II – MODULATION TECHNIQUES

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Energy Optimization Using Different Modulation Techniques for Wireless Sensor Networks

Vibhav Kumar Sachan¹, Saurabh Kumar² and Syed Akhtar Imam³

1, 2

Department of Electronics & Communication Engineering, KIET Group of Institutions, Ghaziabad, UP, India

3 Department of Electronics & Communication Engineering, Faculty of Engineering & Technology, Jamia Millia Islamia, New Delhi, India E-mail :[email protected], [email protected], [email protected]

Abstract

Wireless communication systems are attractive because of its capability to provide mobility to end users. Compared with the traditional radio frequency (RF) technology and millimeter-wave systems, optical wireless (OW) technology has multiple advantages, such as the unregulated large bandwidth available, immunity to electromagnetic interference, and the possibility of frequency reuse and security at physical layer where optical beam does not penetrate walls or opaque objects. In Wireless systems nodes operate on batteries that leads minimization of battery consumption while satisfying delay requirements.

Different modulation schemes are designed to minimize energy consumption required to send given number of bits.

The total energy consumption includes both the circuit energy and transmission power consumption. Un-coded systems are designed for optimizing the transmission time and the modulation parameters which gives 80% energy savings over non-optimized systems. For coded systems, energy consumption varies with the modulation techniques and transmission distance.

Keywords: - Optical communication, BER performance, Footprint, data rates, Modulation techniques (MQAM, MFSK), Energy consumption.

I – INTRODUCTION

With the advancement of hardware signal processing functionality integrated on a single chip, it is possible to integrate RF transceiver, A/D and D/A converter on a single chip. Wireless nodes operate on wireless batteries for replacement which is very difficult and expensive. The wireless should operate without battery replacement.

Minimizing energy consumption is very important. The authors proved that link layer, MAC layer, and all other higher layers designed to minimize the total energy consumption.

Joint design across the layers of network protocol stack is quite challenging.

Investigating energy consumption with both the transmitted path and the received path is the total energy required to convey a given number of bits to the receiver for reliable detection.

Assuming all nodes transmits and receives about the same amount of data, minimizing the energy consumption with both the transmitted path and the received path at the same time is more appropriate than minimizing them separately.

Energy saving is significant in wireless node as battery energy is finite and node only transmit finite number of bits.

The maximum number of bits that can be sent is defined by the total battery energy divided by the required energy per bit.

Energy-constrained communication that focuses on transmission schemes to minimize the transmission energy per bit. There is some strategy to minimize the energy per bit required for reliable transmission in the wide-band. To minimize transmission energy by maximizing the transmission time for buffered packets.

There are many methods to minimize the transmission energy.

The practice of minimizing transmission energy is reasonable in the traditional wireless link for large transmission distance (≥ 100 m), so that the transmission energy is dominant in total energy consumption.

Wireless ad-hoc networks (e.g., sensor networks) the nodes are densely distributed, and the average distance between nodes is usually below 10 m.

Energy consumption during path becomes comparable to the transmission energy in the total energy consumption.

Thus in optimal transmission, the overall energy consumption including both transmitted and circuit energy consumption needs to be considered.

It is observed that M-ary modulation enable energy savings over binary Modulation for short-range applications.

Uncoded MQAM modulation and optimal strategies are analysed to minimize the total energy consumption for AWGN channels. The circuit energy consumption, the transmission time, and the constellation size for both uncoded and coded MQAM and MFSK in AWGN channels.

This analysis takes peak-power and delay constraints into account.

For both MQAM and MFSK, minimizing energy consumption required to given BER requirement by the optimization of the transmission time.

In optimization, we also find the optimal constellation size for MQAM and for MFSK. The effects of coding are modelled by the coding gain and the corresponding bandwidth expansion wherever applicable. For MQAM, trellis-coded modulation is studied for the energy minimization problem.

II – MODULATION TECHNIQUES

There are two types of modulation categories:- 1) Analog modulation techniques

2) Digital modulation techniques

1) Analog modulation techniques

There are basically three types of analog modulation schemes.

