This paper investigates destination-aided simultaneous wireless information and power transfer (SWIPT) for a decode-and-forward relay network, in which massive multiple-input multiple-output antennas are deployed at relay to assist communications among multiple source-destination pairs. During relaying, energy signals are emitted from multiple destinations when multiple sources are sending their information signals to relay. With power splitting and unlimited antennas at relay, asymptotic expression of harvested energy is derived. The analysis reveals that asymptotic harvested energy is independent of fast fading effect of wireless channels; meanwhile transmission powers of each source and destination can be scaled down inversely proportional to the number of relay antennas. To significantly reduce energy leakage interference and multipair interference, zero-forcing processing and maximum-ratio combing/maximum-ratio transmission are employed at relay. Fundamental trade-off between harvested energy and achievable sum rate is quantified. It is shown that asymptotic sum rate is neither convex nor concave with respect to power splitting and destination transmission power. Thus, a one-dimensional embedded bisection algorithm is proposed to jointly determine the optimal power splitting and destination transmission power. It shows that destination-aided SWIPT are beneficial for harvesting energy and increasing sum rate. The significant sum rate improvements of the proposed schemes are verified by numerical results.
Recently, simultaneous wireless information and power transfer (SWIPT) have been envisioned for wireless relay networks [
In the above mentioned destination-aided EF transmission schemes [
One challenge in relay-assisted SWIPT is a limited amount of harvested energy. Due to path-loss and inefficient RF-to-DC conversion, only a small fraction of energy emitted by a source can be harvested at relay. In order to harvest energy efficiently, smart antennas were employed in SWIPT systems (see [
Recently, massive MIMO techniques were applied to improve wireless transmission capacity by exploiting its large array gain [
In this paper, we propose a two-phase relaying protocol with destination-aided EFs for a decode-and-forward (DF) relay network, where multiple source-destination pairs communicate via a massive MIMO relay [ The important performance metrics including asymptotic harvested energy and asymptotic achievable rate are derived for the case in which the number of relay antennas grows without bound. We show that destination-aided EFs are beneficial for boosting energy harvesting and, hence, the achievable sum rate can be improved significantly with the aid of destination-aided EFs. The optimal destination transmission power that maximizes the achievable sum rate is derived in closed-form. The optimal PS factor that maximizes the achievable sum rate is derived in closed-form. We also show that by using zero-forcing (ZF) processing and maximum-ratio combing/maximum-ratio transmission (MRC/MRT) at relay, energy leakage interference (ELI) and multipair interference (MI) can be cancelled completely as the number of relay antennas grows without bound. When the number of relay antennas is large, transmission powers of each source and each destination can be scaled inversely proportional to the number of relay antennas. We show that asymptotic sum rate is neither convex nor concave with respect to PS and destination transmission power, such that conventional convex optimization methods cannot be applied. We propose a one-dimensional embedded bisection (EB) algorithm to jointly determine the optimal PS and destination transmission power, so that the sum rate can be improved significantly.
The rest of this paper is organized as follows. Section
A block diagram of the considered multipair massive MIMO DF relay network is depicted in Figure
Multipair massive MIMO relay network.
