6.5 Effect of parameters
6.5.1 The effect of physical layer parameters
Circuitry power
According to the definition of EDRb (6.10) and (6.3) (6.4), it is deduced easily that the increase of circuitry power leads to the increment of total energy consumption which coincides with our intuition. Meanwhile, Ec is independent of Popt and dopt under
a delay constraint. Therefore, we should reduce the circuitry power in the design of sensor node and should select a node which has minimum circuitry power.
Channel coding 0.040 0.06 0.08 0.1 0.12 0.14 0.2 0.4 0.6 0.8 1 1.2 1.4x 10 −4
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in AWGN channel
No coding Hamming code (7,4)
(a) AWGN channel
0.1 0.15 0.2 0.25 0.3 0.35 3 3.5 4 4.5 5 5.5x 10 −5
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh block fading channel No coding Hamming code (7,4)
(b) Rayleigh block fading channel
0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2x 10 −4
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh flat fading channel No coding Hamming code (7,4)
(c) Rayleigh flat fading channel
94 Effect of parameters
Coding can reduce the probability of bit or block error but introduce more bits resulting to more energy consumption. What is the benefit of coding in the viewpoint of energy-delay trade-off will be revealed in the following part in three kinds of channels. Here, Hamming code (7, 4) is used as an example. The results in Fig.6.7indicate that this kind of coding brings some benefit in both energy and delay in Rayleigh flat fading channel, however, introduces more energy and delay in AWGN channel and Rayleigh block fading channel. Therefore, it is dependent on the type of channel to decide if a coding scheme should be used.
Modulation 0.06 0.08 0.1 0.12 0.14 0.16 0.8 1 1.2 1.4 1.6 1.8 2x 10 −5
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in AWGN channel
4QAM 8QAM 16QAM 32QAM 64QAM
(a) AWGN channel
0.05 0.1 0.15 0.2 0.25 1.4 1.6 1.8 2 2.2 2.4 2.6x 10 −5
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh block fading channel
4QAM 8QAM 16QAM 32QAM 64QAM
(b) Rayleigh block fading channel
0.2 0.4 0.6 0.8 1 1.2 5.5 6 6.5 7 7.5 8 8.5 9 9.5x 10 −5
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh flat fading channel
8QAM 16QAM 32QAM 64QAM 128QAM
(c) Rayleigh flat fading channel
Figure 6.8: Effect of modulation on energy-delay trade-off in different channels High order modulation brings high BER but reduces the transmission time and energy when in the same symbol rate due to the increase of bit rate. The effect of modulation on the lower bound of energy-delay trade-off in three kinds of channel is shown in Fig.6.8.
Transmission Rate 0.060 0.08 0.1 0.12 0.14 0.16 0.5 1 1.5 2 2.5 3 3.5x 10 −4
mean delay per bit per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in AWGN channel
100Kbps 250Kbps 500Kbps
(a) AWGN channel
0.1 0.15 0.2 0.25 0.3 0.35 0 0.2 0.4 0.6 0.8 1x 10 −4
mean delay per bit per meter (mS/bit/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh block fading channel
100Kbps 250Kbps 500Kbps
(b) Rayleigh block fading channel
0.4 0.6 0.8 1 1.2 0 1 2 3 4 5 6 7 8x 10 −4
mean delay per bit per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh flat fading channel
100Kbps 250Kbps 500Kbps
(c) Rayleigh flat fading channel
Figure 6.9: Effect of Rs on energy-delay trade-off in different channels
On the basis of (6.10) and (6.12), we know that the higher transmit rate is, the smaller Ecand DDR is in any type of channel. Meanwhile, the increase of transmission
rate leads to the decrease of SNR according to (2.11) which brings the rise of BER. In other words, the increase of transmit rate will bring two oppositive effect on the optimal EDRb and thus an optimal transmit rate should be existed. While, the results in Fig. 6.9 show that EDRb and DDR decrease simultaneously with respect to the increase of transmit rate in the three kinds of channel. Hence, the energy saving from the decrease Ec can compensate for the increase of energy consumption because of the
augment of BER. Finally, according to this conclusion, the maximum transmit rate that a node can reach should be used in order to minimize both EDRb and DDR.
