IEEE 802.16a 分時雙工正交分頻多重進接之下行通道估測之研究與技術

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(1)國立交通大學電子工程學系電子研究所碩士班碩. 士. 論. 文. IEEE 802.16a 分時雙工正交分頻多重進接之下行通道估測之研究與技術. Study and Techniques of IEEE 802.16a TDD OFDMA Downlink Channel Estimation. 研究生：陳盈縈指導教授：林大衛博士. 中華民國九十三年六月.

(2) IEEE 802.16a 分時雙工正交分頻多重進接之下行通道估測之研究與技術 Study and Techniques of IEEE 802.16a TDD OFDMA Downlink Channel Estimation. 研究生: 陳盈縈. Student: Ying-Ying Chen. 指導教授: 林大衛博士. Advisor: Dr. David W. Lin. 國立交通大學電子工程學系. 電子研究所碩士班. 碩士論文. A Thesis Submitted to Department of Electronics Engineering & Institute of Electronics College of Electrical Engineering and Computer Science National Chiao Tung University in Partial Fulfillment of Requirements for the Degree of Master in Electronics Engineering June 2004 Hsinchu, Taiwan, Republic of China. 中華民國九十三年六月.

(3) IEEE 802.16a 分時雙工正交分頻多重進接之下行通道估測之研究與技術研究生：陳盈縈. 指導教授：林大衛博士. 國立交通大學電子工程學系電子研究所碩士班. 摘要. 正交分頻技術近來因為能在行動環境中穩定高速傳輸而廣受注目，IEEE 802.16a 即是一個基於正交分頻多重進接技術用於無線區域網路和大都會網路的標準。本論文主要在討論 IEEE 802.16a 下行通道估測中的兩個重點:內插的技巧以及使用時域的資料來做改善的方法。我們使用最小平方差的估測器來估計在導訊上的通道頻率響應而不用線性平均最小平方差的估測器，除了因為硬體的計算方便，也因為我們不知道通道的統計特性而不能使用線性平均最小平方差的估測器。而內插的方法我們則研究了線性內插，二次式內插以其三次樣條函數內插（cubic spline）。而在用時域的資料改善的方法有下列四種：移動平均 (moving average)，指數平均 (exponential average)，最小平均平方差適應 (LMS adaptation）以其二維內插法。我們的在靜態以及瑞雷通道上模擬，在靜態通道上時，當雜訊比高於 24 分貝時，二維的內插法有最好的表現。而當雜訊比小於 24 分貝時，最小平均平方差適應的方法最好。因為在瑞雷通道時通道的變化，我們所提出的方法需要做一些修改。而在瑞雷通道上的模擬則也是二維的內插法有最好的表現。當接收者時速 27 公里時，二維內插法加上使用四組可變導訊的效果最佳，且在二維內插時若再頻率域使用二次內插也會有較佳的結果。而這個結果與理想的結果相差約十分貝左右。. i.

(4) Study and Techniques of IEEE 802.16a TDD OFDMA Downlink Channel Estimation. Student: Ying-Ying Chen. Advisor: Dr. David W. Lin. Department of Electronics Engineering & Institute of Electronics National Chiao Tung University. Abstract. OFDM (orthogonal frequency division multiplexing) technique has drawn much interest recently for its robustness in the mobile transmission environment and its high transmission data rate. IEEE 802.16a is a wireless local and metropolitan area networks standard which is based on OFDMA (orthogonal frequency division multiple access) technique. This work considers two main subjects of the downlink channel estimation under the specifications of IEEE 802.16a, the interpolation schemes and the time-domain improvement techniques. We use LS instead of LMMS estimator for estimations of pilot carriers, not only because we do not know the statistical properties of channels but also for its low computational complexity. We study the linear, the second-order and the cubic spline interpolations. And the 4 kinds of time-domain improvement skills are the moving average, exponential average, the LMS adaptation, and the two-D interpolation. We did the simulation on both static and Rayleigh fading channels. In the static channel, the two-D interpolation performs the best when Eb/N0 > 24dB; meanwhile, the LMS adaptation technique has the best performance when Eb/N0 < 24dB. In the Rayleigh fading channel, due to the change of the channel impulse response, the time-domain improvement skills mentioned above need to be modified. When the speed of the vehicle is 27 km/h, the two-dimensional interpolation with four sets of variable location pilots and with second-order interpolation on the frequency domain can estimate the channel best and is about 10 dB worse than the ideal one. ii.

(5) 誌謝這篇論文能夠順利完成，最要感謝的人是我的指導教授林大衛博士。謝謝老師在兩年的研究所生涯中給我的指導與教誨，在此對老師獻上最大的感激之意。此外，感謝實驗室中所有的成員，包含各位師長、同學、學長姐與學弟妹們。我要感謝吳俊榮學長、崑健肥學長與林郁男學長給予我在研究過程上的指導與建議，還有宗書、筱晴、明哲、馬克、長毛、仰哲、岳賢等同學與我彼此勉勵、互相討論，讓我這兩年的生活中充滿了快樂的回憶。我也要感謝我的父母、妹妹及其他的朋友，不論我在失意或是開心的時候，都能分擔分享我的心情。還有我的男友小賴，在這兩年與我一起努力獲得碩士學位，當我的出氣筒，培養我的 EQ，感恩啦！最後，我要感謝校門口的土地公伯伯，謝謝你終於讓我順利畢業了，將要踏入一段新的生涯，我會繼續加油的，耶! 誌於 2004.7 風城交大盈縈.

(6) Contents 1 Introduction. 1. 2 Overview of OFDM and OFDMA 2.1 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Concept and brief mathematical expression of OFDM . . . . . . 2.1.2 Continous-time model of OFDM including the concept of cyclic prefix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Discrete-time model . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Imperfections of OFDM . . . . . . . . . . . . . . . . . . . . . . 2.2 OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 3 3 6 9 10 11. 3 Introduction to IEEE 802.16a [4] 3.1 Background of 802.16a . . . . . . . . . . . . . . . . 3.2 Generic OFDMA Symbol Description . . . . . . . . 3.2.1 Frequency domain description . . . . . . . . 3.2.2 Time domain description . . . . . . . . . . . 3.3 OFDMA Symbol Parameters and Transmitted Signal 3.3.1 Primitive parameters . . . . . . . . . . . . . 3.3.2 Derived parameters . . . . . . . . . . . . . . 3.3.3 Transmitted signal . . . . . . . . . . . . . . 3.4 OFDMA Carrier Allocation . . . . . . . . . . . . . . 3.4.1 DL assignment of pilots . . . . . . . . . . . 3.4.2 Partitioning of data carriers into subchannels 3.5 Modulation . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Data modulation . . . . . . . . . . . . . . . 3.5.2 Pilot modulation . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. 13 13 15 15 16 16 16 17 17 18 18 19 21 21 22. 4 Downlink Channel Estimation 4.1 Channel Estimation on Pilot Subcarriers . . 4.1.1 Pilot information . . . . . . . . . . 4.1.2 LS and MMSE estimations . . . . . 4.2 Interpolation Schemes . . . . . . . . . . . 4.2.1 Linear interpolation . . . . . . . . 4.2.2 Second order interpolation . . . . . 4.2.3 Cubic spline interpolation [17], [18]. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 24 24 24 25 26 27 27 28. iii. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . ..