(a) amplitude modulation (b) Frequency modulation (c) Phase modulation

In case of the Amplitude Modulation there are several derivatives and it is evident from the comparative table -3 that the Single Side Band Suppressed Carrier (SSS-SC) has smaller bandwidth and power requirements in contrast with Double Side Band Suppressed Carrier (DSB SC) and Double Side Band Full Carrier (DSB FC) and Single Side Band Full Carrier (SSB FC) but for detection of this signal, we require sharp cut- off Low Pass Filter (LPF) which is not practically viable.

Using the Vestigial Side Band (VSB) technique in place of (SSB SC), we can achieve a low pass filter with a gradual cut off but it requires more BW and power than SSB-SC and less then the DSBSC and DSB-FC and hence ideally SSB-SC is proves to be better than other AM schemes but practically, VSB proves to be a much better candidate then the other amplitude modulation techniques.

2) Digital modulation techniques

After the conversion of an Analog signal to digital by sampling different type of digital modulation schemes can be achieved by the variation of different parameter of the carrier signal for example the Amplitude variation gives BASK, Frequency

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326 variation gives BFSK and the phase variation gives BPSK.

Also sometimes a combinational variation of this parameter is done to generate the hybrid modulation technique viz. a combinational variation of Amplitude and Phase Shift Keying (APSK). Many more digital modulation techniques are

available and can also be designed depending upon the type of signal and the application.

Thus a better digital modulation technique is to be thought over by the designer which has an ability of exploiting the available transmitted power and the bandwidth to its full extent.

Digital modulation techniques a) M-Frequency shift key(FSK) b) Phase shift key

c) Amplitude shift key(ASK) M-Frequency shift key (FSK)

When two different frequencies are used to represent two different symbols, then the modulation technique is termed as BFSK. BFSK can be a wideband or a narrow band digital modulation technique depending upon the separation between the two carrier frequencies, though cost effective and provides simple implementations but is not a bandwidth efficient technique and is normally ruled out because of the receiver design complexities.

Phase shift key (PSK)

For the perfect detection of a phase modulated signal, it become evident that the receiver needs a coherent reference signal but if differential encoding and phase shift keying are incorporated together at the transmitter then the digital modulation technique evolved is termed as Differential Phase Shift Keying. For the transmission of a symbol 1, the phase is unchanged whereas for transmission of symbol 0, the phase of the signal is advanced by pi. The track of the phase change information which becomes essential in determining the relative phase change between the symbols transmitted. The whole process is based on the assumption that the change of phase is very slow to an extent that it can be considered to be almost constant over two bit intervals.

III –

SYSTEM MODELLING

To minimize the total energy consumption, all processing blocks in transmitter and the receiver must consider in the optimum condition.

Energy-constrained wireless networks have throughput requirement is low so that the baseband symbol rate is low.

The power consumption in the baseband is mainly defined by the symbol rate and the complexity of the digital logic. Power consumption is small compared with to power consumption in the RF circuit, which is closely related to carrier frequency.

Thus the energy consumption of baseband signal blocks is reduced to simplify the model.

At receiver, the RF signal is filtered and amplified by the Low Noise Amplifier (LNA) and cleaned by the anti-aliasing filter which is down-converted by the mixer, which is then filtered through the Intermediate Frequency Amplifier (IFA) whose gain is adjusted converted back to a digital signal via the Analog to Digital Converter (ADC).

The last demodulation is done digitally. In this model a generic low-IF transceiver structure, our framework can be easily modified to analyse other architectures as well. When a signal is transmitted to a circuit in active mode, there is no signal to transmit if they work in sleep mode, and when switching from sleep mode to active mode there is a transient mode.

Considering a node with L bit has to transmit in time limit T through a sensor network where each sensor takes measurements periodically. These measurements should arrive to the processor in a specific manner to achieve good accuracy.

The transceiver spends time � � to communicate these bits, where Ton is a parameter to optimize, and then go to the

sleep mode where all the circuits in signal path are shut down for energy saving.

The transient duration from active mode to sleep mode is short enough to be negligible and the start-up process from sleep mode to active mode will be slow due to finite Phase Lock Loop (PLL) settling time.