96 Effect of parameters
Number of bits in a ACK packet Nack
According to (6.3) (6.4) and the definition of EDRb (6.10), it is deduced easily that the increase of Nack leads to the increment of total energy consumption because of increase
of τack. Therefore, similarly to P2P communications, Nback should be removed or
reduced as less as possible. Number of bits in a packet Nb
As analyzed above, diminishing τackcan improve the energy efficiency. Another method
of diminishing τack is to increase Nb according to (2.5). Meanwhile, this will lead to the
decrease of link probability based on (6.5), which results in more energy consumption. Finally, these two contrary effects bring on an optimal number of bits. Fig. 6.10, Fig. 6.11 and Fig. 6.12 show how the optimal EDRb varies with Nb in three kinds
of channel. Because τack is related with both Nack and Nb, the optimal Nb is tightly
dependent on Nack. This kind of impact is also shown in Fig. 6.10, Fig. 6.11 and
Fig. 6.12. The conclusion obtained from these figures is the increase of Nack will lead
to the great increase of optimal Nb.
It should be noticed that the difference of EDRb from the different number of bits is small when Nackis very small especially in AWGN channel and Rayleigh block fading
channel. Considering the conclusion about Nack, we should do our best to reduce Nack
so that the optimization about Nb can be neglected.
0.02 0.03 0.04 0.05 0.06 1.5 2 2.5 3 3.5 4 4.5 5x 10 −5
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in AWGN channel
80 Bytes 160 Bytes 320 Bytes
(a) ACK = 11 bytes
0.021 0.03 0.04 0.05 0.06 2 3 4 5 6 7x 10 −5
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in AWGN channel
80 Bytes 160 Bytes 320 Bytes
(b) ACK = 26 bytes
Figure 6.10: Effect of Nb on energy-delay trade-off in AWGN channels
Delay from MAC protocol
According to (6.12) , the increase of Tqueue will lead to the increment of Dhop and it
can be deduced that the transmission power should be increased to satisfy the same delay constraint on the basis of (6.18). In turn, the EDRb will increase. The results
0.022 0.04 0.06 0.08 0.1 2.5 3 3.5 4 4.5x 10 −5
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in Rayleigh block fading channel
80 Bytes 160 Bytes 320 Bytes
(a) ACK = 11 bytes
0.022 0.04 0.06 0.08 0.1 4 6 8 10 12 14x 10 −5
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in Rayleigh block fading channel
80 Bytes 160 Bytes 320 Bytes
(b) ACK = 78 bytes
Figure 6.11: Effect of Nb on energy-delay trade-off in Rayleigh block fading channels
0.1 0.2 0.3 0.4 0.5 1 1.2 1.4 1.6 1.8 2 2.2x 10 −4
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in Rayleigh flat fading channel
80 Bytes 160 Bytes 320 Bytes
(a) ACK = 78 bytes
0.1 0.2 0.3 0.4 0.5 1 1.5 2 2.5 3 3.5 4 4.5x 10 −4
mean delay per bit per meter (uS/bit/m)
mena EDRb (mJ/bit/m)
Energy−latency trade−off in Rayleigh flat fading channel
80 Bytes 160 Bytes 320 Bytes
(b) ACK = 150 bytes
Figure 6.12: Effect of Nb on energy-delay trade-off in Rayleigh flat fading channels
in Fig. 6.13 verify the above analyses. This conclusion shows that during the design of protocol the process leading to the increase of Tqueue should be reduced or removed
such as RTS and CTS process to improve the energy efficiency of a network.
Besides the above parameters, the integration of several parameters can be ana- lyzed also according to the different applications because this framework includes every parameters in physical and protocol layer. On the basis of these analysis result, we can adjust the parameter to obtain the best performance of a network.
6.6
Simulations
The purpose of this section is to verify the lower bound on the energy-delay trade- off and on the energy efficiency in a 2-dimensional Poisson distributed network using simulations. The goal is to show that the theoretical results obtained in a linear network using approximation approach still hold for such a more realistic scenario. First, we
98 Simulations 0.060 0.08 0.1 0.12 0.14 0.16 0.5 1 1.5 2 2.5 3 3.5x 10 −4
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in AWGN channel
0 mS 10 mS 20 mS
(a) AWGN channel
0.1 0.15 0.2 0.25 0.3 0.35 2 3 4 5 6 7 8x 10 −5
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh block fading channel
0 mS 10 mS 20 mS
(b) Rayleigh block fading channel
0.4 0.6 0.8 1 1.2 0 1 2 3 4 5 6 7 8x 10 −4
mean delay per meter (mS/m)
mean EDRb (mJ/bit/m)
Energy−delay trade−off in Rayleigh flat fading channel
0 mS 10 mS 20 mS
(c) Rayleigh flat fading channel
Figure 6.13: Effect of Tqueue on energy-delay trade-off in different channels
introduce a new opportunistic protocol on the basis of the theoretical analyzes.