Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 8238234, 12 pages

https://doi.org/10.1155/2017/8238234

## Phase Noise Effect on MIMO-OFDM Systems with Common and Independent Oscillators

^{1}School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China^{2}Keysight Laboratories, Keysight Technologies, Inc., 9220 Aalborg, Denmark^{3}Department of Electronic Systems, Aalborg University, 9000 Aalborg, Denmark^{4}Vodafone Chair Mobile Communications Systems, Dresden University of Technology, 01062 Dresden, Germany^{5}Qamcom Research & Technology AB, 41285 Gothenburg, Sweden^{6}Department of Electrical Engineering, Chalmers University of Technology, 41296 Gothenburg, Sweden^{7}Huawei Technologies Duesseldorf GmbH, 80992 Munich, Germany

Correspondence should be addressed to Wei Fan

Received 26 July 2017; Revised 13 October 2017; Accepted 22 October 2017; Published 12 November 2017

Academic Editor: Jose F. Monserrat

Copyright © 2017 Xiaoming Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The effects of oscillator phase noises (PNs) on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems are studied. It is shown that PNs of common oscillators at the transmitter and at the receiver have the same influence on the performance of (single-stream) beamforming MIMO-OFDM systems, yet different influences on spatial multiplexing MIMO-OFDM systems with singular value decomposition (SVD) based precoding/decoding. When each antenna is equipped with an independent oscillator, the PNs at the transmitter and at the receiver have different influences on beamforming MIMO-OFDM systems as well as spatial multiplexing MIMO-OFDM systems. Specifically, the PN effect on the transmitter (receiver) can be alleviated by having more transmit (receive) antennas for the case of independent oscillators. It is found that the independent oscillator case outperforms the common oscillator case in terms of error vector magnitude (EVM).

#### 1. Introduction

Due to the spectrum congestion in the lower microwave frequency range, millimeter wave (mmWave) communications have received a lot of attention due to the broad bandwidth. Multiple-input multiple-output (MIMO) techniques are usually employed for the radio access application, to overcome the high propagation attenuation in mmWave bands [1–3] and to enable high throughput [4, 5]. The orthogonal frequency division multiplexing (OFDM) technique [6] (that has been adopted in many modern communication systems) is recently chosen to be the main waveform for 5G communications below 40 GHz [7].

It is well-known that OFDM systems are sensitive to oscillator phase noises (PNs) that increase with increasing (carrier) frequency [8, 9]. The PN effects on OFDM or MIMO-OFDM systems have been extensively studied in the literature [10–26]. Most of the works assume free-running oscillators, except for [10–13], where phase locked loop (PLL) based oscillators were also assumed. Most of the studies assume a common oscillator for all the transmit (receive) antennas, except for [12, 24–26], where independent oscillators (i.e., each antenna is equipped with a different oscillator) were also considered. (The independent oscillator case is also considered for single carrier systems in [27, 28].) Moreover, most works did not distinguish different effects of PNs on the transmitter (Tx PN) and on the receiver (Rx PN), except for [16] where the effects of PNs of free-running (common) oscillators on receivers and transmitters were analyzed separately. The variance of the PN of a free-running oscillator increases with time. As the PN grows large, common phase error (CPE) correction (that is necessary for reliable data detection) tends to reduce the signal-to-noise ratio (SNR) [23]. Therefore, in practice the PLL is usually used to stabilize the PN. As a result, we assume PLL-based oscillators in this work for simulations and verifications (even though the analysis is applicable to both free-running and PLL-based oscillators). In mmWave MIMO systems, distribution of the high frequency clock signal of a common oscillator for all the transmit/receive antennas may cause high attenuation and waveform distortion, especially for large antenna arrays. To avoid this problem, an independent oscillator can be used for each antenna (at the cost of increased complexity). Nevertheless, the common oscillator is still the most popular assumption in the literature. In this work, we consider both common oscillators and independent oscillators at the transmitter and the receiver and compare their impairments on MIMO-OFDM systems.

