Distributed Transmit Beamforming - ANU College of Engineering
2012 IEEE Wireless Communications and Networking Conference: PHY and Fundamentals
Distributed Transmit Beamforming: Phase Convergence Improvement Using Enhanced One-Bit Feedback Wayes Tushar†∗ , David B. Smith∗† , Andrew Zhang‡ , Tharaka A. Lamahewa§ and Thushara Abhayapala† † The Australian National University, Email:(wayes.tushar, thushara.abhayapala)@anu.edu.au ∗ National ICT Australia (NICTA), Email: [email protected] § Defence Science and Technology Organization (DSTO), Email: [email protected] ‡ CSIRO, Marsfield, Sydney, Email: [email protected]
Abstract—Transmission of signals using multiple antennas can significantly improve the energy efficiency of a wireless network, and the proper alignment of the transmitted signals’ phases at the receiver is one of the key factors so this efficiency improvement can be realized. In a time-varying channel, due to the relative motion between the transmitters and the receiver, the development of a scheme that guarantees such alignment is very challenging. In this paper, considering a distributed transmit beamforming scenario, an algorithm to achieve such phase alignment of signals in a time-varying channel is proposed. A simple formula is derived, which can be adopted by each transmitter to compute its beamforming weight’s phase, and it is shown that the use of this perturbation results in a significant improvement in terms of speed of convergence at the receiver. With simulation it is shown that, using the proposed scheme, the transmitted signals’ phase aligned at the receiver 33% faster than the one-bit feedback scheme. The average theoretical bit error rate is achieved 50% faster relative to the one-bit feedback scheme with on average 18% less number of antennas at the transmitter. Keywords: convergence speed, multi-antenna transmission, timevarying channel, one-bit feedback, Rayleigh fading, phase feedback.
I. I NTRODUCTION The use of multiple antennas for signal transmission, such as distributed transmit beamforming, to improve the received signal strength (RSS) at the receiver, and thus, to achieve a low bit error rate and an improved capacity is not new [1]–[5]. Non-coherent addition of transmitted signals can significantly reduces the signal strength at the receiver [1] and, thus, the use of such scheme largely depends on the proper alignment of transmitted signals’ phase at the receiver. Various research has taken place to investigate suitable methods for coherent addition of signals at the receiver. The authors in [1] and [2] proposed a one-bit feedback scheme that achieves nearly perfect carrier phase alignment at the receiver after a large number of iterations. They addressed the information theoretic approach of this work in [4] with a proposed analytic model that provides guidelines for parameter choices. Although the methods for achieving higher RSS at the receiver are well ∗ National ICT Australia is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.
978-1-4673-0437-5/12/$31.00 ©2012 IEEE
investigated, the improvement of the speed of convergence of the transmitted signals’ phase at the receiver is still an important aspect of multi-antenna transmission scenarios to be investigated [6]. In this paper, considering distributed transmit beamforming in a time-varying channel, we study how to improve the speed of convergence of the received signals’ phase to a steady state value, so that the signals are added coherently at the receiver. If the phase offset due to different transmitter location is assumed to be known, misalignment of the multiple transmitted signals’ phases at the receiver is due to the time-varying channel response. In this study, we propose a scheme in which the transmitters can track the average channel effect on the transmitted signals and, use this to compute a perturbation to add to their beamforming weight’s phase in each time slot. We derive a simple formula, using a phase feedback from the receiver, that each transmitter can use to compute this phase perturbation. Thus, we propose an algorithm, namely a ”Enhanced OneBit Feedback” introducing a phase feedback in conjunction with a one-bit feedback to capture the effect of average timevarying channel response on the transmitted signals and to mitigate this effect by suitably choosing a phase perturbation to add to the beamforming vector’s phase of each transmitter. The feedback phase conveys the information of the average channel effect on the signals from transmitters in the previous time slot and the one-bit feedback is adapted as in [2]. A known binary phase shift keying (BPSK) is transmitted at each iteration and the beamforming weight is dynamically adapted for each transmitter. The use of this perturbation results in a significant improvement in convergence speed of the alignment of received signal phase. The rest of the paper is organized as follows. The system model is described in Section II. The model for perturbation is derived in Section III-A and the algorithm is described in Section III-B. We explain the simulation and results in Section IV. We conclude this paper in Section V. II. S YSTEM M ODEL We consider a system as in Fig. 1 where at time slot n, M transmitters cooperatively transmit a common known message
533
Feedback signal b, ψ Moving receiver Beamformed signal
Transmitters in a cluster
i=1
Master sensor Slave sensor
Fig. 1: System Model for Distributed Beamforming with multiple stationary transmitters and a mobile receiver. m[n] to a moving receiver. All the transmitters are assumed to be frequency locked to a reference carrier signal from the master sensor using master-slave architecture [1]. The total received signal at the receiver is, r[n] = m[n]
M X
hi [n]ejφi [n] + w[n],
(1)
i=1
where m[n] is the known transmitted signal and hi [n] = ai [n]ejψi [n] ,
(2)
is the channel from transmitter i to the receiver, which is assumed to be a time-varying flat fading channel that remains constant √ in a time slot but varies across multiple time slots. j = −1, φi [n] is the phase of the transmitted signal from transmitter i and w[n] is the additive white Gaussian noise with mean 0 and variance σn2 . The transmission angle φi [n] consists of two parts: φi [n] = γi + ζi [n].
