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

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


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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


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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.


Dept. ECE, BIT

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


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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.


Dept. ECE, BIT

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


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(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.


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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.


Dept. ECE, BIT

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.


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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.


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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 =


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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


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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


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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.


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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.


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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)


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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.


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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.


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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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