Shuowen Zhang

MISO Multicasting With Constant Envelope Precoding

In this letter, we study a multiple-input single-output (MISO) multicast system, where a multi-antenna transmitter sends a common message to multiple single-antenna users via constant envelope (CE) precoding. We aim to minimize the maximum symbol error rate over all users by jointly optimizing the CE precoding at the transmitter as well as the constellation scaling and rotation at each of the user receivers. First, we present a general problem formulation for any given symbol constellation. Then, we focus on the N-ary phase shift keying and show the corresponding problem is equivalent to a quadratically constrained quadratic program, which is non-convex and thus difficult to solve. We propose an approximate solution by applying the semi-definite relaxation technique and a customized Gaussian randomization method. Numerical results show that our proposed scheme significantly outperforms other benchmark schemes in MISO multicasting with CE precoding, and also performs closely to the optimal non-CE multicasting under the same total transmit power.

Constant Envelope Precoding With Adaptive Receiver Constellation in MISO Fading Channel

Constant envelope (CE) precoding is an appealing transmission technique, which enables the realization of high power amplifier efficiency. For CE precoding in a single-user multiple-input single-output (MISO) channel, a desired constellation is feasible at the receiver if and only if it can be scaled to lie in an annulus, whose boundaries are characterized by the instantaneous channel realization. Therefore, if a fixed receiver constellation is used for CE precoding in a fading channel, where the annulus is time-varying, there is in general a non-zero probability of encountering a channel that makes CE precoding infeasible, thereby causing a high probability of error. To tackle this problem, this paper studies the adaptive receiver constellation design for CE precoding in a single-user MISO flat-fading channel with an arbitrary number of antennas at the transmitter. We first investigate the fixed-rate adaptive receiver constellation design to minimize the symbol error rate (SER). Specifically, an efficient algorithm is proposed to find the optimal amplitude-and-phase shift keying (APSK) constellation with two rings that is both feasible and of the maximum minimum Euclidean distance, for any given constellation size and instantaneous channel realization. Numerical results show that by using the optimized fixed-rate adaptive receiver constellation, our proposed scheme achieves significantly improved SER performance over CE precoding with a fixed receiver constellation. Furthermore, based on the family of optimal fixed-rate adaptive two-ring APSK constellation sets, a variable-rate CE transmission scheme is proposed and numerically examined.

Receive beamforming optimization for MIMO system with constant envelope precoding

In this paper, we study the receive beamforming design to minimize the symbol error rate (SER) in a point-to-point multiple-input multiple-output (MIMO) system with constant envelope (CE) precoding. In this case, a constellation is feasible at the combiner output of the receiver if and only if it can be scaled to lie in an annular region, whose boundaries are determined by channel realization, receive beamforming and per-antenna transmit power. By approximating the exact SER with its union bound, we aim to optimize the receive beamforming weights to maximize the minimum Euclidean distance (MED) between any two signal points at the combiner output for any desired constellation and given channel realization, subject to the feasibility constraint of the constellation. We first show that under the assumption of independent and identically distributed (i.i.d.) Rayleigh fading channel, this problem is feasible as long as there are no more transmit antennas than receive antennas. Then, we assume the aforementioned condition holds and reformulate this problem into an equivalent quadratically constrained quadratic program (QCQP), for which we find an approximate solution by applying the semidefinite relaxation (SDR) technique and a customized Gaussian randomization method. Numerical results show that our proposed receive beamforming scheme achieves significantly improved SER performance than other benchmark schemes.

Constant Envelope Precoding for MIMO Systems

Constant envelope (CE) precoding is an appealing transmission technique which enables highly efficient power amplification. In this paper, we consider a point-to-point multiple-input multiple-output (MIMO) system with CE precoding under frequency-flat fading, and investigate the joint transceiver design by exploiting multiple antennas at both the transmitter and the receiver, which has not been addressed in prior work. We consider both single-stream transmission (i.e., beamforming) and multi-stream transmission (i.e., spatial multiplexing). For single-stream transmission, we optimize the receive beamforming vector to minimize the symbol error rate (SER) for any given channel realization and desired constellation at the combiner output. By reformulating the problem as an equivalent quadratically constrained quadratic program, we propose an efficient semi-definite relaxation based algorithm to find an approximate solution. Next, for multi-stream transmission, we propose a new scheme based on antenna grouping at the transmitter and minimum mean squared error or zero-forcing based beamforming at the receiver. The transmit antenna grouping and receive beamforming vectors are then jointly designed to minimize the maximum SER over all data streams. Numerical results show that our proposed schemes for both single- and multi-stream transmissions achieve superior error-rate performances as compared with various benchmark schemes. Finally, the error-rate performances of our proposed single- versus multi-stream transmission schemes are compared via simulations under different setups, which provide useful insights to the transmission mode selection for CE-precoded MIMO systems.

Constant envelope transmission in MISO system with adaptive online constellation

In this paper, we study a single-user multiple-input single-output (MISO) system with constant envelope (CE) transmission. To enable the nonlinear mapping from a fixed receiver signal constellation to the transmitter CE signal vectors, the availability of perfect channel state information at the transmitter (CSIT) is assumed in existing literature. However, traditionally, CSIT needs to be acquired at the cost of additional channel training and feedback overhead, which increases with the number of transmit antennas. In this paper, we propose a novel adaptive online signal constellation design for MISO CE transmission with significantly reduced training time and feedback complexity compared to the traditional training with fixed constellation set. Numerical results show that our proposed scheme outperforms the traditional scheme in terms of average throughput and yet with less training time required.