(7) . . . . . .. 30 31 31 33 34 37. 5 Simulation Study 5.1 Channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Definitions of SER and channel MSE . . . . . . . . . . . . . . . . . . . 5.3 Simulations on Static (Stationary) Channels . . . . . . . . . . . . . . . . 5.3.1 Comparison of interpolation methods . . . . . . . . . . . . . . . 5.3.2 Result of moving averaging . . . . . . . . . . . . . . . . . . . . 5.3.3 Comparison of different weightings in exponential averaging . . . 5.3.4 Comparison of different weightings in LMS adaptation method . 5.3.5 Comparison of the sets of variable location pilots taken in the 2-D interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Comparison of all the methods of time domain improvement . . . 5.3.7 The relation of channel MSE and SER . . . . . . . . . . . . . . . 5.4 Simulations of Fading Channels . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Comparisons of All Methods of Time Domain Improvement . . .. 39 40 41 41 41 42 42 45. 6 Conclusion and Future Work 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58 58 59. 4.3. 4.2.4 Comparison and illustration of the three interpolations Time Domain Improvement Methods . . . . . . . . . . . . . . 4.3.1 Moving average . . . . . . . . . . . . . . . . . . . . . 4.3.2 Exponential average . . . . . . . . . . . . . . . . . . 4.3.3 LMS adaptation . . . . . . . . . . . . . . . . . . . . . 4.3.4 Two-Dimensional interpolation . . . . . . . . . . . .. iv. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 45 47 50 53 54.

(8) List of Figures 2.1 2.2. The cyclic prefix is a copy of the last part of the OFDM symbol. . . . . . A symbolic picture of the individual subchannels for an OFDM system with N tones over a bandwidth W (from [7]). . . . . . . . . . . . . . . . Baseband OFDM system model (from [7]). . . . . . . . . . . . . . . . . The continuous-time OFDM system interpreted as parallel Gaussian channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discrete-time OFDM system (from [7]). . . . . . . . . . . . . . . . . . .. 9 10. 3.2 3.3 3.4. OFDMA frequency symbol description (example for 3 subchannels) (from [4]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carrier allocation in 802.16a OFDMA DL (from [4]). . . . . . . . . . . . QPSK, 16QAM and 64 QAM constellations (from [4]). . . . . . . . . . PRBS generator for pilot modulation. . . . . . . . . . . . . . . . . . . .. 15 20 22 23. 4.1 4.2 4.3 4.4. The result of different interpolation methods. . . . . Block diagram of adaptive transversal filter. . . . . . Illustration of LMS adaption for channel estimation. . Illustration of the 2-D interpolation scheme. . . . . .. . . . .. 32 34 36 38. The flow chart of the simulations. . . . . . . . . . . . . . . . . . . . . . The simulation result on AWGN channel. . . . . . . . . . . . . . . . . . The (a) MSE and (b) SER of diffrent interpolation schemes. . . . . . . . The (a) MSE and (b) SER of using different weightings in exponential averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The (a) MSE and (b) SER for different weightings and different step-size parameters in LMS method. . . . . . . . . . . . . . . . . . . . . . . . . 5.6 The (a) MSE and (b) SER of the 2-D interpolation with different sets of variable location pilots and different interpolation schemes on frequency domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 The (a) MSE and (b) SER of all the time domain improvement methods. . . 5.8 The MSE of all the time domain improvement methods when (a)

(9) (b) and . . . . . . . . . . . . . . . . . . . . . . 5.9 The data MSE and channel MSE versus each subcarrier in the linear interpolation case when SNR=40dB. . . . . . . . . . . . . . . . . . . . . . 5.10 The SER of the LMS and average all the former algorithm when = (a) 27 km/h and (b) 54 km/h. . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 40 43. 2.3 2.4 2.5 3.1. 5.1 5.2 5.3 5.4. v. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 4 6 6. 44 46. 48 49 51 52 56.

(10) 5.11 The SER of the 2-D interpolation when = (a) 27 km/h and (b) 54 km/h.. vi. 57.

(11) List of Tables 3.1. OFDMA DL Carrier Allocation . . . . . . . . . . . . . . . . . . . . . .. 21. 4.1. Comparison of Computation Complexities of Several Channel Interpolation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31. 5.1 5.2 5.3 5.4. Channel Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . Interpolation Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Computation Complexities and Extra Registers of Several Time Domain Improvement Techniques . . . . . . . . . . . . . . . . . . The Theoretical SER and the Simulated One in Linear Interpolation . . .. vii. 40 41 52 52.

(12) Chapter 1 Introduction Because the demand for high data rate wireless communications grows rapidly recently, orthogonal frequency division multiplexing (OFDM) has been studied widely in wireless communications due to its high transmission capability with high bandwith efficiency and its robustness to multipath delay. OFDM system transmits data using a set of parallel low bandwidth subcarriers. The subcarriers are independent from each other even though their spectra overlap, which results in its bandwidth efficiency and resistance to the ICI (inter-carrier-interference) effect. And due to the low bandwidth of subcarriers, each subcarrier can resist worse channel whose coherence bandwidth is smaller. That is, subcarriers can suffer longer delay spread, thus ISI (inter-symbol-interference) is also reduced. High data rate systems are also achieved by using a large number of carriers. OFDM can be easily generated using an inverse fast Fourier transform (IFFT) and received using a fast Fourier transform (FFT). It is also a technique that can achieve the spectral efficiency requirements and the high data capacity at the same time, so it has been commonly used in wireless LAN stantards such as the IEEE802.11 series, the European HIPERLAN/2, the Japanese Multimedia Mobile Access Communications [1], Digital Audio Broadcasting (DAB) and Digital Video Broadcasting (DVB) in Europe and Australia [2], [3]. In this thesis, we consider the IEEE 802.16a [4] WirelessMAN OFDMA system, which specifies the air interface of. 1.

(13) fixed (stationary) broadband wireless access systems providing multiple access, but we consider its use and performance also in mobile wireless communication. And we focus on the downlink channel estimation. There are two major items of work done in the thesis: the different schemes of interpolations to estimate the channel frequency response on data carriers, and the time-domain improvement skills to use the information of other symbols for better estimations. This thesis is organized as follows. First, we introduce the concepts of OFDM and OFDMA in chapter 2. And the standard IEEE 802.16a, as our system is based on, is introduced in chapter 3. In chapter 4, the channel estimation algorithm for downlink transmission is discussed. The different interpolation schemes and time-domain improvement methods are also introduced in chapter 4. Chapter 5 presents the simulation results based on the algorithm in chapter 4. Finally, conclusions and future works are given in chapter 6.. 2.

