I. Introduction
Adoption of MIMO-OFDM techniques in 802.11n Wi-Fi standard have revolutionized wireless communications. These techniques together offer increased data rates (upto 600Mbps), improved reception and reliability, better spectral efficiency and larger range [1], [2]. About 40% of data rate improvement comes from OFDM which is a special case of multicarrier communication system. It uses multiple orthogonal sub-channels called subcarriers for modulating and transmitting information in parallel. Another major factor for this superior performance comes from the use of multiple antennas (MIMO) at transmitting and receiving nodes [2]. In addition to higher data rates, MIMO also brought with it the new possibility of location tracking capability for commodity hardware by making phased array signal processing possible. Off-the-shelf Wi-Fi chip families such as Intel [3] and Atheros [4] expose PHY layer information called Received Signal Strength (RSS) and Channel State Information (CSI). CSI is a complex matrix that represents signal attenuation and phase distortion for each wireless MIMO link between TX-RX pair. CSI matrix is usually used for beamforming at the TX and for cancelling the effect of end-to-end phase distortion in the equalization process at RX [2], [5]. Recently, CSI phase difference [6]–[9] across MIMO antennas is used extensively to estimate the direction of the signl arrival. Classical direction finding algorithms like Multiple Signal Classification (MUSIC) [10] produces Angle of Arrival (AoA) pseudo-spectrum by AoA estimation techniques or by Time of Flight (ToF) ranging or produces joint estimation of AoA and ToF [6]–[8], [11], [12]. MUSIC uses the principle of orthogonality between noise and signal space to find AoA. Many location-aware applications for indoor navigation demand sub-centimeter accuracy. Few meters of errors are not acceptable because of smaller indoor space; a meter error may direct you to a different office room than intended. To achieve decimeter level accuracy using commodity hardware is challenging [4], [6], [7], [11] because of random hardware noises and dynamic multipath reflection in indoor environments. The reported CSI includes phase distortion due to channel along with non-trivial phase noises owing to the lack of fine-grained synchronization between oscillator clocks at TX-RX nodes [13]–[15]. In order to exploit the phase information provided by the Network Interface Cards (NICs), one must first eliminate the noises from CSI measurements before applying MUSIC or other direction finding algorithms. Triangulation and trilateration are the two underlying methods commenly used by the current localization systems.