On Uplink Channel Estimation in WiMAX Systems

In this paper, channel estimation algorithms are proposed and compared for uplink WiMAX systems, which are OFDMA based. These algorithms are investigated based on a dynamic resource allocation scheme, and it is shown that each of them is suitable to specific system scenarios. For example, for a system with a bandwidth of 10MHz operating in the low frequency region (2-11GHz), a two-dimensional averaging algorithm outperforms other algorithms, such as a bilinear interpolation algorithm, because the correlations between the pilots and signals are sufficiently high in both the frequency and the time dimensions. DOI: 10.4018/jmcmc.2010040105 68 International Journal of Mobile Computing and Multimedia Communications, 2(2), 67-77, April-June 2010 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. viewed as being sampled at the pilot positions, and the channel characteristics between pilots are estimated by interpolation. The two basic aspects of OFDM channel estimation are the arrangement of pilot positions, and the design of the channel estimator to interpolate between the pilots. The goal in designing channel estimators is to solve this problem with a satisfactory tradeoff between complexity and performance. Channel estimation techniques for OFDM systems have been widely studied. In particular, Edfors, Sandell, Beek, and Wilson (1998) and Coleri, Ergen, Puri, and Bahai (2002) presented algorithms for OFDM channel estimation with a block-type pilot arrangement and a comb-type pilot arrangement, respectively, and Shen and Martinez (2006) summarized and compared these two basic channel estimation strategies. The two fundamental principles behind these algorithms are to reduce the computational complexity by adopting one-dimensional (1D) rather than two-dimensional (2D) channel estimators, and to improve the interpolation accuracy by employing second-order statistics of the fading channel in either the frequency or in the time dimension. In WiMAX systems standardized by IEEE-SA Standards Board (2005), however, a different transmission structure and corresponding arrangement of pilot positions are used to fully employ the diversities in both the time and the frequency dimensions. The subcarriers allocated to a subscriber are both separated in frequency and hopped periodically in time. This dynamic resource allocation scheme makes it unfeasible to employ second-order statistics in either the frequency or the time dimension for uplink channel estimation, in other words, it is unfeasible to apply traditional OFDM channel estimation algorithms to WiMAX systems. However, on the other hand, because channel estimation has been constrained inside a small basic transmission unit, 2D interpolation is tolerable in terms of computational complexity Shen and Martinez (2007). This paper is organized as follows. In Section II, the baseband model and the dynamic resource allocation scheme in an uplink WiMAX system are illustrated. In Section III, possible uplink channel estimation algorithms are proposed for the WiMAX system model described in Section II. In Section IV, the proposed algorithms are analyzed and compared under different scenarios, with respect to the system bandwidth, the center frequency, and the speed of the mobile subscriber. Simulation results and conclusions are presented in Section V. BASEBAND MODEL OF WIMAX SYSTEM We consider the uplink of an OFDMA system. Assume there are K subcarriers, among which Ku are active subcarriers used for data and pilot transmission, and the others are null subcarriers used for guard bands and a DC carrier. The active frequency bands (Ku subcarriers) are allocated among multiple users, and each subcarrier is assigned to a unique mobile station (MS). As shown in Figure 1, the MS of the desired user inserts its information bits at the subcarriers allocated to it, inserts zeros at the active subcarriers allocated to other users, and adds the null subcarriers. Then, a K-point IFFT is used to transform the data sequence into the time domain. A cyclic prefix (CP), which is chosen to be larger than the maximal expected delay spread, is inserted to avoid inter-symbol and inter-carrier interferences. At the base station (BS), the arriving waveform is given by the superposition of the signals from all active users, each of which experience independent fading and additive white Gaussian noise (AWGN). The demodulation is the inverse process of the OFDMA modulation process. Let the vector X=[X1 ... XK] and the vector Y=[Y1 ... YK] denote the input data of IFFT block at the transmitter and the output data of FFT block at the receiver, respectively (see Figure 1). Let H=[H1 ... HK] denote the corresponding frequency domain elements of the sampled impulse response of the channel experienced by the desired user, and let N=[N1 ... NK] denote the vector of noise samples. Define the input matrix X = diag(X). It is shown [3-6] that, under International Journal of Mobile Computing and Multimedia Communications, 2(2), 67-77, April-June 2010 69 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the assumption that the CP is chosen to be