(14) Chapter 2 Overview of OFDM and OFDMA 2.1 OFDM The material in this chapter is largely taken from [5], [6], and[7].. 2.1.1 Concept and brief mathematical expression of OFDM In a single carrier system, a single fade or interference can cause the entire link to fail, but in a multicarrier system, only a small percentage of subcarriers will be affected. Error correction coding can then be used to correct for the few erroneous subcarriers. And OFDM is a special case of multicarrier transmission. In a classical parallel data system, the total signal frequency band is divided into nonoverlapping frequency channels. It seems good to avoid spectral overlap of channels to eliminate inter-channel interference. However, this leads to inefficient use of the available spectrum. To cope with the inefficiency, the concept of using parallel data transmission by means of frequency division multiplexing (FDM) was published in mid-1960s. The concept of FDM was to use parallel data streams with overlapping carriers. The basic idea of OFDM is to divide the available spectrum into several subchannels (subcarriers). By making all subchannels narrowband, they experience almost flat fading, which makes equalization and channel estimation easier. To obtain a high spectral efficiency, the frequency response of the subchannels are overlapping and orthogonal, hence the name OFDM. This orthogonality can be completely maintained, even though the signal passes 3.

(15) Fig. 2.1: The cyclic prefix is a copy of the last part of the OFDM symbol.. through a time-dispersive channel, by introducting a cyclic prefix. A cyclic prefix is a copy of the last part of the OFDM symbol which is prepended to the transmitted symbol, see Figure 2.1. This makes the transmitted signal periodic, which plays an important roll in avoiding intersymbol and intercarrier interference [8]. Although the cyclic prefix introduces a loss in signal-to-noise ration (SNR), it is usually a small price to pay to mitigate interference. For this system we employ the following assumptions: The channel impulse response is shorter than the cyclic prefix. Transmitter and receiver are perfectly synchronized. The fading is slow enough for the channel to be considered constatn during one OFDM symbol interval. Channel noise is additive, white, and complex Gaussian. The brief mathematical description of the OFDM system allows us to see how the signal is generated. Mathematically, each carrier can be described as a complex wave:.

(16) The real signal is the real part of. . . Both . and !. (2.1). . , the amplitude and phase of. one carrier, can vary on a symbol-by-symbol basis. But the values of the parameters are constant over the symbol duration " .. 4.

(17) An OFDM signal consists of many carriers. Thus the complex signal represented as:. where .

(18)

(19) . . . . . . This is a continuous-time signal. The variables. can be. (2.2). and ! . . on the frequency of a particular carrier are fixed values over one symbol period, thus can be rewritten as constants:. . !. ! . . If the signal is sampled with a sampling frequency of be represented by. . . . , then the sampled signal can.

(20) !#"

(21) . (2.3). Besides, the symbol time is restricted to be longer than what the signal can be analyzed to. . samples. It is convenient to sample over the period of one data symbol, thus. $ ". To simplify the signals, let . . % . . . Then the signal becomes. & .

(22) !'"

(23) . (2.4). As we know, the form of the inverse discrete Fourier transform (IDFT) is. ( Since the factor.

(24) ,+.-0/

(25) 1 *) . . (2.5).

(26) is constant in the sampled frequency domain, (2.4) and (2.5) are. equivalent if. 32 . . 45. . $ ". (2.6). which is equivalent to the condition for “orthogonality” discussed before. Thus as a conclusion, using DFT to define the OFDM signal can maintain the orthogonality. Figure 2.2 displays a schematic picture of the frequency response of the individual subchannels in an OFDM symbol. In this figure, the individual subchannels of the system are separated and orthogonal from each other. 5.

(27) Fig. 2.2: A symbolic picture of the individual subchannels for an OFDM system with N tones over a bandwidth W (from [7]).. Fig. 2.3: Baseband OFDM system model (from [7]).. 2.1.2 Continous-time model of OFDM including the concept of cyclic prefix The continuous-time OFDM model presented in the Figure 2.3 can be considered as the ideal baseband OFDM system model, which in practice is digitally synthesized and will be discussed in the next section. We start to introduce the continuous model with the waveforms used in the transmitter and proceed all the way to the receiver. Transmitter Assumeing an OFDM system with. . subcariers, a bandwidth of 6. Hz and aymbol.

(28) length of. . seconds, of which. . seconds is the length of the cyclic prefix, the. transmitter uses the following waveforms. ! where prefix. . . . " "

(29) 1 " if . $. . Since !. . . Note that !. . . !. (2.7). otherwise. . . when is within the cyclic. is a rectangular pulse modulated on the carrier frequency. , the common interpretation of OFDM is that it uses. carrying a low bit-rate. The waveforms !. . . subcarriers, each. are used in the modulation and the. transmitted baseband signal for OFDM symbol number as. ( ( . ( . . where ( . ! . (2.8). are complex numbers from a set of signal constellation. points. When an infinite sequence of OFDM symbols is transmitted, the output from the transmitter is a juxtaposition of individual OFDM symbols as. . . . . ( ! !. (2.9). Physical channel. . We assume that the support of the (possibly time variant) impulse response " "$#. % $. of the physical channel is restricted to the interval ". . . , i.e., to the length of. the cyclic prefix. The received signal becomes. & where. ,. "(' *) " " "# + ". " - , . (2.10). is additive, white, and complex Gaussian channel noise.. Receiver The OFDM receiver consists of a filter bank, matched to the last part transmitter waveforms !. , i.e.,. 0 21 !3 . . . . . if. 45 6 otherwise. 7. . /. of the. (2.11).

(30) Effectively this means that the cyclic prefix is removed in the receiver. Since the cyclic prefix contains all ISI from the precious symbol, the sampled output from the receiver filter bank contains no ISI. Hence we can ignore the time index when. . calculating the sampled output at the th matched filter. By using (2.9), (2.10), and (2.11), we get. &. . "" " " "$# ( ! " , " !3. " 0 0. ' &. ". " !3 . (2.12). . We consider the channel to be fixed over the OFDM symbol interval and denote it. . by " " , which gives. ) " ) " " " ! ! " " ! 3 ) " , ! 3 (2.13) " " " , which implies that The integration intervals are and

(31) " and the inner integral can be written as " " " ! ! " " " " " +.-0/

(32) 1 " " ". +.- /

(33) ! 1 " " " & #"%$'& " ( " ". . . (2.14) The latter part of this expression is the sampled frequency response of the channel at frequency. 2 *) . , i.e., at the. + -, % ) where. , 2 . *). th subcarrier frequency:. ) ". . " ". . ".$'& " . (2.15). . is the Fourier transform of " " . Using this notation, the output from. the receiver filter bank can be simplified to. " , ( " " +.- /

(34) ! 1 + !63 / " " ". ( + " " !. ! 3 8. . !3 . (2.16).