Thus, the transmission period � is given by � = � + � +

�

Where � - transient mode duration = frequency synthesizer settling time

� - sleep mode duration

Similarly, Total energy consumption E required to send L bits defined as:

� = � � + � � + � �

= � + � � + � � + � � (1) Where � - Power consumption for active mode

� - Power consumption for sleep mode � - Power consumption for transient mode The active mode power

� = � + � Where � - Transmission signal power

� - Circuit power consumption in the signal path

� = � � + �� + �� + � + �� + ��

+ � + � + �

Where � � - Mixer power consumption �� - LNA power consumption

�_� + � + �_� + �_� + � + � + � � - Frequency synthesizer power consumption

�� - IFA power consumption

�� - Active filter power consumption at transmitter �_� - Active filter power consumption at transmitter � - DAC power consumption

� - ADC power consumption

� - Power amplifier power consumption Where � = � � and � = ξ η −

η - Drain efficiency of RF power amplifier

ξ - Peak to Average Ratio (PAR), which is depends on modulation.

The maximum power available for the transmitter signal path is denoted as � , which is equals maximum battery output at transmitting node minus total power consumption inside the same node. The maximum power available for the receiver signal path � is defined in the same manner.

Since � = �{� , � , � } , the peak-power constraints are given by

� = � + � + � = + � � + � � (2)

� = � � (3) Where � - Value of � at the transmitter

� - Value of � at the receiver.

� = � _� + � + �_� + �

� = � _� + � + �_� + � + �_�� + �_�

Shows circuit power consumption in the active mode at both transmitter and receiver. In the following sections � � =

� + � ) � will used to denote total circuit energy consumption.

Using equation 1 & 2 we can considerP_p = 0 and P ≈ P_yn Now, the energy consumption per information bit

� = �/ is given by

� = + � � + � � + � � /

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327 ≈ + � � + � � + � � / (4)

Where � = � �

Transmission energy � is a monotonically increasing function of the bandwidth efficiency defined as � = /�� (in bits/s/Hz).

For MFSK the � term in all the energy consumption formulas should exclude the energy terms related to the mixer and the DAC on the transmitter side. Finally, the energy-constrained modulation problem can be modelled as

Minimize �

Subject to � � − �

+ � � + � � (5)

IV-

UNCODED MQAM

Analysis of MQAM is done over an AWGN channel. For MQAM, the number of bits per symbol is defined as = log . The number of MQAM symbols needed to send L bits is denoted as = . If the symbol period is denoted as Ts, we can also represent Ls as

Ls = ^�

� , Thus ^� = ^�_�

If square pulses are used and Ts ≈ 1/B is assumed, we have b

= _�^�

Since the bandwidth efficiency is defined as Be = ^�

� , we can see that

b ≈ Be for MQAM. A bound on the probability of bit error for MQAM is given

By � < (1-_√ ) Q (√ ₋ � ) < (1-_√ ) ⁻ − �

Q(x) = ∫^∞_{√ �} ⁻ du

The signal to noise ratio (SNR) is defined as �= _{� �}^�

�

Where Pr is received signal power, � is the power spectral density of the AWGN and is the receiver noise defined as =^�

�

On approximating, the bound as equality we obtain

Pr = �� − ln ⁻_�^√ The transmission power is equal to

� = � �

Where � = � , is the power gain factor with is link margin compensating the hardware process and additive background noise, interference and � the gain factor at d = 1 m which is defined by the antenna gain, carrier frequency and other system parameters. Where k = 3.5 and � = 30 dB for our model. The transmission energy as

� = � � =

�� ^��^� ^.− ln ⁻�^{− �}^�� ^.

�� .� � B�

It can be shown that � is a decreasing function over the product �� when MQAM is well defined, i.e. when � =

/�� . When the packet size and bandwidth B are fixed, the maximum allowable � minimizes the transmission

energy .According to Eq. (4) expression for the total energy consumption per information bit in terms of Ton is given by

� = + � �� ^��^� ^.− ln ⁻�^{− �}^�� ^.