ζi [n] = ρ[n] + ξi [n],
(5)
where ρ[n] is a phase perturbation at time slot n that we introduce in this paper to compensate the effect of the timevarying channel on the signal at each time slot and ξi [n] is another perturbation, which we consider from a specific pseudo-random sequence ξ[n] of length M (or larger) in the interval [−ξ0 , ξ0 ]1 . In the specific sequence table Ξ, each typically ξ0
Distributed Transmit Beamforming: Phase Convergence Improvement Using Enhanced One-Bit Feedback Wayes Tushar†∗ , David B. Smith∗† , Andrew Zhang‡ , Tharaka A. Lamahewa§ and Thushara Abhayapala† † The Australian National University, Email:(wayes.tushar, thushara.abhayapala)@anu.edu.au ∗ National ICT Australia (NICTA), Email: [email protected] § Defence Science and Technology Organization (DSTO), Email: [email protected] ‡ CSIRO, Marsfield, Sydney, Email: [email protected]
Abstract—Transmission of signals using multiple antennas can significantly improve the energy efficiency of a wireless network, and the proper alignment of the transmitted signals’ phases at the receiver is one of the key factors so this efficiency improvement can be realized. In a time-varying channel, due to the relative motion between the transmitters and the receiver, the development of a scheme that guarantees such alignment is very challenging. In this paper, considering a distributed transmit beamforming scenario, an algorithm to achieve such phase alignment of signals in a time-varying channel is proposed. A simple formula is derived, which can be adopted by each transmitter to compute its beamforming weight’s phase, and it is shown that the use of this perturbation results in a significant improvement in terms of speed of convergence at the receiver. With simulation it is shown that, using the proposed scheme, the transmitted signals’ phase aligned at the receiver 33% faster than the one-bit feedback scheme. The average theoretical bit error rate is achieved 50% faster relative to the one-bit feedback scheme with on average 18% less number of antennas at the transmitter. Keywords: convergence speed, multi-antenna transmission, timevarying channel, one-bit feedback, Rayleigh fading, phase feedback.
I. I NTRODUCTION The use of multiple antennas for signal transmission, such as distributed transmit beamforming, to improve the received signal strength (RSS) at the receiver, and thus, to achieve a low bit error rate and an improved capacity is not new [1]–[5]. Non-coherent addition of transmitted signals can significantly reduces the signal strength at the receiver [1] and, thus, the use of such scheme largely depends on the proper alignment of transmitted signals’ phase at the receiver. Various research has taken place to investigate suitable methods for coherent addition of signals at the receiver. The authors in [1] and [2] proposed a one-bit feedback scheme that achieves nearly perfect carrier phase alignment at the receiver after a large number of iterations. They addressed the information theoretic approach of this work in [4] with a proposed analytic model that provides guidelines for parameter choices. Although the methods for achieving higher RSS at the receiver are well ∗ National ICT Australia is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.
978-1-4673-0437-5/12/$31.00 ©2012 IEEE
investigated, the improvement of the speed of convergence of the transmitted signals’ phase at the receiver is still an important aspect of multi-antenna transmission scenarios to be investigated [6]. In this paper, considering distributed transmit beamforming in a time-varying channel, we study how to improve the speed of convergence of the received signals’ phase to a steady state value, so that the signals are added coherently at the receiver. If the phase offset due to different transmitter location is assumed to be known, misalignment of the multiple transmitted signals’ phases at the receiver is due to the time-varying channel response. In this study, we propose a scheme in which the transmitters can track the average channel effect on the transmitted signals and, use this to compute a perturbation to add to their beamforming weight’s phase in each time slot. We derive a simple formula, using a phase feedback from the receiver, that each transmitter can use to compute this phase perturbation. Thus, we propose an algorithm, namely a ”Enhanced OneBit Feedback” introducing a phase feedback in conjunction with a one-bit feedback to capture the effect of average timevarying channel response on the transmitted signals and to mitigate this effect by suitably choosing a phase perturbation to add to the beamforming vector’s phase of each transmitter. The feedback phase conveys the information of the average channel effect on the signals from transmitters in the previous time slot and the one-bit feedback is adapted as in [2]. A known binary phase shift keying (BPSK) is transmitted at each iteration and the beamforming weight is dynamically adapted for each transmitter. The use of this perturbation results in a significant improvement in convergence speed of the alignment of received signal phase. The rest of the paper is organized as follows. The system model is described in Section II. The model for perturbation is derived in Section III-A and the algorithm is described in Section III-B. We explain the simulation and results in Section IV. We conclude this paper in Section V. II. S YSTEM M ODEL We consider a system as in Fig. 1 where at time slot n, M transmitters cooperatively transmit a common known message
533
Feedback signal b, ψ Moving receiver Beamformed signal
Transmitters in a cluster
i=1
Master sensor Slave sensor
Fig. 1: System Model for Distributed Beamforming with multiple stationary transmitters and a mobile receiver. m[n] to a moving receiver. All the transmitters are assumed to be frequency locked to a reference carrier signal from the master sensor using master-slave architecture [1]. The total received signal at the receiver is, r[n] = m[n]
M X
hi [n]ejφi [n] + w[n],
(1)
i=1
where m[n] is the known transmitted signal and hi [n] = ai [n]ejψi [n] ,
(2)
is the channel from transmitter i to the receiver, which is assumed to be a time-varying flat fading channel that remains constant √ in a time slot but varies across multiple time slots. j = −1, φi [n] is the phase of the transmitted signal from transmitter i and w[n] is the additive white Gaussian noise with mean 0 and variance σn2 . The transmission angle φi [n] consists of two parts: φi [n] = γi + ζi [n].
ζi [n] = ρ[n] + ξi [n],
(5)
where ρ[n] is a phase perturbation at time slot n that we introduce in this paper to compensate the effect of the timevarying channel on the signal at each time slot and ξi [n] is another perturbation, which we consider from a specific pseudo-random sequence ξ[n] of length M (or larger) in the interval [−ξ0 , ξ0 ]1 . In the specific sequence table Ξ, each typically ξ0