(35) Fig. 2.4: The continuous-time OFDM system interpreted as parallel Gaussian channels.. where. . =. " " , . . ! 3 . . Since the transmitter filters !. . are orthogonal,. the following equation is thus obtained.. ) ". " !. ! 3 . " $'& & " $'& ) " 6 ". . ) . (2.17). According to (2.16), we know that. + ( . (2.18). The benefit of a cyclic prefix is twofold: it avoids both ISI (since it acts as a guard space) and ICI (since it maintains the orthogonality of the subcarriers). By re-introducing the time index , we may now view the OFDM system as a set of parallel Gaussian channels, according to Figure 2.4.. 2.1.3 Discrete-time model An entirely discrete-time model of and OFDM systme is displayed in Figure 2.5. Compared to the continous-time model, the modulation and demodulation are replaced by an inverse DFT (IDFT) and a DFT respectively and the channel is a discrete-time convolution. The cyclic prefix operates in the same fashion in this system and the calculations can be performed in essentially the same way. The main difference is that all integrals are replaced by sums. As far as the receiver is concerned, the use of a cyclic prefix longer than the channel response will transform the linear convolution in the channel into a cyclic convolution.. 9.

(36) Fig. 2.5: Discrete-time OFDM system (from [7]).. Denoting cyclic convolution by “ ”, we can write the whole OFDM system as.

(37) (2.19) where contains the received data points, is the transmitted constellation points, . g is the channel impulse response of the channel (padded with zeros to obtain a length of. . ), and. the term.

(38). is the channel noise. Since the channel noise is assumed to be white Gaussian,.

(39) . represents uncorrelated Gaussian noise. Furthermore, we use. the fact that the DFT of two cyclically convolved signals is equivalent to the product of their individual DFTs. Denoting element-by-element multiplication by “ ” , the above expression can thus be written as. where. . . (2.20). is the frequency response of the channel. Therefore we have. obtained the same type of parallel Gaussian channels as the continuous-time model. The only difference is that the channel attenuations. . are given by the. . -point DFT of the. discrete-time channel, instead of the sampled frequency response as in (2.15).. 2.1.4 Imperfections of OFDM Depending on the mathematical analyzed situation disscused before, imperfections in a real OFDM system may be ignored or explicitly included in the model. Below we mention of the imperfections and their corresponding effects. 10.

(40) Dispersion Both time and frequency dispersion of the channel can destroy the orthogonality of the system, i.e., introduce both ISI and ICI. If these effects are not sufficiently mitigated by e.g., a cyclic prefix and a large inter-carrier spacing, they have to be included in the model. One way of modelling these effects is an increase of the additive noise. Nonlinearities and clipping distortion OFDM systems have high peak-to-average power ratios and high demands on linear amplifiers. Nonlinearities in amplifiers may cause both ISI and ICI in the system. Especially, if the amplifiers are not designed with proper output back-off (OBO), the clipping distortion may cause severe degradation. External interference In wireless systems, the external interference usually stems from radio transmitters and other types of electronic equipment in the vinciniy of the receiver.. 2.2 OFDMA The basic idea of OFDMA is OFDM based frequency division multiaccess. In OFDM, a channel is divided into carriers which are used only by one user. In OFDMA, the carriers are divided into subchannels. Each subchannel is also divided into subcarriers that form one unit in frequency allocation. A subchannel may be intended for more than one receiver (user) in the downlink. Likewise, a transmitter (user) may be assigned one or more subchannels in the uplink, and several transmitters can transmit in parallel. Thus the bandwidth can be assigned dynamically to the users according to their needs. In order to support multiple users, the control mechanism becomes more complex. Besides, the OFDMA system has more implementation issues. For example, the power control may be needed for the uplink to make signals from different users have equal. 11.

(41) power at the receiver, and all users have to adjust their transmitting times to make them aligned. Some issues in the context of IEEE 802.16a will be discussed in the next chapter.. 12.

(42) Chapter 3 Introduction to IEEE 802.16a [4] 3.1 Background of 802.16a The following three paragraphs are largely taken from [9]. Broadband wireless access (BWA) is a way to meet escalating business demand for rapid internet connection and integrated data, voice and video services. BWA can extend fiber optic networks and provide more capacity than cable networks or digital subscriber lines (DSL). One of the most compelling aspects of BWA technology is that networks can be created in just weeks by deploying a small number of base stations on buildings or poles to create high-capacity wireless access systems. BWA has had limited reach so far, in part because there was not a universal standard. While providing such a standard is important for developed countries, it is even more important for the developing world where wired infrastructures are limited. The Institute of Electrical and Electronics Engineers Standards Association (IEEESA) sought to make BWA more widely available by developing IEEE Standard 802.16. The 802.16 standard defines the Wireless MAN (metropolitan area network) air interface specification (officially known as the IEEE WirelessMAN standard). This wireless broadband access standard could supply the missing link for the “last mile” connection in wireless metropolitan area networks [10]. It focuses on the efficient use of bandwidth between 10 and 66 GHz and defines a medium access control (MAC) layer that supports multiple physical layer specifications customized for the frequency band of use. 13.

(43) IEEE 802.16’s Task Group developed IEEE Standard 802.16a, an amendment to IEEE Standard 802.16. The amendment covers “Medium Access Control Modifications and Additional Physical Layer Specifications for 2-11 GHz.” Both licensed and license-exempt bands are included [11]. This standard was published in April 2003. It specifies the air interface of fixed (stationary) broadband wireless access systems providing multiple services. The medium access control layer is capable of supporting multiple physical layer specifications optimized for the frequency bands of application. There are several system mode in 802.16a: SC (single carrier), OFDM, and OFDMA. We consider the OFDMA option in our research. Before a more detailed technical overview of the IEEE 802.16a standard, we introduce some frequently used terms below [4]. SS: subscriber station. It is usually known as the mobile station or the user. BS: base station. It is a generalized equipment set providing connectivity, management, and control of the subscriber station. DL: down-link. The direction of transmission from the BS to the SS. UL: up-link. The direction of transmission from the SS to the BS, which is opposite to DL. MAC: medium access control layer. It is used to control the system access and provide the link of data from the upper layer to the lower layer (i.e., the PHY layer). The system access functions include bandwidth allocation, connection establishment, connection maintenance, and security. PHY: physical layer. It handles the data trnsmission and may include use of multiple transmission technologies, each appropriate to a particular frequency range and application. TDD: time division duplex. A duplex scheme where uplink and downlink transmissions occur at different times but may share the same frequency. 14.

(44) Fig. 3.1: OFDMA frequency symbol description (example for 3 subchannels) (from [4]).. CP: cyclic prefix. A cyclic prefix is a copy of the last part of the OFDM symbol which is prepended to the transmitted symbol. We stress more on the DL of PHY layer in the below subsections.. 3.2 Generic OFDMA Symbol Description 3.2.1 Frequency domain description An OFDMA symbol in frequency domain is made up from several carrier types: Data carriers — for data transmission. Pilot carriers — for various estimation purposes. Null carriers — no transmission at all, for guard bands and DC carrier. (The purpose of the guard bands is to enable the signal to naturally decay and create the FFT “brick wall” shaping.) The allocations of the three kinds of carriers will be given later. In the OFDMA mode, active carriers are devided into subsets of carriers, each subset is termed a subchannel. In the DL, a subchannel may be intended for different groups of receivers; similarly, a transmitter may be assigned on or more subchannels in the UL, serveral transmitters may transmit in parallel. The concept is shown in Fig. 3.1.. 15.