�� .� � B� +�

� +2 � )/L

Where α = _�^ξ − 1 is also a function of � since for MQAM ξ = ^√M−_√M+

M = ^��^�

From the expression for � we see that the maximum Ton minimizes the transmission energy while the minimum � minimizes the circuit energy consumption.

The peak-power constraint can be rewritten as + � �� ^��^� ^.− ln ⁻�^{− �}^�� ^.

�� .� � B

= � -�

Which is equivalent to � � _� , where � _� is the solution for � .Thus, for MQAM the optimization model can be rewritten as minimize � subject to � _� � � − � . If we take into account that = L/�� , an equivalent

representation for the optimization model follows minimization of Ea subject to _� , where is upper bound on corresponds to lower bound .

� given by =. ^�

� _� . The lower bound on b is given by � = max { ^�

�−� 2}

� = + � � ⁽ ^.^{− )} ln _b�⁻ ^{− .} � + �

� +2 � )/L

In that case, we can use coding or MFSK modulation to reduce the peak power requirement.

The transmission energy is dependent on the transmission distance d while circuit energy consumption is independent of d. Thus saving energy by optimizing Ton is only when the circuit energy consumption is nontrivial relative to the transmission energy. Since the transmission energy increases with d, threshold for the value of d above which there is no energy savings possible by optimizing� , which should j be set to the maximum value T.

V- UNCODED MFSK

For MFSK, the number of orthogonal carriers is M = . We assume that the carrier separation is equal to

� , where Ts is the symbol period. Thus, the data rate R=

� and the total bandwidth can be approximated as B ≈ _� .

As a result, the bandwidth efficiency for MFSK is given by Be = 2b/ (b/s/Hz). The bandwidth efficiency can also be represented as

Be = ^�

� � .

The relationship between the constellation size and the bandwidth time product for MFSK is given by

2b/ = ^�

�

Which is different from the MQAM where b = ^�

� . However, one-to-one relationship between b and �� product for fixed value of L except for b = 1 and b = 2, corresponds to the same

�� product. Most practical MFSK receivers use non- coherent detectors, the probability of error for non-coherent MFSK detection is used in our derivation

� = ⁻ ⁻^�

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328 Approximating �=_�

�� ≈ 2 ln _�⁻ .

Where� is the energy per information bit at the receiver and

=2� Hence

� ^��= ln ⁻

� .

In MQAM case, the transmission power and the transmission energy are given by

� = _� ln ⁻

� �

� = � � = _� ln ⁻

� � ^�

Where � = ^�

The total energy consumption per information bit is given by

� = + � � ln _�⁻ � ^� +� � + � � )/L)

VI CODED MQAM AND MFSK

Forward Error Correction Codes (ECCs) [13] can reduce the required value of SNR to meet a given target probability of bit error, where � refers to the received energy per information bit, which is proportional to the transmission energy per information bit. However, whether the total energy

consumption per information bit can be reduced is not clear due to the possible bandwidth expansion caused by the ECC redundancy and the extra baseband energy consumption of the ECC codec.

The error-correction capability of ECCs is enabled by introducing controlled redundancy, which usually causes bandwidth expansion in order to communicate the extra redundant bits.

VII- SIMULATION & RESULT [A] UNCODED MQAM

MQAM PARAMETERS

S No. Parameter Value

1 � � 30.3 mW

2 �� 20 mW

3 � 250 mW

4 � 50 mW

5 �_� 3 mW

6 �_� = �_� 2.5 mW

7 � ⁻

8 2.5 GHz

9 k 3.5

10 B 10 KHz

11 T 100 ms

12 10 dB

13 � 5 us

14 � -174 dBm/Hz

15 40 dB

16 � 30 dB

17 Η 0.35

18 L 2 kb

For a specific numerical example, the circuit-related

parameters need to be defined first. For radios in other bands or with significantly different hardware architectures we need to use different parameters. The corresponding parameter where η = 0.35, and the values for B, L, and T are set up such that = L/�� = 2. The constellation size for MQAM is well defined inside the feasible region. The vertical axis is the energy consumption per information bit (in terms of dB relative to a mill joule:

. dBmJ. The horizontal axis

is the normalized transmission time. The total energy

consumption is not a monotonically-decreasing function of Ton when the transmission distance d is small. The optimization results in an 80% energy saving. It is shown that even when d=100 m, the peak-power constraint is violated even when b=2.

