Carrier Frequency Offset Correction for Uplink Multi-User MIMO for Next Generation Wi-Fi Nirav Shah, Monisha Ghosh, Pengfei Xia, Zihao You, Frank La Sita, Robert Olesen, Oghenekome Oteri {nirav.shah, monisha.ghosh, pengfei.xia, zihao.you, frank.lasita, robert.olesen, oghenenkome.oteri}@interdigital.com InterDigital Communications, Inc. Abstract— In this paper, we study carrier frequency offset estimation and correction for uplink multi-user MIMO (UL MU-MIMO) for Wi-Fi, where distributed stations (STAs) send multiple data streams to a common access point (AP) with multiple receive antennas. We provide a description of the proposed system, and propose a three-step approach using a joint phase estimation algorithm for carrier frequency synchronization that takes advantage of the existing pilot signals to deliver good performance and also has low complexity. We provide simulation results to demonstrate that the proposed approach incurs negligible performance loss due to carrier frequency offsets. Index Terms—Uplink, UL MU-MIMO, WLAN, Carrier Frequency Offset, Common Phase Error, Phase Tracking, LTF I. INTRODUCTION Multi-input multi-output (MIMO) technology has been successfully adopted in past IEEE 802.11 specifications thus enabling high throughput and robust performance. An example of this is the introduction of single-user (SU) MIMO in IEEE 802.11n where a station (STA) or access point (AP) with multiple transmit antennas may send multiple data streams at the same time to another STA or AP with multiple receive antennas. The maximum number of data streams supported in 802.11n is four [1]. IEEE 802.11ac further introduced downlink MU-MIMO (DL MU-MIMO), where an AP with multiple transmit antennas is able to send multiple data streams to multiple distributed STAs at the same time. This is especially useful when many STAs in the same basic service set (BSS) need to simultaneously download large files or video streams. 802.11ac specified a maximum number of 8 data streams and 4 simultaneous users [1]. With the proliferation of smart phones and burgeoning of user generated content (UGC), we see substantially increased uplink traffic in use with mobile devices today. While 802.11ac improved the downlink throughput, there is still a need to improve the uplink throughput to satisfy this requirement. Mobile devices have become a predominate user of WiFi services, however the number of antennas that may be accommodated on them may be limited. This has accentuating the need for supporting uplink multi-user MIMO (UL MU-MIMO) where individual STAs may support a limited number of antennas (one or two). Conceptually, UL MU-MIMO is similar to SU-MIMO. A fundamental difference is that the originally co-located multiple transmit antennas are now distributed spatially. As a result, many design issues (e.g. transmit power control, timing synchronization, carrier frequency synchronization, sampling frequency synchronization, common phase error estimation etc.) need to be properly addressed to enable the adoption of practical UL MU-MIMO implementations in future Wi-Fi systems. In this paper, we focus specifically on carrier frequency offset (CFO) correction for an 802.11 based system, and propose a simple but effective method that is shown to incur almost no performance loss when compared to an ideal system with no frequency offset. In [2], the authors develop a joint blind estimation scheme for phase and channel estimation that is very complex. Our approach here is to utilize the synchronization signals available in 802.11ac, such as the short training fields (STFs), long training fields (LTFs), and pilots: and develop a carrier frequency offset algorithm that is easy to implement and has good performance. Further, we analyze the performance using a more realistic model for residual phase error than that proposed in [3]. The paper is organized as follows. Section II provides a general description of an UL MU-MIMO system for Wi-Fi. Section III proposes a three-step approach for carrier frequency synchronization for UL MU-MIMO, with numerical simulation results presented in Section IV. Finally, conclusions are provided in Section V. II. UPLINK MU-MIMO SYSTEM DESCRIPTION Consider an N-user (N-transmitters) UL MU-MIMO transmission to a single receiver equipped with  ௥ receive antennas as shown in Figure 1. Note that  ௥ should be always greater than or equal to the total number of transmit antennas over all STAs. For simplicity, we consider one transmit antenna and one data stream per STA in this paper. With OFDM modulation for each user, let x ୧,୩ be the QAM symbol transmitted from the i-th STA on OFDM subcarrier , and define the transmit symbol vector ܠ ୩ = [x ଵ,୩ ,x ଶ,୩ ,…,x ୒,୩ ] ୘ ; let ܐ ୧,୩ be the length- ௥ frequency domain wireless channel response vector from the i-th STA on the k-th subcarrier, and define the composite channel matrix ۶ ୩ =[ ܐ ଵ,୩ , ܐ ଶ,୩ ,…, ܐ ୒,୩ ], of size  ௥ × , to be the channel for all N users on subcarrier k. The received signal vector on the k-th subcarrier may be expressed as: ܡ ௞ = ۶ ௞ ܠ ௞ + ࢔ ௞ (1) 2015 International Conference on Computing, Networking and Communications, Wireless Communications Symposium 978-1-4799-6959-3/15/$31.00 ©2015 IEEE 1004