(45) 3.2.2 Time domain description Inverse-Fourier-transforming from frequency domain OFMDA symbol creates the time domain waveform; this time duration is referred to as the useful symbol time of the last. 6. .. . A copy. s of the useful symbol period is termed cyclic prefix,as we introuduced in. section 2.1. It is used to collect multipath while maintaining the orthogonality of the tones. The transmitter energy increases with the length of the guard time while the receiver energy remains the same, so the loss in SNR (in dB) can be calculated as,. . . " / 6 " 6 where the defination of. . and. . (3.1). are the same as in chapter 2. Using a cyclic exten-. sion, the samples required for performing the FFT at the receiver can be taken anywhere over the length of the extended symbol. This provides multipath immunity as well as a tolerance for symbol time synchronization errors.. 3.3 OFDMA Symbol Parameters and Transmitted Signal 3.3.1 Primitive parameters Four primitive parameters characterize the OFDMA symbol:. . . This is the nominal channel bandwidth. And it equals 10 MHz in our system. simulation.. . . This is the ratio of “sampling frequency” to the nominal channel band width. This value is set to . . This is the ratio of CP time to “useful” time. We use ". in our system.. . This is the number of points in the FFT. The OFDMA PHY defines this. value to be equal to 2048.. 16.

(46) 3.3.2 Derived parameters The following parameters are defined in terms of the primitive parameters.. . . = sampling frequency. The value equals. . ' . 4. MHz.. $2 . . $2. ". = useful time =. 6 6 . 6. . = carrier spaing =.

(47)

(48) . . s.. 4 4 . s.. = CP time =. = OFDM symbol time =. = sample time = .

(49)

(50) . 4 . KHz.. s.. ns.. 3.3.3 Transmitted signal Eq. (3.2) specifies the transmitted signal voltage to the antenna, as a function of time, during any OFDMA symbol..

(51) .

(52) & / 1.

(53) + . .

(54) & " . (3.2). where:. . = time, elapsed since the beginning of the subject OFDM symbol, with. . . .. = a complex number; the data to be transmitted on the carrier whose frequency. . offset index is , during the subject OFDM symbol. It specifies a point in a QAM constellation.. 6. = guard time.. . = OFDM symbol duration, including guard time.. $2. = carrier frequency spacing. 17.

(55) 3.4 OFDMA Carrier Allocation We will compare the different carrier allocations between DL and UL, but this thesis is focused on the DL carrier allocation. For OFDMA,. ". . . . . Subtracting the DC carrier and the guard tones from. , one obtains the set of used carriers. . The carriers are allocated to pilot carriers. and data carriers in both DL and UL. But the difference beween DL and UL is that, in the downlink, the pilot tones are allocated first. The remainder of carriers are subchannels which are used exclusively for data. On the other hand in the UL, the set of used carriers is first partitioned into subchannels, and then the pilot carriers are allocated from within each subchannel. Thus, in the DL, there is one set of common pilot carriers, but in the UL, each subchannel contains its own set of pilot carriers. In the sequel, carriers are identified by a carrier index. The frequency offset index of a particular carrier is specified terms of its carrier index as. . . . . . 4 4 4 4 . (3.3). where:. . . . = frequency offset index, = carrier index, and. . = number of used carriers.. 3.4.1 DL assignment of pilots The.

(56) . used carriers are partitioned into fixed-location pilots, variable location pilots,. and data subchannels. The carrier indices of the fixed-location pilots never change. These indices are the members of the set BasicFixedLocationPilots, and will be listed later. The variable-location pilots shift their location every symbol repeating every 4 symbols,. 18.

(57) according to the following formula: & . . 4 . (3.4). where: & . . . . . . = carrier index of a variable-location pilot,. . is a function of the symbol index, modulo 4,.

(58) . 4 . Notice that, L does not simply increment from one symbol to the next, but follows the sequence L=0, 2, 1, 3, 0, 2, . In some cases, a variable-location pilot will coincide with a fixed-location pilot. The sets of BasicFixedLocationPilots are designed so that the number of coinciding pilots is the same for every L, i.e. 8. The allocation of pilot carriers is illustrated in Figure 3.2.. 3.4.2 Partitioning of data carriers into subchannels After mapping the pilots, the remainder of the used carriers are the data subchannels. Since the variable location pilots change location in each symbol, repeating every fourth symbol, the locations of the carriers in the data subchannels also need to change. The remaining carriers are partitioned into groups of contiguous carriers. Each subchannel consists of one carrier from each of these groups. The number of groups is there . Likefore equal to the number of carriers per subchannel, which is denoted wise, the number of carriers in a group is equal to the number of subchannels, and it is de . Thus the number of data carriers is equal to ' . noted The exact subchannels partition is given by & & & . . . " . . where: 19.

(59)

(60) 0

(61) !

(62) . .

(63) #

(64) '

(65) !

(66) . (3.5).

(67) Fig. 3.2: Carrier allocation in 802.16a OFDMA DL (from [4]).. & & & . . . =carrier index of carrier. . in subchannel .. = index number of a subchannel, from the set [0, ,. . = carrier-in-subchannel index from the set [0, ,. . . . . . . . ].. ].. = number of subchannels.. = the series obtained by rotating & . . . which is given in the. table 3.1 cyclically to the left times.. . . = ceiling function which rounds its argument up to the next integer.. . = a postive integer assigned by the MAC to identify this particular base20.

(68) Table 3.1: OFDMA DL Carrier Allocation Parameter Number of DC carriers Number of guard carriers, left Number of guard carriers, right , number of used carriers Total number of carriers

(69) . Value 1 173 172 1702 2048 142 32 8. . Number of fixed-location pilots Number of variable-location pilots which coincide with fixed-location pilots Total number of pilots Number of data carriers per subchannel Number of data carriers per subchannel BasicFixedLocationPilots . & . . . 166 1536 32 48 48 0, 39, 261, 330, 342, 351, 522, 636, 645, 651, 708, 726, 756, 792, 849, 855, 918, 1017, 1143, 1155, 1158, 1185, 1206, 1260, 1407, 1419, 1428, 1461, 1530, 1545, 1572, 1701 3, 18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21, 5, 28, 31, 23, 17, 4, 24, 0, 13, 12, 19, 14, 30. station cell.. ). . . = the remainder of the quotient ). . , which is at most. . .. The numerical parameters are given in Table 3.1.. 3.5 Modulation 3.5.1 Data modulation There are three types of modulations, namely, QPSK, 16QAM and 64 QAM, in IEEE 802.16a OFDMA mode. Gray-mapped QPSK and 16QAM as shown in Figure 3.3 shall be supported, whereas the support of 64QAM is optional. The constellations of the three kinds of modulations shall be normalized by multiplying the constellation point with the 21.

