Power allocation for secure OFDMA systems with wireless information and power transfer Xiaobin Huang, Quanzhong Li, Qi Zhang and Jiayin Qin For simultaneous wireless information and power transfer (SWIPT), secure transmission is an important issue. The power allocation problem is investigated to maximise the achievable secrecy rate in a downlink orthogonal frequency division multiple access system with a power splitting SWIPT scheme. Unlike the traditional wireless communication systems, it is assumed that the legitimate receivers have no energy storage capability. The legitimate receivers harvest the energy from the received signals by using a power splitting scheme to meet the circuit-power constraint for information decoding. The problem is formulated as a power allocation optimisation problem under the transmit power constraint and the energy harvesting constraint which is solvable. It is shown from simulations that the proposed optimal power allocation scheme outperforms the conventional uniform power allocation scheme.
Introduction: Simultaneous wireless information and power transfer (SWIPT), which belongs to energy harvesting (EH) techniques, is promising for solving the energy scarcity problem in wireless communications [1–5]. In [1], for co-located information decoding (ID) and EH receivers, Zhang and Ho proposed two SWIPT schemes, i.e. the ‘time switching’ and the ‘power splitting’, where the former allocates different time blocks for ID and EH, whereas the latter splits the signal into two streams for ID and EH. In [2], the dynamic power splitting approach for the SWIPT in single-input-single-output and multiple-input-singleoutput (MISO) systems was proposed. In [3–5], the power splitting SWIPT scheme in orthogonal frequency division multiple access (OFDMA) systems was investigated. The aforementioned research papers have not considered the secrecy issue. Owing to the openness of the wireless transmission medium, wireless information is susceptible to eavesdropping. Thus, secure communication is a critical issue for the SWIPT. The secure beamforming schemes for the SWIPT in a MISO broadcast channel were studied in [6, 7]. However, to the best of our knowledge, the research on a secure transmission scheme for the SWIPT in OFDMA systems is missing. In this Letter, we study the power allocation problem to maximises the achievable secrecy rate in a downlink OFDMA system with a power splitting SWIPT scheme. The achievable secrecy rate is defined as the rate at which confidential information can be transmitted to legitimate receivers while an eavesdropper obtains no information from the transmitted signal. Unlike the traditional wireless communication systems, we assume that the legitimate receivers, such as radio frequency identification (RF-ID) tags, have no energy storage capability. The legitimate receivers harvest the energy from the received signals by using a power splitting scheme to meet the circuit-power constraint for ID [5]. We formulate the problem as a power allocation optimisation problem under the transmit power constraint and the EH constraint which is solvable. System model: Consider a downlink OFDMA SWIPT system which consists of a transmitter, K legitimate receivers and an eavesdropper. Each of the nodes is equipped with a single antenna. The entire bandwidth is divided into K orthogonal subcarriers, each of which is assigned to a legitimate receiver. The eavesdropper eavesdrops on any signal transmitted from the transmitter over all the subcarriers. With a loss of generality, we assume that the kth, k [ K = {1, 2, . . . , K}, subcarrier is assigned to the kth legitimate receiver. The transmitted signals for the transmitter over each subcarrier experience a flat channel fading. The channel response from the transmitter to the kth legitimate receiver is denoted as hk. The channel response from the transmitter to the eavesdropper over the kth subcarrier is denoted as gk. We assume that the transmitter knows the channel state information (CSI) on hk and gk, k [ K. This assumption is valid when the eavesdropper is active. When the eavesdropper is passive, it is shown in [8] that at a high signal-to-noise ratio (SNR), the additional knowledge of the eavesdropper CSI does not yield any gains in terms of the secrecy rate for slow-fading channels. The received signals at each of the legitimate receivers are split into two streams for ID and EH, respectively. At the kth legitimate receiver,
