Low Complexity Residual Phase Tracking Algorithm for OFDM-based WLAN Systems Suvra S. Das†,Ratnam V.Rajakumar§, Muhammad I.Rahman†, Arpan Pal‡, Frank H.P.Fitzek†, Ole Olsen†,Ramjee Prasad† † Department of Communications Technology, Aalborg University,e-mail: [email protected] ‡ Tata Consultancy Services,§ IIT Kharagpur,India Abstract— This paper presents the design of an efficient low complexity Low Pass ADC LNA Time Synch Frequency Synch residual phase tracking algorithm for Orthogonal Frequency Division X Filter converter Multiplexing (OFDM) based Wireless Local Area Network receivers. In Low Noise Amplifier this paper the focus is on mitigation of the residual carrier frequency Local Channel Phase Tracking FFT synchronization offset and sampling frequency offset. We propose a novel Oscillator Equalization algorithm that uses piecewise linear approximation to estimate the com- Front End(Inner Receiver) Fast Fourier Transform plex exponential of the phase angle at pilot locations instead of estimating De-Mapper Channel Decoder Bit(s) output the actual phase angle by highly complex (costly) angle computation and Back End (OuterReceiver) search functions. This helps in reducing the implementation cost of an OFDM receiver. By means of analysis and simulation we show that our Fig. 1. OFDM receiver front end architecture design combines both high performance and low complexity. I. INTRODUCTION blocks placed at the receiver front end are not able to estimate the Wireless Local Area Networks (WLAN) are becoming part exact carrier frequency offset due to circuitry noise and fixed word of omnipresent communication infrastructures. WLANs are being length effects. Moreover due to sampling frequency offset there is applied in hotels, airports, cafes and various other locations. Different a slowly increasing timing offset. The receiver has to continuously types of terminals are already (or planed to be) equipped with WLAN track and compensate for these effects in order to improve the such as laptops, PDAs, and mobile phones. After the first phase efficiency of the system. Literatures describing correction algorithms where WLANs were penetrating the consumer market, now we are in use the search function argmax [2], [3], [6], [7] after complex– the next phase supporting enhanced quality of services (QoS). First conjugate–multipy–add operations. They also need to compute the systems were based on direct sequence or frequency hopper spread inverse tangent [3], [5], [8], [9], [10] to find the phase angles. spectrum technology. Currently Orthogonal Frequency Division Mul- The implementation complexity is very high for all these necessary tiplexing (OFDM) is the chosen technology for enhanced and future function blocks [3]. high data rate WLAN systems. In this paper we propose a novel algorithm for residual phase OFDM is a key technology to mitigate the multi-path effect of the tracking without using either of the afore mentioned complex (costly) wireless channel. It has been already used in DVB–T, IEEE 802.11a arithmetic functions. It computes the complex exponential of the and 16a. It is being considered for IEEE 802.20 and IEEE 802.11n as phase angle at the pilot-tone locations instead of the phase angles well. OFDM will remain as the key enabling technology for achieving to minimize the implementation complexity. The design of our higher data rates in wireless packet based communication in next few algorithm is such that it can be very easily applied to any coherent years to come [1]. Targeting the mass market of wireless modules low OFDM demodulation scheme for WLAN type of networks. cost solution has to be found, having in mind the tradeoff between The remainder of the article is organized as follows. In Section II efficiency and price. Cost of an OFDM receiver largely depends on we describe the system under investigation. Then we briefly present the implementation complexity of the synchronization and channel the well known mathematical analysis describing residual synchro- estimation algorithms. High accuracy is needed in synchronization nization errors in OFDM systems. Our proposed novel algorithm is since coherent demodulation of OFDM is extremely sensitive to such described in Section IV. A detailed discussion on the performance errors. Carrier and sampling frequency acquisition and maintenance evaluation of our scheme is given in section V. with high accuracy is vital for successful transmission of long packets. Residual Carrier Frequency Offset (CFO) and Sampling II. SYSTEM UNDER INVESTIGATION Frequency Offset (SFO) tracking (phase tracking Figure 1) are thus very critical part of OFDM receivers. But, the tracking module is A. Frame Format highly complex [2], [3], and thus has significant