(70) Fig. 3.3: QPSK, 16QAM and 64 QAM constellations (from [4]).. indicated factor to achieve equal average power.. 3.5.2 Pilot modulation Pilot carriers shall be inserted into each data burst in order to constitute the symbol, and they shall be modulated according to their carrier location within the OFDMA symbol.. . The PRBS which denotes pseudo random binary sequence. shown in Fig. 3.4. The polynomial for the PRBS generator is ). should be generated as. . ). . .. When using data transmission on the DL, the initialization vector of the PRBS is [11111111111] except for the OFDMA DL PHY preamble, which is [01010101010]. These initializations result in the sequence. . = 11111111111000000001 in the DL. data signal. The PRBS shall be initialized so that its first output bit coincides with the first usable carrier. A new value shall be generated by the PRBS on every usable carrier. The pilot cariers shall be modulated according to the following formula:. . 4 . . . . . . . We now turn to the downlink channel estimation in the next chapter. 22. (3.6).

(71) Fig. 3.4: PRBS generator for pilot modulation.. 23.

(72) Chapter 4 Downlink Channel Estimation There are three main subjects in this chapter, which are channel estimation on pilot subcarriers, interploation schemes and time domain improvement methods. We use the LS technique to estimate the channel response on pilots. Three kinds of interpolation schemes are used, including of linear, second order and cubic spline interpolations. And the four kinds of time domain improvement methods are moving average, exponential average, LMS adaption and 2-Dimensional interpolation. All the techniques are discussed individually in the following sections.. 4.1 Channel Estimation on Pilot Subcarriers 4.1.1 Pilot information Channel estimators usually need some kind of pilot information as a point of reference. A fading channel requires constant tracking, so pilot information has to be transmitted more or less continuously. Decision-directed channel estimation can also be used, but even in these types of schemes, pilot information has to be transmitted regularly to mitigate error propagation [7]. In general, the fading channel can be viewed as a two-dimensional (2-D) signal (time and frequency), which is sampled at pilot positions and the channel attenuations between pilots are estimated by interpolation.. 24.

(73) 4.1.2 LS and MMSE estimations Based on a priori known data, we can estimate the channel information on pilot carriers roughly by the least-square (LS) or the minimun mean square error (MMSE) estimator. An LS estimator minimizes the following squared error [12]:. . . . . (4.1). where Y is the received data and X is priori known pilots, and both are N ' 1 vectors where is the OFDM FFT size. is a N ' N matrix whose values are 0 except at pilot locations . . . . . .

(74). . . . where . . . . . . . . . . . + + . . . . 1 1 . . . (4.2). Therefore the (4.1) can be rewritten as. . . . . . . ). for all . . . (4.3). Then the estimate of pilot signals, based on one observed OFDM symbol, is given by. . . . . ). . ) ). ). is the complex white Gaussian noise on subcarrier . We collect. ! , an . (4.4). . . . is the total pilot numbers as " # # # $ " (4.5) &' % ' % ' % " ( and are the collections of the transmitted and the received data on the pilot where ) based on one OFDM symbol only is subcarriers individually. The LS estimate of where. into. '. . vector where . . . . susceptible to Gaussian noise, thus an estimator better than the LS estimator is preferable. 25.

(75) The minimum mean-square error (MMSE) estimate has been shown to be better than the LS estimate for channel estimation in OFDM systems. But the major drawback of the MMSE estimate is its high complexity, which grows exponentially with the observation samples [13]. A low-rank approximation is applied in a linear minimum mean squared error (LMMSE) estimator that uses the frequency correlation of the channel. The mathematical representation for the LMMSE estimator [13] of pilot signals is. " . . (4.6) is the least-square estimate of in (4.5), is the variance of the Gaussian where . . . . . . . . . . white noise, and the covariance matrices are defined by. . . . . " ! . . . (4.7). . (4.8) (4.9). . Note that there is a matrix inverse involved in the MMSE estimator, which must be calculated every time, and the computational complexity of matrix inversion requires. #.

(76) . arithmetic operations [14]. We also need to use the statistical properties of the unknown channel. Therefore, we use the LS estimator which requires only. . operations in-. stead of the LMMSE one due to the concerns of complexity and the unknown information.. 4.2 Interpolation Schemes After knowing the channel response on the pilot carriers, we need to use interpolation to get the response on the rest of the carriers. Three interpolation methods are introduced here, and the performance comparison will be discussed in the next chapter.. 26.

(77) 4.2.1 Linear interpolation Linear interpolation is a commonly used method of interpolations. It does the interpolation simply with two known data adjacent to the unknown ones. The following is the mathematical expression [1]:. . where. # % . . # . . $ . . ! . . # . . . . (4.10). is the channel frequency response at pilot subcarriers,. is the distance between the two given data, that is, the pilot sub-carriers spacing, and. . . .. 4.2.2 Second order interpolation Theoretically, using higher-order polynomial interpolation will fit the channel response better than the linear interpolation [15]. However, the computational complexity grows as the order is increased. Here we consider the second order polynomial interpolation,and it is also called Gaussian second order estimation. It is given as a solution to the second. order polynomial with respect to by using three reference signals. The interpolation is obtained using three successive pilot subcarriers signal as follows [16]:. % . . . #. . where. . . . . . . . . . . . . . . # . . . . . The notations are the same as they are in linear interpolation.. 27. # . . (4.11).

(78) 4.2.3 Cubic spline interpolation [17], [18] Cubic Spline is one very effective, well-behaved, computationally efficient interpolation. The approach is to fit cubic polynomials to adjacent pairs of points and choose the values of the two remaining parameters associated with each polynomials such that the polynomails covering adjacent intervals agree with one another in both slope and curvature at their common endpoint. The piecewise-cubic interpolating function " is twice continuously differentiable over. ( . that results. ( ( . And the cubic spline interpolation is. developed by the following algorithm. Development of the cubic spline algorithm. ( that interpolates the real2 points ( ( ( at which the values of valued function ( at the , is 2 ( are known. So, we construct " ( on each interval ( ( , . The goal is to construct a piecewise-cubic polynomial ". a cubic polynomial . ( . . ( ( . . Once we find the coefficients , any point ( in. . ( ( ;. . . . . ( (. . (4.12). , we can evaluate " ( . for. ( ( . And the boundary condition gives us the following two equations: . Eq. (4.14) implies that to be continuous on. ( . ( ( .. ( . ( 2 ( . As we mentioned before, each . ( . . 2 ( . (4.13). 2 ( . (4.14). . which in turn guarantees ". ( . is required to interpolate at only two points.. But since a cubic polynomial can interpolate a function at four points, we have freedom remaining in choosing the . ( .. 28.

