IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.XX, NO.X, XXXX XXXX 1 Deterministic Multiuser Carrier Frequency Offset Estimation for Interleaved OFDMA Uplink Zhongren Cao, Student Member, IEEE, Ufuk Tureli, Member, IEEE, Yu-Dong Yao, Senior Member, IEEE Abstract— In orthogonal frequency division multiple access orthogonality of subcarriers guarantees that there is no inter- (OFDMA), closely spaced multiple subcarriers are assigned to carrier interference (ICI), which prevents MAI among users in different users for parallel signal transmission. An interleaved OFDMA systems. subcarrier assignment scheme is preferred because it provides maximum frequency diversity and increases the capacity in fre- OFDMA inherits from OFDM the weakness of being sensi- quency selective fading channels. The subcarriers are overlapping tive to inaccurate frequency references [7]. Carrier frequency but orthogonal to each other such that there is no inter-carrier offset (CFO) between the transmitter and the receiver causes interference. Carrier frequency offsets between the transmitter the loss of orthogonality among subcarriers and introduces and the receiver destroy the orthogonality and introduces inter- ICI. In OFDMA, CFO will further cause MAI, which degrades carrier interference resulting in multiple access interference. This paper exploits the inner structure of the signals for carrier the system performance [8]. CFO estimation for OFDM has frequency offsets estimation in the uplink of interleaved OFDMA been extensively studied in recent years [9]–[14]. In OFDMA, systems. A new uplink signal model is presented and an esti- CFO estimation is relatively simple in the broadcast link mation algorithm based on the signal structure is proposed for (downlink), where different users’ signals are multiplexed estimating the carrier frequency offsets of all users using only one by the same transmitter, and the orthogonality among all OFDMA block. Diversity schemes are also presented to improve the estimation performance. Simulation results illustrate the high subcarriers is maintained. Each user can perform the frequency accuracy and efficiency of the proposed algorithm. synchronization by estimating a single CFO, which is the one between itself and the transmitter, and compensate accord- Index Terms— Orthogonal frequency division multiplex ingly. Many CFO estimation algorithms proposed for OFDM (OFDM), multiple access, carrier frequency offset (CFO), pa- are applicable for the OFDMA downlink. The real challenge rameter estimation, matrix decomposition. exists in the uplink of OFDMA, where a number of users share the total number of subcarriers and each user has its own CFO. CFO estimation in this case becomes a multiple- I. INTRODUCTION parameter estimation problem. CFO estimation in the OFDMA uplink is closely related Orthogonal frequency division multiplexing (OFDM) [1] to the subcarrier assignment scheme adopted by the system. has been selected as the physical layer technology for a There are two major subcarrier assignment schemes [8], sub- number of wireless applications, such as digital audio broad- band based and interleaved. The former, sub-band based casting (DAB) [2] and terrestrial digital video broadcasting subcarrier assignment, divides the whole bandwidth into small (DVB) [3]. It has also been adopted by IEEE 802:11a [4] continuous sub-bands and each user is assigned to one or and HIPERLAN/2 [5] for high data rate wireless packet several sub-bands similar to traditional FDMA. In the latter, transmissions. In OFDM, a set of equally spaced subcarriers interleaved subcarrier assignment, subcarriers assigned to dif- are used for parallel data transmissions. To increase the ferent users are interleaved over the whole bandwidth. frequency efficiency, these subcarriers are overlapping in the CFO estimation in the uplink of sub-band based OFDMA frequency domain but orthogonal to each other such that systems has been investigated and reported recently in [15]– there is no inter-carrier interference (ICI). The most important [17], where a frequency guard band was used between sub- feature of OFDM is the capability of mitigating frequency- bands so that signals from different users can be separated dependent distortion across the channel band and simplifying by filter banks. Existing CFO estimation algorithms that were the equalization in a multipath fading environment. proposed for OFDM are applied on each single user after its Recently, orthogonal frequency division multiple access signal is isolated. (OFDMA) was proposed for broadband wireless multiple Sub-band based OFDMA systems are vulnerable to fre- access systems in IEEE 802:16a [6]. In OFDMA, closely quency selective fading. In channels with a large coherent spaced and overlapped subcarriers are divided into groups bandwidth, several consecutive subcarriers may be subject to and assigned to multiple user for simultaneous transmissions. deep fading at the