We evaluate the PN effect on the mmWave MIMO-OFDM system in terms of the error vector magnitude (EVM) [21, 27, 29], which is a popular performance metric for hardware impairment evaluations, especially in the industry. A conference version of this paper has been published in [30], where the study was confined to single-stream beamforming OFDM systems. In this paper, we extend the work by including the spatial multiplexing OFDM systems as well. Spatial multiplexing means transmitting multiple spatial streams simultaneously in the same band. Note that, in the literature, sometimes it is also referred to as adaptive beamforming with multiple layers (streams), for example, [31]. In this work, beamforming refers to single-stream beamforming in order to distinguish it from spatial multiplexing. It is noted that the (digital/analog) hybrid beamforming [5] is the most popular assumption for mmWave cellular communications. Nevertheless, other beamforming/precoding architectures are also considered in practice. For example, fully digital schemes with small MIMO orders and high gain antennas are used for mmWave backhauling in the industry.

*New Contributions and Relation to Previous Work*. It is shown in this work that,* for the common oscillator case*, Tx PN and Rx PN have the same level of influence on the beamforming OFDM system (in terms of EVM), yet different levels of influences on the singular value decomposition (SVD) based spatial multiplexing OFDM system (in the latter case, the conclusions are the same as in [16], where open-loop spatial multiplexing MIMO-OFDM systems with zero-forcing (ZF) decoders are considered). These findings (including the link between SVD-based spatial multiplexing OFDM and open-loop spatial multiplexing MIMO-OFDM system with ZF decoder) have not been shown in the previous literature. It is also shown that,* for the independent oscillator case*, Tx PN and Rx PN have different levels of influences on the beamforming and spatial multiplexing OFDM systems, whose adverse effect reduces as the number of antennas increases. Interestingly, it was reported in [28] that the effect of Rx PNs of independent oscillators reduces with increasing receive antennas for single carrier MIMO systems with maximum ratio combining. In this work, we show that the effect of PNs of independent oscillators can be alleviated with more antennas at either Tx or Rx side for both beamforming and SVD-based spatial multiplexing MIMO-OFDM systems. Moreover, our results show that the independent oscillator case can achieve better EVM performance than the common oscillator case. Finally, it is noted that, although digital beamforming is assumed for tractable analysis, the findings hold for hybrid beamforming [5] as well. This is rather intuitive if one regards each antenna in our analysis as a (analog) phase-controlled subarray in hybrid beamforming. This is verified by hybrid beamforming simulations using a sophisticated mmWave channel model.

The rest of the paper is organized as follows. Section 2 presents the system models. PN effects of common and independent oscillators on beamforming and spatial multiplexing OFDM systems are derived and discussed separately in Section 3. Section 4 verifies the analytical results of the previous section by simulations. Finally, Section 5 concludes this paper.

*Notations*. Throughout this paper, , , and denote complex conjugate, transpose, and Hermitian operators, respectively. Lower case bold letter () and upper case bold letter () represent column vector and matrix, respectively. is the identity matrix. denotes the diagonal matrix whose diagonal elements are given by . denotes the trace of . denotes the Kronecker product.

#### 2. System Model

##### 2.1. Phase Noise Model

In this work, we consider the PLL-based oscillator that is used ubiquitously in practical transceivers. The PN of the PLL-based oscillator consists of three main noise sources, that is, noises from the reference oscillator , the phase-frequency detector, the loop filter , and the voltage controlled oscillator (VCO) , as shown in Figure 1. The Laplace transform of the PN of the PLL-based oscillator is given as [9]where denotes the gain of the phase-frequency detector, represents the sensitivity of the VCO, represents the loop filter, and is the frequency divider [9]. The noise sources include both white noise (thermal noise) and colored noise (flicker noise) [8]. The detailed modeling parameters are listed in Table 4-2 of [9]. As an example, Figure 2 shows the estimated power spectral density (PSD) of the carrier phase noise [11] (using the periodogram method with PN samples) at 28 and 60 GHz, respectively.