(79) We choose our two remaining constraints as that . ( . must agree with . ( . in. both slope and curvature; that is, we want. ) ( . and. ) ) ( . for . . . . ) ) ( . . at (. Intergrating (4.17), we get. ) ( . Intergrating (4.18) gives. ( . . where. . . ( ( . and. . (4.15). ) ) ( . (4.16). . ( ( . . ( ( . . at ( . . be parameters of . . That is. ( ( ( (. ( ( ( ( . ( 4 ( . The equation is equivalent to. . . and. )) ( . ( . . . . . ) ( . ( . Since ( is ) ) ( is a linear polynomial constrained such that ) ) ( and . We let the curvatures a cubic polynomial, . . ( ( . (4.17). (. ( ( ( . 4. ( ( . (. ( ( ( . ( ( ( . ( . (. . . (4.18). ( . (4.19). ( ( ( . . . (4.20) are constants of integration.. Applying the constraint given by (4.13), we get from (4.20) that . or. . ( . 2 ( . ( . 2 ( ( ( . . ( ( ( . ( . ( 29. . . (4.21). . (4.22).

(80) Similarly, by applying the constraint given by (4.14), we get from (4.20) that. ( . . or . 2 ( . 2 ( ( ( . ( . . . ( . ( ( ( . ( . . . (4.23). . (4.24). The final constraint to be satisfied is that the first derivative must be continuous. Ac-. + + ( . cording to (4.15), (4.18) becomes . ) ( . . . ( . 4 . ( . . . ( . . . . . . . . Again, using (4.15) we can obtain. . . . . 4. ( . . . . . ( . . . . . ( . . ( . . . . . (4.25). (4.26). . . Once (4.26) is solved for all the , we have everything we need for to find the coefficients of the ( , which in turn can get the interpolator " ( . linear equation in unknowns , . Eq. (4.26) is a system of and to solve all the . In this work, the two values Thus we have to determine and are set to be 0. This is equivalent to assuming that ( and ( approach . linearity at their outer extremities.. 4.2.4 Comparison and illustration of the three interpolations The complexity of the three interpolations is compared in Table 4.1. Fig. 4.1 shows some results obtained by interpolation using the three different interpolation schemes. The channel frequency response in static case in our simulation which will be introduced in chapter 5 is partly chosen to be the original data in the figure. And the sampled data positions is the corresponding pilot carriers. We can see from the figure, for the pilot ratio is obviously insufficient that the performances are not very good in each kind of interpolations. Thus we need to use the information of other symbols to achieve better estimation. 30.

(81) Table 4.1: Comparison of Computation Complexities of Several Channel Interpolation Techniques Interpolation Technique Linear Interpolation Second Order Interpolation Cubic Spline. Computation Complexity for Each Carrier 4MPYs + 4Adds 6MPYs +4Adds At least 6MPYs + 6Adds. 4.3 Time Domain Improvement Methods After doing the interpolation, we obtained the overall estimated channel response in frequency domain. And the simulations of our channel estimation are based on static and mobile Rayleigh fading channel. Both have correlation between channel frequency responses of diffrent symbols, thus we develop a few methods to use the data of different symbols to improve our estimation. But the estimated channel is still given in frequency domain.. 4.3.1 Moving average Assuming the receiver which is the SS, has a velocity of 100 km/hr, or equivalently, 27.78 m/s. The Doppler frequency with a center frequency is 2 GHz can be calculated according to [19]. 2 2. where light,. 2. . is the Doppler frequency,. . 2. . . (4.27). is the velocity of the receiver, is the velocity of . is the center radio frequency and is the angle between the. transmitter and receiver. We thus obtain. 2. . and line of sight of. =185.2 Hz And the corresponding coherence. time can be approximately obtained by [19]. where. 2 . . 5 2 . is the maximum Doppler shift given by. 2. (4.28) . . . This yields. . = 966.788 us. Coherence time is actually a statistical measure of the time duration over which the channel impulse response is essentially invariant, and quantifies the similarity of the chan31.

(82) 1. 0.9. 0.8. 0.7. 0.6. 0.5. 0.4. Original Data Cubic Spline Linear Interpolation Second Order Interpolation Sampled Data. 0.3 10. 40. 30. 20. 90. 80. 70. 60. 50. 100. Fig. 4.1: The result of different interpolation methods.. nel resonse at different times. As this OFDMA system is operated with a data bandwidth %4 4

(83) = 201.9 s (with a equals 10 MHz, the symbol period time is then CP rate of. . ). And the channel can be seen as a slow fading one if the coherence time. is greater than the symbol period. The channel impulse response changes at a rate much slower than the transmitted baseband signal. . in a slow fading channel. In this case, the. channel may be assumed to be static over one or several reciprocal bandwidth intervals. Following the calculations above, the channel response over symbols. . is assumed to be static. Thus we use an averaging methods over 5 symbols to reduce the noise term as. . . . . . , , , , , +, 2 + 2 + 2 +

(84) 2 + 2 + 2 32. (4.29).

(85) +, 2 where. . , 2 + is the estimated channel after the moving average and , n=1 4 is. . the interpolated channel response at th previous symbol time.. 4.3.2 Exponential average The OFDM system can be described as. . (4.30). . where Y is the received symbol, H is the channel response, X is the transmitted symbol, and N is the complex additive white Gaussian noise with variance . If ) is a pilot. ". subcarrier, the instantaneous channel estimate is obtained as . (4.31). Because the noise term N is the complex additive white gaussian noise whose mean is 0. If the channel H remains static, compared with the former method to take five symbols to do the averaging, the more symbols we take, the more we can eliminate the noise term. However, the more symbols we take, the more complicated the hardware is, since we have to use more registers to store the estimated channel responses. Thus we think of a alogorithm to use all the former symbols without store them. It is the simple exponential averaging as follows:. . . . + , 2 / + , 2 +, 2 . +, 2 where . . . . . . . is the estimated channel after using this method at. . . +, 2 . . (4.32). . , 2 + th symbol time, . . . is the channel response by using only interpolations discussed before at th symbol time, , 2 , 2 / + + and is the weighting of the , likewise, the weighting of is .. . . The performance is better than the moving averaging one in static channel simulation. But the channel varies in the mobile transmission, the estimation brought all the former information may not be suitable in this situation. The data and the different weighting comparison will be given in the next chapter. 33. .

(86) Fig. 4.2: Block diagram of adaptive transversal filter.. 4.3.3 LMS adaptation The LMS algorithm [20] is a linear adaptive filtering algorithm, which in general, consists of two basic processes: A filtering process The filter process involves (i) computing the output of a linear filter in response to an input signal and (ii) generating an estimation error by comparing this output with a desired response. An adaptive process The process involves the automatic adjustment of the parameters of the filter in accordance with the estimation error. The combination of these two processes working together constitutes a feedback loop, as illustrated in the block diagram of Fig. 4.2. First, we have a transversal filter, around which the LMS algorithm is built, and this component is responsible for performing the filtering process. Second, we have a mechanism for performing the adaptive con trol process on the tap weights of the transversal filter, hence the designation . . . ". +. . . & . . . +. . in the figure.. The LMS adaptation algorithm equations has been broadly known and used:. 34.

