3.4 Optimal Design for Throughput
3.5.5 Throughput Performance with Multiple-Antenna Jammer
Fig. 3.7(a) plots the optimal throughput from Proposition 2. We also present the subopti- mal performance which is achieved by the asymptotically optimal rate parameters obtained in Corollary 10. We can see that the throughput increases withPsunbounded. Also we can see that the suboptimal performance is reasonably good whenPs>20dBm.
Fig. 3.7(b) plots the throughput achieved with the optimal design given in Proposition 2 for differentNJ. The source transmit power isPs=30dBm. We also include the suboptimal performance achieved by the asymptotically optimal rate parameters in the large NJ regime (Corollary 11) as well as the upper bound on throughput in Corollary 11.
We can see that with the increment of NJ, although theoretically the throughput is upper bounded as NJ → ∞, the available throughput within practical range of NJ is far from the upper bound. Hence, increasing NJ is still an efficient way to improve the throughput with practical antenna size. Also we can see that the suboptimal performance is acceptable but the
−100 0 10 20 30 40 50 2 4 6 8 10 12 14 16 Ps(dBm) T h ro u g h p u t, π (b p cu ) ε= 0.1, optimal results ε= 0.05, optimal results ε= 0.01, optimal results ε= 0.1, suboptimal results ε= 0.05, suboptimal results ε= 0.01, suboptimal results
(a) Throughput vs. source transmit powerPsforNJ=8.
0 10 20 30 40 50 0 5 10 15 20 NJ T h ro u g h p u t, π (b p cu
) Upper boundε= 0.1, optimial results ε= 0.05, optimial results
ε= 0.01, optimial results Suboptimal results
(b) Throughput vs. number of antennas at the jammer,NJ ≥2.
Figure 3.7:Throughput forNJ>1.
gap from the optimal throughput performance is still noticeable.
3.6
Summary
In this chapter, we investigated secure communication with the help from a wireless-powered jammer. We proposed a simple communication protocol and derived its achievable through- put with fixed-rate transmission. We further optimized the rate parameters to achieve the best throughput subject to a secrecy outage probability constraints. As energy harvesting and wire- less power transfer become emerging solutions for energy constrained networks, this work has demonstrated how to make use of an energy constrained friendly jammer to enable secure communication without relying on an external energy supply.
SWIPT System with Practical
Constraints
In Chapter 3, we investigated a WPT-assisted secure communication system, where the energy receiver, i.e., the jammer, can only harvest RF energy from the received signal. As the RF wave can carry both energy and information, it is desirable to consider a receiver that is able to absorb energy and extract information from the received signal.
In this chapter, we shift our focus on a point-to-point SWIPT system adopting practical
M-ary modulation, where the receiver leverages the received RF signal for both RF EH an in- formation detection. We take into account the fact that the receiver’s radio-frequency (RF) en- ergy harvesting circuit can only harvest energy when the received signal power is greater than a certain sensitivity level. For both power-splitting (PS) and time-switching (TS) schemes, we derive the energy harvesting performance as well as the information decoding performance for the Nakagami-mfading channel. We also analyze the performance tradeoff between energy harvesting and information decoding by studying an optimization problem, which maximizes the information decoding performance and satisfies a constraint on the minimum harvested energy. Our analysis shows that (i) for the PS scheme, modulations with high peak-to-average power ratio achieve better energy harvesting performance, (ii) for the TS scheme, it is desirable to concentrate the power for wireless power transfer in order to minimize the non-harvested en- ergy caused by the RF energy harvesting sensitivity level, and (iii) channel fading is beneficial for energy harvesting in both PS and TS schemes.
This chapter is organized as follows. Section 4.1 presents the system model. Sections 4.2 and 4.3 analyze the performance tradeoff between energy harvesting and information decoding for the PS and TS schemes, respectively. Section 4.4 presents the numerical results. Finally, Section 4.5 concludes the chapter.
4.1
System Model
We consider a SWIPT system consisting of a transmitter (Tx) and a receiver (Rx). The receiver comprises an information-decoding circuit and an RF-EH circuit [7]. Each node is equipped with a single omnidirectional antenna. The transmitter and receiver adopt block-wise operation with block time duration,T. We assume that the receiver is located in the far field, at a distance
d from the transmitter. Thus, the channel link between the two nodes is composed of large scale path loss with exponentλand small-scale Nakagami-mfading. Note thatmrepresents
the fading parameter, which controls the severity of the fading. The fading channel gain,h, is assumed to be constant within one block time and independent and identically distributed from one block to the next [7, 49, 35]. We assume instantaneous channel state information (CSI) is available only at the receiver.
We consider that the transmitter adopts a practical modulation scheme for information transmission (IT). Let the signal constellation set be denoted byX. The size ofX is denoted byMwithM =2l, andl≥1being an integer. Theith constellation point inX is denoted by
xi,i= 1, 2, ...,M, with equal probabilitypi = 1/M,1and the average power of signal setX is normalized to one, i.e.,∑iM=1|xi|2/M=1. In this work, we consider three most commonly used coherent modulation schemes for IT:M-PSK,M-PAM, andM-QAM.2
At the receiver, during a symbol period Ts, assuming the received power at the RF-EH circuit isPrx, the amount of harvested energy can be represented as [35]
E =ηTs(Prx− Pth)+, (4.1)
where 0 ≤ η ≤ 1 is the RF-EH efficiency, and (z)+ = max{z, 0}. We assume that the
harvested energy at the receiver is stored in an ideal battery [7, 35, 121]. Note that in (4.1), according to the existing studies [35, 121, 122], the RF-EH circuit can only harvest energy when its received signal power,Prx, is greater than the RF-EH sensitivity level,Pth, and the
harvested energy is proportional toPrx− Pth.