The relaying protocol consists of two time phases. In phase I, all source nodes transmit their information signals R for forwarding. Meanwhile, all destination nodes transmit their EFs to R. Denote the PS factor by
At
We adopt the minimum mean-squared error (MMSE) method to obtain the channel state information (CSI) estimation. A part of coherence time is used for channel estimation. All the sources and destinations simultaneously send their pilot sequences of
The MMSE channel estimates of
The relay employs linear processing for DF relaying. In phase I, R uses a linear receiver matrix
After detecting the received signal, the relay node applies linear precoding to the detected signal before broadcasting. With DF relaying, the relay first decodes the original source signal and then regenerates the signal [
Since both the
The ZF processing matrices at
Since ZF processing neglects the noise effect, the corresponding detection performance is poor when the signal-to-noise ratio (SNR) is low. By contrast, MRC/MRT processing neglects MI to maximize the received SNR. As a result, MRC/MRT processing achieves a better detection performance than that of ZF processing in the low SNR region at the cost of achieving a worse detection performance than that of ZF processing in the high SNR region. Similarly to ZF processing, MRC/MRT processes the received signal and amplifies the processed signal according to (
In this section, the asymptotic harvested energy is derived for the case in which
To begin with, the transmission powers at each source and each destination are, respectively, scaled inversely proportional to the number of antennas at
Assume that the number of the source-destination pairs is fixed, the harvested energy at the relay as
See Appendix
To obtain further insights, by letting
The asymptotic harvested energy in (
To cancel ELI, orthogonal projection can be applied in detecting the desired signal. However, projecting ELI into its orthogonal space may contaminate the desired signal. Note that if the subspace spanned by ELI is orthogonal to the desired signal’s subspace when
Assume that the number of source-destination pairs is fixed; the received signal at the relay for decoding the signal of the
See Appendix
The result in Proposition
Assume that the number of source-destination pairs is fixed and the transmission power at the relay is supplied by the harvested energy, the received signal at
See Appendix
To obtain further insights, the expressions in (
By using linear processing at
The end-to-end (e2e) achievable rate of the transmission link
For a finite number of relay antennas, the achievable rate of the system with ZF processing over i.i.d. fading is given by
See Appendix
We can see from (
With ZF processing, the asymptotic sum rate is neither convex nor concave with respect to destination transmission power and the optimal destination transmission power that achieves the allowable maximum asymptotic sum rate is given by
See Appendix
With ZF processing, the asymptotic sum rate is concave with respect to
See Appendix
With ZF processing, the asymptotic sum rate is neither convex nor concave with respect to
See Appendix
Since the asymptotic sum rate is neither convex nor concave with respect to
(1) Initialize (2) If (3) Set Compute Compute (4) If If If (5) Go to step (6) Return
To quantify the trade-off between the harvested energy and achievable sum rate, we solve for
For a finite number of relay antennas, the achievable rate of the system with MRC/MRT processing over i.i.d. fading is given by
See Appendix
We can see from (
With MRC/MRT processing, the asymptotic sum rate is neither convex nor concave with respect to destination transmission power and the optimal destination transmission power that achieves the allowable maximum asymptotic sum rate is given by
By following similar procedure as the proof of Proposition
With MRC/MRT processing, the asymptotic sum rate is concave with respect to
By following similar procedure as the proof of Proposition
With MRC/MRT processing, the asymptotic sum rate is neither convex nor concave with respect to
By following similar procedure as the proof of Theorem
Since Propositions
This section presents some numerical results to verify the performance of the proposed protocol. For simplicity of illustration, the circuit power consumption and EH receiver sensitivity at the relay are ignored [
In Figure
Trade-off between
In Figure
Trade-off between
In Figures
Sum rate versus
Sum rate versus
In Figures
Sum rate versus
Sum rate versus
In Figures
Sum rate versus
Sum rate versus
The sum rate versus the number of the relay antennas is investigated in Figure
Sum rate versus the number of the relay antennas.
A destination-aided SWIPT relaying protocol has been proposed for a multipair massive MIMO relay network, in which a PS relay employs linear processing to cancel MI and ELI. The expressions of asymptotic harvested energy and symmetric sum rate with massive MIMO relay have been derived in closed-form. The trade-off between asymptotic harvested energy and achievable sum rate has been quantified. The effect of destination-aided EFs on the sum rate has been investigated and our results reveal that destination-aided EFs can boost the energy harvesting, so that achievable sum rate can be significantly improved by destination-aided EFs. Meanwhile, the detrimental impact of ELI on sum rate performance can be cancelled out by using a massive MIMO relay with linear processing. It has shown that asymptotic sum rate is neither convex nor concave with respect to PS and destination transmission power and a one-dimensional EB algorithm has been proposed to obtain the optimal PS and destination transmission power. The significant sum rate improvement of the proposed scheme has been verified by numerical results.
First, we recall two important identities for random matrices. As
Next, we consider the ELI term. Note that the vector
By substituting (
The SINRs
For the case of
For the case of
Since the logarithm term
The SINRs
It can be shown that
We first prove that the asymptotic sum rate is neither convex nor concave with respect to
For the proof of the uniqueness of the optimal
Suppose that there is another optimal point
First, we derive
The authors declare that there are no competing interests regarding the publication of this paper.
This work was supported in part by SRF for ROCS, SEM, Shandong Provincial Natural Science Foundation, China, under Grant 2014ZRB019XM, in part by the Ministry of Science, ICT and Future Planning (MSIP), Korea, under the Information Technology Research Center Support Program supervised by the Institute for Information and Communications Technology Promotion under Grant IITP-2016-H8501-16-1019, and in part by the National Research Foundation of Korea, Grant Funded by the Korean Government, MSIP, under Grant NRF-2014K1A3A1A20034987.