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Energy-adaptive Pulse Amplitude Modulation for IR-UWB Communications Under Renewable Energy

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Abstract

Impulse Radio Ultra-wideband (IR-UWB) technique has long been recognized for its unique carrierless operation as compared with other communication techniques. The simple and low-cost structure offers great advantages for self-powered embedded wireless systems, in which energy efficiency is a challenging issue due to the fact that most renewable energy sources only offer limited and unstable power supply. In this paper, we present an energy-adaptive Pulse Amplitude Modulation technique for self-powered IR-UWB based communication systems to improve data rate and or time coverage. The basic idea is derived from the fact that domain-specific information in such applications are often available; thus, by jointly exploiting the wireless channel conditions and the non-deterministic characteristics of renewable energy sources, the proposed technique dynamically adjusts the modulation level to enhance the sustainable operation under the unreliable energy supply. Simulation results demonstrate that the proposed technique achieves a much higher data rate and better time coverage than conventional UWB systems. The proposed technique is also insensitive to many practical issues such as the battery aging effect.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USA

    Dong Zhao, Junlin Chen & Lei Wang

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  1. Dong Zhao
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  2. Junlin Chen
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  3. Lei Wang
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Correspondence to Lei Wang.

Appendix A

Appendix A

1.1 Proof of Eq. 21

In this appendix, we prove the energy thresholds for the energy-adaptive PAM as expressed in Eq. 21.

As discussed in Section 2.2, the power consumption of the IR-UWB circuit employing a PAM scheme can be expressed as a function of the number of bits per symbol N b = log2M as

$$ P_{t}(N_{b})=P_{C}+P_{amp}+P_{S}=P_{C}+\frac{\xi_{N_{b}}}{\eta}\frac{\left(\left(2^{N_{b}}\right)^{2}-1\right)}{3}P_{k}, $$
(27)

where P t (N b ) is an increasing function of N b . As a result, under the same amount of available energy, the circuit on time T o n during a time slot with the period T s decreases with N b , i.e.,

$$ T_{on}(N_{b})=\min\left( T_{s}, \frac{E_{b}+E_{h}}{P_{t}(N_{b})}\right). $$
(28)

Note that T o n (N b ) can also be recast as a piecewise function of the available energy E b + E h as

$$\begin{array}{rcl} T_{on}(N_{b}) \,=\, \begin{cases} (E_{b}\,+\,E_{h})/P_{t}(N_{b}) & E_{b}\,+\,E_{h} \le P_{t}(N_{b})T_{s}\\ T_{s} & \text{otherwise}\\ \end{cases} \end{array} $$
(29)

Substituting T o n (N b ) from Eq. 29 into Eq. 14, the average data rate over the time period T s can also be expressed as a piecewise function as

$$\begin{array}{@{}rcl@{}} r_{N_{b}}= \begin{cases} N_{b}\frac{(E_{b}+E_{h})/P_{t}(N_{b})}{T_{s}} & E_{b}+E_{h} \le P_{t}(N_{b})T_{s}\\ N_{b} & \text{otherwise}\\ \end{cases} \end{array} $$
(30)

From Eq. 30, when the available energy is insufficient for the IR-UWB circuit to work over the entire time period T s , i.e. \(E_{b}+E_{h} \le P_{t}(N_{b})T_{s}\), \(r_{N_{b}}\) is a linearly increasing function of the available energy, as shown in Fig. 9 for 2-, 4-, and 8-PAM under normalized energy values. Note that the 2-PAM has the largest slop whereas the 8-PAM has the smallest slop in their corresponding linear ranges. This reflects the practical scenario where, when the available energy is smaller than a certain threshold, e.g, less than T s P t (1), 2-PAM will be selected as it achieves a higher data rate. This is consistent with the observation that, when the available energy is small, a low level modulation scheme should be selected.

Figure 9
figure 9

Illustration of determining energy thresholds.

Full size image

Figure 9 clearly shows that the energy threshold between two modulation levels N b and N b + 1 is the crosspoint between the constant range of the modulation level N b and the linear range of the modulation level N b + 1. For example, consider the crosspoint corresponding to E 2, 3. When the available energy is less than E 2, 3, 4-PAM has a larger data rate; whereas when available energy is larger than E 2, 3, the data rate of 8-PAM becomes larger. At this crosspoint, the data rates of the two modulation schemes are equal, which can be expressed as,

$$ N_{b}=(N_{b}+1)\frac{E_{N_{b},N_{b}+1}}{P_{t}(N_{b}+1)T_{s}}. $$
(31)

Substituting P t (N b + 1) from Eq. 27 into Eq. 31, the energy threshold is obtained as

$$ E_{N_{b},N_{b}+1} = \frac{N_{b} T_{s}}{N_{b}+1}\left(P_{C}+\frac{\xi_{N_{b}+1}}{\eta} \frac{4^{N_{b}+1}-1}{3}P_{k} \right), $$
(32)

which proves the energy thresholds for the energy-adaptive PAM as expressed in Eq. 21.

Another interesting observation is that in Fig. 9, the shadowed areas reflect the degradation in data rate if a full-time coverage is required, as discussed in Eq. 3.2. For example, when the available energy is larger than E 2, 3, 8-PAM would be selected but this scheme cannot achieve full-time coverage, i.e., T o n (3) < T s . To achieve a full-time coverage, 4-PAM should be select, resulting the data rate degradation as visualized by the shadowed area between E 2, 3 and T s P t (3).

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Zhao, D., Chen, J. & Wang, L. Energy-adaptive Pulse Amplitude Modulation for IR-UWB Communications Under Renewable Energy. J Sign Process Syst 76, 121–132 (2014). https://doi.org/10.1007/s11265-013-0855-y

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