the RF-band signal from the antenna is corrupted by an additive noise nk introduced by the receiver antenna. The RF-band signal is fed into a power splitter where a portion of signal power split to the EH receiver is denoted by ρk ∈ [0, 1], and that to the ID receiver by 1 − ρk. The signal split to the ID receiver is converted from the RF band to a baseband. During this process, the signal is corrupted by another noise zk which is modelled as a circularly symmetric complex Gaussian (CSCG) random variable (RV) with zero mean and variance σ 2. Generally, the power of noise nk is much smaller than the power of noise zk [2]. Thus, we omit the noise nk. In this Letter, we assume that the legitimate receivers have no energy storage capability. Consequently, the instantaneous power harvested by a legitimate receiver is required to meet the circuit-power constraint for ID as in [5]. Furthermore, we assume that the bandwidth of RF components at the legitimate receiver is the same as the bandwidth assigned to each subcarrier. Thus, each legitimate receiver only harvests energy from the assigned subcarrier as in [5]. The assumption is reasonable for the legitimate receivers such as RF-ID tags whose RF chain is simple. If the kth legitimate receiver participates in ID, it should be satisfied that (1 − rk )pk |hk |2 ≥ Q
(1)
where pk denotes the transmitted power over the kth subcarrier from the transmitter and Q is the EH constraint for the legitimate receivers. The transmit power of the transmitter is restricted by K
pk ≤ P
(2)
k=1
where P is the transmit power constraint. By modelling the additive noise over each subcarrier at the eavesdropper as a CSCG RV with zero mean and variance σ 2, we express the achievable secrecy rate over the kth subcarrier, denoted as Rk, as follows [8]: + r pk |hk |2 + s2 Rk = log2 k (3) pk |gk |2 + s2 The total achievable secrecy rate of the system is R=
K
Rk
(4)
k=1
From (3), if the channel gain from the transmitter to the legitimate receiver is weaker than that from the transmitter to the eavesdropper, Rk is zero. In addition, the kth legitimate receiver may not able to harvest sufficient power to meet the circuit-power constraint for ID. Under these conditions, the transmitter should not allocate transmit power over the kth subcarrier. In this Letter, the subcarrier which has been allocated transmit power by the transmitter is named as the active subcarrier. The set of active subcarriers is denoted as Ω. We should maximise the cardinality of Ω to allow as many legitimate receivers as possible to participate in ID. From EH constraint (1), we know that the optimal power splitting ratio of the kth legitimate receiver is
r∗k = 1 −
Q pk |hk |2
for k ∈ Ω. On substituting (5) into (3), we have + 2 2 k = log2 pk |hk | − Q + s R 2 pk |gk | + s2
(5)
(6)
From (6), the necessary condition for k ∈ Ω and Rk ≠ 0 is pk .
Q Dk
(7)
where Dk = |hk |2 − |gk |2
(8)
On substituting (7) into the transmit power constraint in (2), we have Q ,P D k[V k
ELECTRONICS LETTERS 30th January 2014 Vol. 50 No. 3 pp. 229–230
(9)
When Δk ≤ 0, from (3), the achievable secrecy rate over the kth subcarrier, Rk, is zero. The transmitter should not allocate transmit power over the kth subcarrier, i.e. pk = 0. Thus, the active subcarrier set, Ω, should satisfy both Δk > 0, k ∈ Ω and (9). We search for the optimal Ω which has the maximum cardinality. Let
jk =
Q Dk
(10)
for k [ K. Arrange {jk , k [ K} in decreasing order such that
j1ˆ ≥ j2ˆ ≥ · · · ≥ jkˆ ≥ j ≥ · · · ≥ jKˆ k +1
(11)
Conclusion: In this Letter, we have investigated the power allocation problem to maximise the achievable secrecy rate in a downlink OFDMA system with a power splitting SWIPT scheme. The above problem is formulated as a power allocation optimisation problem under the transmit power constraint and the EH constraint which is solvable. It is shown from computer simulations that the proposed optimal power allocation scheme outperforms the conventional uniform power allocation scheme. Acknowledgments: This work was supported by the National Natural Science Foundation of China (61173148 and 61202498) and the Scientific and Technological Project of Guangzhou City (12C42051578).