potential for cost OFDM systems vary greatly in their implementation. It is thus optimization of OFDM receivers. important that we describe the frame format referred in this article. The synchronization impairments that an OFDM receiver has We consider the IEEE802.11a [11] frame format as described in to mitigate are Frame Timing Offset (FTO) or Symbol Timing Figure 2. A transmitted packet has an all pilot (known data at Offset (STO), taken care of in the Time Synch, CFO compensated Transmitter (Tx) and Receiver (Rx)) training sequence known as by the Frequency Synch block of Figure 1. Such algorithms are very PREAMBLE at its beginning. It is used for packet start identification, well discussed in several literatures [4], [5] and many more. In this automatic gain control system, symbol timing synchronization, initial article, we deal with the residual CFO and SFO errors, jointly termed carrier frequency synchronization and channel estimation. A Guard as Residual Phase Errors. Residual Phase Error is the combined Interval (GI) follows the PREAMBLE which in turn is followed by error due to non-exact carrier frequency offset correction and existing the SIGNAL field. The SIGNAL field has information about the packet sampling frequency offset. In a real environment the synchronization length and modulation format used in the frame. It is a Binary Phase G G G G S I G N A L D A T A D A T A where n(t) is additive white gaussian noise. Here, Hk is the channel P R E A M B L E I I I I transfer function (CTF) for kth subcarrier. N-1 S Time U III. RESIDUAL PHASE ERROR IN THE RECEIVER B Pilots (Amplitde +/-1) Residual Phase Error has already been defined in Section I. FTO C Zero (Amplitude 0 ) A and CFO corrected signal after FFT can be expressed from [2], [5] R N −1 Data Sub-carrier j 2π (N +lN )φ j(π d φ +θ) sin(πφk) R R = H X e N CP sym k e N k I l,k k l,k “ ” πφk E sin Nd R S 0 + Nl,k (4) Fig. 2. OFDM frame format Where φk ≈ kζ + ξTd; θ the carrier phase offset; ξ = δ(Frx − Ftx); Ftx and Frx are the local oscillator frequencies at the transmitter and the receiver respectively and δ implies residual error after initial car- rier frequency offset correction. ζ is the receiver sampling frequency Shift Keying (BKSP) modulated OFDM symbol. Then follows a 0 0 sequence of DATA fields separated by GIs, i.e the OFDM symbols offset defined through Ts = Ts(1 + ζ); where Ts is the receiver carrying information. There are 64 subcarriers used in the Fast Fourier sampling period and Ts the transmitter sampling period. Residual Transform (FFT) block of the OFDM system under consideration. carrier frequency offset in the signal even after CFO correction Not all subcarriers are used to carry information. Some subcarriers together with the sampling frequency offset cause phase rotation in such as the zero frequency component (to avoid carrier transmission) each subcarrier to increase with OFDM symbol index l as can be and the higher frequency subcarriers are made zero in order to avoid seen from Equation 4. Cumulative phase increment severely limits the filtering effect on the subcarriers due to analogue components. the number of OFDM symbols that can be transmitted in one packet. Hence only 52 subcarriers carry non-zero power, among which, pilots The receiver thus has to continuously track and compensate for the tones (values ±1) are present at four distinct locations (subcarriers effect (Phase Tracking block of Figure 1). -21,-7,7 and 21). Thus only 48 subcarriers carry data information. Since the time invariant terms are inseparable from the channel transfer function, we can write 0 B. OFDM Transmission Signal Model jlφkC Rl,k = Xl,kHke + Nl,k (5) An OFDM symbol consists of a sum of subcarriers that are 0 2π Nd−1 sin(πφ ) j N NCP φk j(π N φk+θ) k where Hk = Hke e “ πφ ” modulated by using any linear modulation method, such as Binary sin k Nd Phase Shift Keying (BPSK) or Quadrature Amplitude Modulation Nsym th and C = 2π N . (QAM). The transmitted baseband signal for l OFDM symbol, sl(t) 0 2 So, we can call Hk as the equivalent channel transfer function. σN = can be expressed as [2]: 2 E{|Nl,k| } is the additive noise power [2], where E{...} denotes N/2−1 2π expected value. There is an ICI term present in the received signal 1 X j T k[t−lTsym−TCP ] sl(t) = √ Xl,ke d (1) which can be represented as additional noise term. This leads to T d k=−N/2 degradation in the available SNR. The power of the ICI term of the th th th k sub-carrier of the l OFDM symbol is given by [6] Where Xl,k are constellation points to IDFT input at k subcarrier of th π2 l OFDM symbol; Tsym, Td, TCP and Ts are duration of complete σ2 ≈ (kζ)2 (6) OFDM symbol, data part, Cyclic Prefix (CP or GI) and sampling l,k−ICI 3 period respectively.