.
In digital network coding, Alice transmits its bits to the router, and then Bob transmits
its bits to the router. Router then XORs the bits received from Alice and Bob and then
transmit the combined signal. At receiving end Alice and Bob again XOR their bit streams
with the one received from the router and get the desired packets from each other. This
scenario needs three time slots to accomplish the task as shown in Figure 3.1(c).
In analog network coding, Alice and Bob transmit signal to router which adds them
and broadcasts. At receiving end, Alice and Bob subtract their own signals with the received
one to get their desired signals. It requires two time slots to accomplish the task. Thus analog
network coding gives two fold increase in throughput as compared to traditional approach. It
also gives a gain of 1.5 as compared to digital network coding. It looks quite simple to add
two signals and transmit the resultant signal and at the receiving end, receive the signal by
subtracting original value. But in fact it is not that simple. Signal has to traverse the channel
before reaching the receiver. Channel imparts many distortions to the signal. Thus a
modulation scheme is needed such that it can bear all these distortions from the channel. In
the following sections we will analyze different modulation schemes for signal encoding and
decoding and compare their performances.

CHAPTER 4
SIGNAL DECODING IN ANC
In this project, modulation schemes such as ASK (Amplitude Shift Keying), FSK
(Frequency Shift Keying) are used for decoding the received signal in analog network coding
(ANC).
4.1 Amplitude Shift Keying:
In this discussion we will consider two possibilities of amplitudes that are 0 and 1.
This type of amplitude shift keying (ASK) is also called On-Off keying (OOK). ASK signal
can be represented by the following equation.
SASK = pAcos(ωct + θ)………………………………………………………………………....1
Where,
P = Probability of the signal being 0 or 1
ωc = Frequency of the carrier
θ = Phase of the carrier
The two nodes of Alice and Bob will transmit the same signal to the router with the
same carrier frequency and phase. The only difference between the two signals is the
message that both nodes want to transmit. Let S1 be the signal transmitted from one node and
S2 be the signal of the second node. The router will broadcast the sum of these two signals
which can be written as:
Srouter = S1 + S2………………………………………………………………………………....2
Srouter = pAlcos(ωct + θ) + pA2cos(ωct + θ)…………………………………………………….3
Since frequency and phase of the carrier is the same we can come up with a new equation
given by:
Srouter = (Al+ A2)pcos(ωct + θ)…………………………………………………………………4
At the receiving end, receiver will get somewhat distorted signal. Since information is only in
the amplitude, only parameter of concern is the amplitude.

At the receiver, the signal can be represented by the following equation:
Sreceiver = hpAcos(ωct + θ)…………………………………………….......................................5
Where,
h = distortion factor from the channel
A = Al + A2
This distortion factor fortunately can be catered in thresholding. At the receiving end,
receiver can subtract its value to get the desired transmitted value. Only thing that remains of
concern is that which signal was transmitted. We can set a threshold γ such that if the
received value is greater that this threshold we can infer that signal transmitted was A and 0 if
the received value is less than the threshold. Now it becomes simple problem of detecting the
transmitted signal.
Figure 4.1: Proposed model for retrieving signal in ASK
At the receiving end, the receiver integrates the received signal, multiplied with the carrier.
Then decision is made on the basis of threshold. The probability of error can be represented
by the equation:
…………………………………………………………………..6
Where,
Tb = Bit duration
N0 = Noise power.

4.2 Frequency Shift Keying:
In frequency shift keying, the frequency of the carrier is determined by the message
signal. That is, the information we want to transmit, is in the frequency of the transmitted
signal. We can write FSK mathematically as,
S1 = Acos(ω1t + θ1)
S2 = Acos(ω2t + θ2)………………………………………………………………….7
Where,
S1 and S2 are the two signals sent
ω1 = Frequency of the first transmitted signal S1
ω2 = Frequency of the second transmitted signal S2
Consider the same scenario as discussed in previously, where two nodes Alice and
Bob want to exchange the message to each other. Now, the router will mix the two signals
received from those two nodes and broadcast. When these two signals are added, it will take
the form as shown below:
Srouter = S1 + S2…………………………………………………………………………………8
After adding these two signals, the above equation takes the form:
Srouter = A[cos(ω1t + θ1) + cos(ω2t + θ2)]………………………………………………………9
The router broadcasts the signal described in (8). At the receiving end, all it needs is to
multiply the signal with the carrier of same frequency of that node. Let us see how this
happens mathematically.
Let us assume that the broadcasted signal is at the node which transmits its signal with
a carrier frequency ω1. Now the signal in (8) is multiplied with a carrier of frequency ω1 and
the signal takes the form:
Sreceiver = A[cos(ω1t + θ1) cos(ω1t + θ1) + cos(ω2t + θ2) cos(ω1t + θ1)]………………………10
U sing the trigonometric identity and using the fact that information is in the frequency, not
in the phase we omit the phase part in the equation to emphasize on the frequency, we get:
Sreceiver = A/2[cos(2ω1t) + 1 + cos{(ω1 + ω2)t} + cos{(ω1 – ω2)t}]………………………..….11
SFSK =