Find kˆ1 such that
jkˆ 1 . 0 and j ≤ 0 k1 +1
(12)
Find kˆ2 such that kˆ 1
kˆ 1
jk , P and
k=kˆ 2
jk ≥ P
(13)
k=k 2 −1
k [V
Xiaobin Huang, Quanzhong Li, Qi Zhang and Jiayin Qin (School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, People’s Republic of China) E-mail:
[email protected]
+ 1, . . . , kˆ 1 . After obtaining Ω, we Thus, we have V = kˆ 2 , k2 should optimise the power allocation to maximise the total achievable secrecy rate subject to the transmit power constraint and the EH constraint. Thus, the optimisation problem is formulated as follows: k s.t. pk ≤ P, pk . jk ∀k [ V (14) R max {pk }
© The Institution of Engineering and Technology 2014 17 October 2013 doi: 10.1049/el.2013.3447
k [V
The optimisation problem (14) is a concave optimisation problem which is solved effectively by using the interior point method [9]. Simulation results: In this Section, we consider a downlink OFDMA SWIPT system which includes K = 8 legitimate receivers. The channel responses hk and gk, k [ K, are modelled as zero mean independent and identically distributed CSCG RVs whose variances are assigned by adopting a path loss model with a path loss exponent equal to 3. Without a loss of generality, we assume that the distances from the transmitter to the K legitimate receivers and the eavesdropper are 10 m which results in the variances of hk and gk being −30 dB. In all the simulations, the variance of additive Gaussian noises over each subcarrier is σ 2 = 0.01 mW. In Fig. 1, we present the total achievable secrecy rate comparison of the proposed optimal power allocation scheme (denoted as ‘optimal’ in the legend) and the scheme which uniformly allocates the transmit power over all the subcarriers (denoted as ‘uniform’ in the legend) when the EH constraint Q is 0.05, 0.1 and 0.15 mW. The transmit power constraint P sweeps from 25 to 50 dBm. From Fig. 1, it is observed that the proposed optimal power allocation scheme outperforms the uniform power allocation scheme. When P ≥ 45 dBm, the total achievable secrecy rate of the uniform power allocation scheme is close to that of the proposed scheme. This is because at a high SNR region, the EH constraint is always satisfied. Furthermore, from (3), the achievable secrecy rate is independent of the transmit power when the SNR is high.
References 1 Zhang, R., and Ho, C.K.: ‘MIMO broadcasting for simultaneous wireless information and power transfer’, IEEE Trans. Wirel. Commun., 2013, 12, (5), pp. 1989–2001 2 Liu, L., Zhang, R., and Chua, K.C.: ‘Wireless information and power transfer: a dynamic power splitting approach’, IEEE Trans. Commun., 2013, 61, (9), pp. 3990–4001 3 Ng, D.W.K., Lo, E.S., and Schober, R.: ‘Wireless information and power transfer: energy efficiency optimization in OFDMA systems’, IEEE Trans. Wirel. Commun., to be published 4 Zhou, X., Zhang, R., and Ho, C.K.: ‘Wireless information and power transfer in multiuser OFDM systems’, arXiv:1308.2462 5 Huang, K., and Larsson, E.G.: ‘Simultaneous information and power transfer for broadband wireless systems’, IEEE Trans. Signal Process., to be published 6 Ng, D.W.K., and Schober, R.: ‘Resource allocation for secure communication in systems with wireless information and power transfer’, arXiv:1306.0712 7 Liu, L., Zhang, R., and Chua, K.C.: ‘Secrecy wireless information and power transfer with MISO beamforming’. IEEE GLOBECOM, Atlanta, GA, USA, December 2013 8 Gopala, P.K., Lai, L., and Gamal, H.E.: ‘On the secrecy capacity of fading channels’, IEEE Trans. Inf. Theory, 2008, 54, (10), pp. 4687–4698 9 Boyd, S., and Vandenberghe, L.: ‘Convex optimization’ (Cambridge University Press, Cambridge, UK, 2004)
8 7
R, bps/Hz
6 5 4 3
optimal, Q = 0.05 mW optimal, Q = 0.1 mW optimal, Q = 0.15 mW uniform, Q = 0.05 mW uniform, Q = 0.1 mW uniform, Q = 0.15 mW
2 1 0 25
30
35
40
45
50
P, dBm
Fig. 1 Total achievable secrecy rate R against transmit power constraint P; comparison of proposed optimal power allocation scheme and conventional uniform power allocation scheme
ELECTRONICS LETTERS 30th January 2014 Vol. 50 No. 3 pp. 229–230