Fig 2 Total Energy Consumption MQAM (AWGN)

We redraw Ea over b for the d = 5 m case in Fig. 3. We see from the figure that bopt ≈ 9 if the total energy consumption is considered versus bopt = 2, its minimum value, when only transmission energy is considered.

Fig 3 Total energy consumption versus constellation size, MQAM (AWGN)

[B] UNCODED MFSK

We draw � and � directly over b as shown in Fig. 4.

The transmission energy � decreases as b increases, since it is well known that the larger M is, the more energy-efficient MFSK is, in an AWGN channel. In other words, M = ∞ is optimal in the sense of minimizing the energy consumption per information bit [13] based only on transmission energy. When the circuit energy consumption is considered, as shown in Fig.

4, b = 2 turns out to be the best choice for both d = 1 m and d = 30 m. For the b = 1 m case, by using bopt = 2 we can achieve about 80% energy savings when compared with the case where b=6 (Ton = T) is used.

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329 In the following sections we consider two coded systems:

trellis-coded MQAM and convolutionally-encoded MFSK. For trellis-coded MQAM, even though there is no bandwidth expansion, there is still an energy penalty caused by the

baseband ECC processing. We first neglect this energy penalty due to its small magnitude compared with the energy

consumption of the RF circuitry and then show its effect with an example where the transmission distance is extremely small.

Therefore, it will be shown in the next section that trellis-coded MQAM always has higher energy efficiency than uncoded MQAM for narrowband systems. For MFSK systems with fixed bandwidth, we cannot implement coding by increasing the constellation size while keeping the transmission time constant, as we do in trellis-coded MQAM.

[C] CODED MQAM

In a trellis-coded MQAM system, each block (of size b) of information bits is divided into two groups of size and , respectively. The first group of bits is convolutionally encoded into bits, which map to constellation subsets.

The second group of bits are used to choose the th constellation point within each subset [13]. The code rate is therefore defined as Cr = / and the constellation size is increased from to ⁺ . A rate Cr = / ( + 1) code is usually used for subset selection. = 2 is a good choice since it provides the major part of the achievable coding gain.

Coding gain � ≈ 3 (4.7 dB).

Due to the embedded ECC, the required SNR threshold γ0 to achieve a given Pb is reduced by the coding gain Gc, i.e., for any b = L/BTon, γ0 = Ebb/GcN0. Therefore, for trellis-coded MQAM the required transmission energy to achieve a given Pb is changed to Etc = Et/Gc and

Total energy consumption � is given as

� = + � � ⁽ ^.^{− )} ln _b�⁻ ^{− .} � + � � +2 � )/L

� = ^�_�=

The plots of minimized energy per information bit over

different transmission distances are shown in Fig. 5, where we see that about 90% energy savings is achieved over the

reference setup for the coded system when d = 1 m. The plots also show that for both the coded and uncoded systems, the optimized performance converges to be the same as the

reference performance when the transmission distance is large.

L=2Mb.

Fig 5 Total Energy Consumption per Information Bit v.s.

Distance for MQAM Table 2:

B(MHz) Ton(ms) b

d=1 10 12 16

d=5 10 20 10

d=30 10 80 3

d=50 10 100 2

For optimized systems, since higher constellation sizes reduce the transmission time, the energy consumption in the Viterbi decoder is compensated by the reduced energy consumption in the circuits. So, the effect of the coding process is not obvious.

That is, adaptive modulation is able to keep the superiority of coded systems down to a very short distance, as shown in the figure where the crossover happens at 0.1 m.

Distance for MQAM (ECC processing energy included) For trellis-coded MQAM, the coding gain is more sensitive to the constraint length of the convolutional encoder than to the code rates. Codes with lower rates may not necessarily generate higher coding gain. Since there is no bandwidth expansion, any codes with higher coding gain are able to reduce the total energy consumption unless the constraint length is so large that the energy consumption in the decoding logic can no longer be neglected.