Now passing the signal described in (10) through high pass filter, eliminating dc value and
normalizing we get:
Sreceiver = A/2[cos(2ω1t) + cos{(ω1 + ω2)t}]……………………………………….………….12
Again multiplying with the carrier of same frequency we get:
Sreceiver = A[cos(2ω1t) cos(ω1t) + cos{(ω1 + ω2)t} cos(ω1t)]…………………………….……13
Again using the same trigonometric identity and expanding the terms we get:
Sreceiver = A/2[cos(3ω1t) + 2cos(ω1t) + cos{(2ω1 + ω2)t} + cos(ω2t)]……………….……..…14
Now passing the signal described in (13) through low pass filter and then through band stop
filter tuned to ω1 we get the term cos(ω2t). This is the signal required at the receiving end.
This whole process can be diagrammatically represented as under:
Figure 4.2: Proposed model for retrieving signal in FSK
Bit error probability for frequency shift keying is given by the following equation:
……………………………………………………………………15
Where,
Tb = Bit duration
N0 = Noise power.
Broadcasted
signal from
router
Srouter

CHAPTER 5
IMPLIMENTATION USING SIMULINK
Simulations are carried out using Matlab/Simulink. The models proposed in previous
sections are validated on Simulink.
5.1 The model for Amplitude Shift Keying (ASK):
Figure 5.1: Simulink model for retrieving signal in ASK

Figure 5.2: Signal from Pulse generator (A2)
Just before the filter, the resulting signal will be the desired signal imposed on the sinusoid.
Following result is obtained by following this procedure:
Figure 5.3: A2 plus Sinusoid (ωc = 2*pi*200Hz)
As can be seen in the figure, the desired signal A2 is super imposed on the sinusoid (cos
signal). After low pass filter, the sinusoid is removed and we get the signal A2 that was
desired.

Figure 5.4: Output for ASK (Bottom) and Desired signal A2 (Top)
As we compare the desired signal with the output signal, the output of ASK is almost same as
the desired signal output A2.

5.2 Model for Frequency Shift Keying (FSK):
Figure 5.5: Simulink model for retrieving signal in FSK
 The original signal of the receiving node is given as under [cos(ω1t)]:
Figure 5.6: Sinusoid Signal S1 (ω1 = 2*pi*200Hz)

 Desired signal [cos(ω2t)]:
Figure 5.7: Desired Output Signal of FSK - S2 (ω2 = 2*pi*50Hz)
Figure 5.8: Comparison of desired signal (Top) and output signal (Bottom)
We see from the figure that output (desired signal)'s frequency is almost the same of
that signal which was transmitted from the transmitter and reached the receiver via router.

CHAPTER 6
CONCLUSION
In this project we discussed different modulation schemes in Analog Network Coding.
Analog Network Coding is a very useful technique as it makes the performance better by
reducing the number of transmissions. ASK and FSK are discussed as modulation schemes.
Receiver models are proposed to retrieve the signal from the one that is transmitted by the
router. The proposed models are checked by simulation software Matlab/Simulink and the
results are according to the expectations. The results are also shown.

REFERENCES
[1] “XORs in the Air: Practical Wireless Network Coding” Sachin Katti, Hariharan Rahul,
Wenjun Hu, Dina Katabi, Muriel Médard, Senior Member, IEEE, and Jon Crowcroft, Fellow,
IEEE.
[2] R. Koetter and M. M´edard. “An algebraic approach to network coding” IEEE/ACM
Transactions on Networking, 2003.
[3] S. Katti, S. Gallakota, D. Katabi. “Embracing Wireless Interference: Analog Network
Coding” In ACM SIGCOMM, 2007.
[3] S. Jaggi, P. Sanders, P. A. Chou, M. Effros, S. Egner, K. Jain, and L. Tolhuizen.
“Polynomial time algorithms for multicast network code construction” IEEE Transactions on
Information Theory, 2003.
[4] Steven T. Karris, “Introduction to Simulink with Engineering Applications”, Orchard
Publications, 2008.
[5] “COOPERATIVE COMMUNICATION WITH WIRELESS NETWORK CODING” by
Wei Guan, Doctor of Philosophy, 2013.
[6] “Network Coded Wireless Architecture” by Sachin Rajsekhar Katti.

SIGNAL DECODING IN ANALOG NETWORK CODING USING ASK AND FSK MODULATION SCHEMES

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