same time and the data transmitted over Unlike traditional frequency division multiple access (FDMA), a whole sub-band may not be recovered even with coding where any overlapping of the frequency spectrum of differ- and interleaving. On the contrary, the interleaved subcarrier ent users introduces multiple access interference (MAI), the assignment scheme provides maximum separation among the subcarriers assigned to the same user, which maximizes the The authors are with the Department of Electrical and Computer Engi- neering, Stevens Institute of Technology, Hoboken, NJ, 07030 USA (email: frequency diversity for each user. However, the interleaved [email protected]; [email protected]; [email protected]). scheme complicates CFO estimation in the OFDMA uplink, 2 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.XX, NO.X, XXXX XXXX since it minimizes the distances between subcarriers assigned Cyclic to different users. When there are frequency synchronization Prefix (k ) S ( k ) errors, the signals from different users are overlapping in the X g , 0 g ,0 time domain by the nature of OFDMA and interfering each S ( k ) X (k ) g ,1 other in the frequency domain due to the loss of orthogonality. g , 1 S ( k ) In order to separate multiple users’ signals and suppress MAI, g ,2 x( k ) ( t ) advanced signal processing algorithms have to be applied at the uplink receiver, as shown in [18]. These techniques rely on the correct estimation of each user’s CFO. Therefore, CFO (k ) Parellel to Serial X ( k) −Point IFFT estimation is a major task in designing OFDMA receivers. g,P −2 ( k ) S g , N −2 N CFO estimation in the interleaved uplink of OFDMA was (k ) Subcarrier Map X ( k) S ( k ) studied and a statistics based CFO estimation algorithm was g,P −1 g , N −1 proposed for the OFDMA, which is applicable to both sub- band based uplink and interleaved uplink [19]. However, the Fig. 1. Uplink OFDMA transmitter structure. algorithm in [19] requires collecting signal samples of many OFDMA blocks to compute unknown parameters on the order of the number of subcarriers and results in a biased estimator. IFFT. For pilot subcarriers, the modulation symbols are pilot When the number of subcarriers is large, such as 2048 as in symbols or training symbols for estimating the channels. IEEE 802:16, the algorithm is computationally prohibitive. Fig. 1 illustrates the signal generation and transmission of The originality of this paper is that it investigates the CFO the kth user. The P (k) modulation symbols are first mapped estimation in the interleaved uplink of OFDMA based on (k) into a set of N modulation symbols, Sg;i ; i = 0; 1; ¢ ¢ ¢ ;N ¡1, the deterministic structure of the signals. In an interleaved according to OFDMA system, signal from each user has a special periodic ½ (k) (k) structure within an OFDMA block, which can be exploited by (k) X ; if i = c ; S = g;p p (1) arranging the received signals into a matrix form to reduce g;i 0; otherwise: the number of unknown frequencies to the number of users. (k) (k) N¡1 A high resolution signal processing technique [20] is used for p = 0; 1;:::;P ¡ 1. The N symbols, fSg;i gi=0 , to estimate the CFO’s of all involving users deterministically are modulated onto the N subcarriers via an N-point IFFT. using only one OFDMA block instead of a large number of The CP is also added to avoid inter-block interference (IBI) blocks as in [19]. Since the number of unknown parameters caused by multipath fading. As a result, the baseband signal equals the number of users, the algorithm is practical for transmitted from the kth user can be represented as OFDMA systems with large number of subcarriers. 1 N¡1 This paper is organized as follows. The signal model of X X x(k)(t) = S(k)F (t) OFDMA is presented in Section II. The periodic signal struc- g;i g;i g=¡1 i=0 ture of the interleaved OFDMA uplink is introduced in Section (k) (2) X1 PX¡1 III. In Section IV, the CFO estimation problem is stated and the (k) = X F (k) (t): g;p g;cp proposed estimation algorithm is derived. Simulation results g=¡1 p=0 are reported in Section V and conclusions are drawn in Section VI. Note Fg;i(t) is given by ½ j2¼(i¢f)(t¡Tcp¡gT ) II. OFDM-BASED MULTIPLE ACCESS – OFDMA e b ; gTb·t<(g + 1)Tb; Fg;i(t) = In this section, we introduce the uplink signal model of 0; otherwise; OFDMA. Consider an OFDMA system consisting of N sub- (3) carriers and K users. The N subcarriers include all available where ¢f is the subcarrier spacing, Tcp is the length of CP subcarriers and virtual subcarriers in the guard band [21]. and Tb = T + Tcp is the duration of one OFDMA block, All subcarriers are sequentially indexed with fng, n = T = 1=¢f. 0; 1;:::;N ¡ 1. Among the N subcarriers, the kth user is The signals are transmitted through slowly time-variant mul- assigned to a subset of P (k) subcarriers with the index set tipath fading channels, i.e. fading coefficients are assumed to (k) (k) (k) (k) be constant during one OFDMA block.