larger than the expected delay spread, Y= X·H+N, which demonstrates that the OFDMA system is equivalent to the transmission of data over a set of parallel channels, and the fading channel of the OFDMA system can be reduced to a 2D lattice in the time-frequency plane. In IEEE 802.16e/D10 (IEEE-SA Standards Board, 2005), the Wireless MAN OFDMA PHY (physical layer) is specified for NLOS (nonline-of-sight) operation for channel bandwidths (denoted by BW) no less than 1MHz, K=2048 and Ku =1680. Three consecutive OFDM symbols in time form a slot, and a tile is defined as a band of four contiguous frequency subcarriers for each slot, each containing a pilot at each of its four corners, as shown in Figure 2, where Hi’s (i=1, ..., 8) donate the channel characteristics at data subcarriers and Pj’s (j=1, ..., 4) those at pilot subcarriers. Thus, there are Ku/4 = 420 tiles. The IEEE standard divides them into six groups, each consisting of 70 contiguous tiles. For each time slot, six subcarriers are pseudorandomly selected, one from each group, and make up a single sub-channel (note that there are 70 sub-channels in total, numbered from 0 to 69), with one or more sub-channels given to each user based on that user’s application requirement. Across time slots, a rotation scheme of the sub-channels is applied at each OFDMA slot-duration. That is, the sub-channel index number(s) allocated to a subscriber, and thus the location of the tiles and the corresponding physical locations of the subcarriers, change on a slot basis during the transmission. A typical illustration of the subcarrier allocation over time is given in Figure 3, where the sub-channel #0 is assumed allocated to the desired user at the start of the transmission. CHANNEL ESTIMATION ALGORITHMS In pilot-based channel estimation techniques, reference signals known at both transmitter and receiver are transmitted periodically. As described in Section II, the subcarriers allocated to a user are separated in frequency in any time slot, and change locations from slot-to-slot. This dynamic allocation scheme takes advantage of potential system diversities in both time and frequency, due to the expected de-correlation in both the time and frequency dimensions. For example, a deep narrow-band fade usually affects only a fraction of subcarriers in each sub-channel, and a deep long-term channel fade may affect a given user for only a short period of time due to the hopping. Also, this scheme provides better capacity performance than the traditional OFDM systems, due to the flexible user transmission start-time and duration of transmission length. However, such a complicated allocation scheme makes accurate channel estimation difficult. It is often not feasible to use the channel correlation across tiles in the frequency dimension, because the tiles can be separated beyond the coherence bandwidth of the channel, and thus, the correlation is weak. It also might not be feasible to employ the channel correlation across tiles in the time dimension, because the locations of tiles change every Figure 1. The OFDMA uplink baseband model 70 International Journal of Mobile Computing and Multimedia Communications, 2(2), 67-77, April-June 2010 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. time slot, and thus depending upon the channel coherence time, it might be difficult to track/ estimate the channel conditions. Based on the above considerations, channel estimation for uplink WiMAX systems can be effectively accomplished by using information within a single tile. This kind of estimation will experience less precision, because we can neither average across tiles nor employ second-order statistics of the channel (correlation, delay, etc). That is why a relatively large number of pilot bits (four out of twelve) is employed in the tile structure. The least squares (LS) estimator is a suitable and efficient technique for WiMAX systems (Edfors, Sandell, Beek, & Wilson, 1998; Coleri, Ergen, Puri, & Bahai, 2002; Shen & Martinez, 2006; Shen & Martinez, 2007), and minimizes the parameter E{(YX·H)H(Y-X·H) }, where (·) H means the conjugate transpose operation. It has been shown (Edfors, Sandell, Beek, & Wilson, 1998) that the LS estimator is given by HLS = X -1·Y. If we assume unit amplitude with zero phase is employed to transmit pilot signals, the corresponding received signal itself will be the LS estimate of the channel characteristics. As illustrated in Figure 2, inside a WiMAX tile, the fading channel characteristics are sampled at pilot subcarriers on the corners (Pj, j=1, ..., Figure 2. Illustration of uplink “tile” structure specified in IEEE 802.16e/D10 Figure 3. Illustration of the sub-channel allocation scheme specified in IEEE 802.16e/D10, where T is the OFDMA slot time duration International Journal of Mobile Computing and Multimedia Communications, 2(2), 67-77, April-June 2010 71 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 4), and the channel characteristics at the data subcarriers (Hi, i=1, ..., 8) are estimated by interpolation. In general, the interpolation can be expressed as a weighted sum of the channel values at the pilot subcarriers, that is,