[D] CODED MFSK

For the coded MFSK system, Code rate Cr= 2/3, a coding gain � ≈ 2.6 (4.2 dB). Since the available frequency band is fixed, the error-control bits are accommodated by bandwidth expansion in the time domain. So, the required transmission energy per information bit for coded systems is

reduced by � at a increased transmission time � = � /� . The total energy consumption per information bit for the coded system is given by

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330

� = + � � ln _�⁻ � +� � + � � )/L)

Due to the coding, the delay constraint is increased to 1.07/�

= 1.61 s for the coded system.

η = 0.75

The total energy consumption per information bit over different transmission distances d is plotted in Fig. 7. This figure shows that optimizing over modulation parameters saves energy for both the coded and uncoded systems, and this energy saving increases with d. In addition, the uncoded system outperforms the coded system when d is small (< 50 m for the optimized cases). This is due to the fact that the ECCenabled savings on transmission energy can no longer balance the extra circuit energy consumption caused by the increase in transmission time.

Distance for MFSK

[E] COMPARISON of CODED MFSK & MQAM and UNCODED MFSK & MQAM

Since the design variable b is defined over integer values, the corresponding optimization problem is a non-convex integer programming problem. Exhaustive search (which is used for the numerical examples in this paper) is a feasible way to solve this problem for the simple point-to-point case, since only one variable is involved and all the constraints are properly

bounded which makes the search algorithm relatively simple.

However, we also investigated efficient algorithms to solve this type of integer programming problem. These algorithm scan be used for example to extend the energy minimization results to multiple users [18]. Specifically, we found that if we use a looser bound on the total energy consumption per bit for MQAM, we are able to use an efficient convex relaxation method to solve this problem. For MFSK, even without using any looser bounds, the problem can be solved with efficient convex relaxation methods.

Fig 8 Total Energy Consumption Comparison Between MQAM and MFSK

From the above figure, we found that if we use a looser bound on the total energy consumption per bit for MQAM, we are able to use an efficient convex relaxation method to solve this problem. For MFSK, even without using any looser bounds, the problem can be solved with efficient convex relaxation methods.

V- CONCLUSION

We have shown that for transmitting a given number of bits in a point-to-point communication link, the traditional belief that a longer transmission duration lowers energy consumption may be misleading if the circuit energy consumption is included, especially for short-range applications. For both

MQAM and MFSK, we show that the transmission energy is completely dependent on the product of B and Ton. To

minimize the transmission energy, maximum transmission time is required. To minimize the total energy consumption, the transmission time needs to be optimized, where we show up to 85% energy savings is achievable via this optimization.

For trellis-coded narrow-band MQAM systems, we have shown that coding always increases energy efficiency, and the improvement increases with the transmission distance d. For MFSK systems, coding can only reduce energy consumption when the transmission distance is large such that the

transmission energy is dominant. For short-range applications, uncoded MFSK outperforms coded MFSK due to the

bandwidth expansion caused by ECC.

We found that uncoded MQAM is not only more bandwidth efficient, but also more energy-efficient than uncoded MFSK for short-range applications. The performance difference is even more pronounced with coding. However, coded MFSK may be desirable in peak-power-limited applications since it requires less transmit power, although its total energy consumption may be higher.

Tables

Table 1: MQAM Parameters Table 2: MQAM Parameters Figures

Figure 1. Total Energy Consumption MQAM (AWGN)

Figure 2. Total energy consumption versus constellation size, MQAM (AWGN)

Figure 3. Energy per Information Bit versus constellation size, for MFSK

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331 Figure 4. Total Energy Consumption per Information Bit vs Distance for MQAM

Figure 5. Total Energy Consumption per Information Bit v.s.

Distance for MQAM (ECC processing energy included)

Figure 6. Total Energy Consumption per Information Bit v.s.

Distance for MFSK

Figure 7. Total Energy Consumption Comparison between MQAM and MFSK

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