(87) Filtering:. . Error estimation:. . . . !. (4.33). . Tap-weight vector adaptation:. 4. (4.34). 3 . The equations above derive a set of tap-weight vector. . (4.35). , which can be used to multiply. another value to do the adaptation. Thus we could use the equations to do like an equalizer, that is, we multiply the recived data by the tap-weight vector. Because the tap-weight vector obtained is the information of the equalizer, which needs to be inversed to get the estimated channel, we try to use the LMS adaptation scheme to estimate the channel frequence response directly. Eq. (4.34) and the cost function in square error sence can be rewritten as. ! . (4.36) (4.37). To do the LMS estimation on the channel directly, we have a new error definition and its corresponding cost function:. . . !. Thus the adaptive equation becomes. 4. . 3. . . (4.38) (4.39). (4.40). To use the same denotions as they are in the previous sections, we rewrite (4.39) as:. . + 35. # . . (4.41).

(88) H(n). X(n). Y(n) ε (n). Fig. 4.3: Illustration of LMS adaption for channel estimation.. " # . and (4.40) as:. . . " # 4 3 . . . (4.42). . . The X(n) is obtained by assuming our estimation is perfect then X(n)= . . . This. #. adaptation algorithm is shown as Fig. (4.3). , the In our simulation, we use the interpolated channel estimation as the is obtained by (4.42) when . Following the algorithm, only the first sym. " #. . #. bol pilot information is used in the whole flow, thus the pilot information of other sym bols is wasted. Therefore, we try to combine the interpolated channel and the which is the estimated channel by using LMS algorithm when. + , # 2 2 + , 2 . this combination can be given as. +,. . #. . . . +, 2 . . . .. . The equation of. . . (4.43). , 2 + where is the channel estimated by the LMS adaptation algorithm with the , 2 + and it is also denoted as , and is the channel estimated , , 2 + + . 2 by interpolation. The and the is the weighting factor for and .. " #. " #. 36. . #. .

(89) 4.3.4 Two-Dimensional interpolation Let us review the downlink variable pilot allocation of IEEE 802.16a in Fig. 3.2. And the equation of the allocation formula is again & . 4 . . (4.44). where: & . . . . . = carrier index of a variable-location pilot is a function of the symbol index, modulo 4.

(90) 4 . Because the position of the variable location pilots varies with a period of four symbols, we could use the variable location pilots at the other three symbols. The maxmimun number of the variable location pilots we can use is.

(91) . . . '. . . 4 . . ' . 4

(92) . (4.45). where the. . is the number of the variable location pilots which are coinci-. dent with the fix location pilots. Thus we can use the extrapolation in the time domain to estimate the channel frequency response on the variable location pilots of other symbols.. . . . . . This method is illustrated in Fig. 4.4. And the mathematical expression is +,

(93) 2 + , 2 +, 2 ! + , 2 +, 2 . where. . +,. . . . . . . . + , 2 ! + , 2 + , 2 + , 2 ! + , 2 + , 2 . 2 . for. . (4.46) is the channel frequency response of pilot carriers in. . the th previous symbol time. We can use interpolations again on the frequency domain ,

(94) 2 +

(95) 4 after knowing . Since the number of the pilots becomes times compared with the original case, the better estimation is obtained. 37.

(96) Fig. 4.4: Illustration of the 2-D interpolation scheme.. However, there are extra seven registers needed to store the channel frequency response on pilot carriers. Except for the hardware concern, the fast fading channel might seriously effect the accuracy of the interpolations on the time domain. Because we need to use the information before seven symbols, the channel may have changed a lot during this period of time. Thus, we can use less variable location pilots in previous symbols which. . . . . . means only 1 or 2 more sets of variable location pilots are taken. Eq. (4.46) becomes +,

(97) 2 +, 2 +, 2 ! +, 2 +, 2 (4.47) +, 2 +, 2 +, 2 and. . . . . . . . . . +,

(98) 2 +, 2 +, 2 ! + , 2

(99) +, 2 . Comparison of these three equations will be discussed in the next chapter.. 38. (4.48).

(100) Chapter 5 Simulation Study The flow of our simulations is as shown in Fig. 5.1. We assume to have perfect synchronization since the aim is to observe channel estimation performance. After doing channel estimation, we can calculate the channel MSE which is mean square error between the real channel and the estimated one. We can also obtain the SER, the symbol error rate, after demapping. The mapping here is based on the 16QAM, thus is . And the constellation of the 16-QAM modulation is introduced bethe fore in Fig. 3.3. The static channel and the Rayleigh fading channel as well are simulated and discussed in this chapter. Before simulating on multipath channel, we do the simulation with an AWGN channel which means we transmit the data through a one-path channel with. + , and then. add AWGN noise on it. The result is shown in Fig. 5.2, and is almost the same with the. Fig. 5.1: The flow chart of the simulations.. 39.

(101) 0. 10. Theoretical Simulated −1. 10. −2. 10. −3. SER. 10. −4. 10. −5. 10. −6. 10. −7. 10. 15. 10. 5. 0. Eb/N0. Fig. 5.2: The simulation result on AWGN channel. Table 5.1: Channel Impulse Response Tap 1 2 3 4 5 6. Delay (OFDM samples) 0 2 17 36 75 137. Amplitude 1 0.3162 0.1995 0.1296 0.1 0.1. Amplitude (in dB) 0 -5 -7 -8.87 -10 -10. theoretical one.. 5.1 Channel model A multipath fading channel models are used in the simulations. Since the specifications IEEE 802.16a did not assign a mobile channel model, we thus refer the channel in the [1]. The channel model is the ATTC (Advanced Television Technology Center) and the Grande Alliance DTV Laboratory’s ensemble E model. Its static impulse response is given in Table 5.1.. 40.

(102) Table 5.2: Interpolation Errors. Theoretical Simulation Result. Linear Interpolation 0.0254 0.0208. Second-Order Interpolation 0.0330 0.0269. Cubic Spline 0.0285 0.0237. 5.2 Definitions of SER and channel MSE. . The SER in the below simulations is denoted for the average symbol error rate at the. . Likewise, the MSE is denoted for the average +. specific. + . at the. . The. averages in above sentences are in the subcarriers senses.. 5.3 Simulations on Static (Stationary) Channels We use the static case of the channel model introduced before to be our static simulation model.. 5.3.1 Comparison of interpolation methods First we want to discuss the error caused by the interpolation scheme. Thus we let the data transmit after the channel without adding noise, using the information on the pilot carriers to get the channel frequency response by doing the interpolation. Then we calculated the average. . ( ( . on each subcarrier by simulating 10000 symbols. The theoretical symbol. error rate with Gaussian noise power . where. . . and we have. / . . for. -ary QAM can be obtained by [19]. . . with. . . here. The. is normalized to be 1 in our simulation. If we subtitude. ( . . (5.1) is. . and the. ( for , we can get a. theoretical symbol error rate and is given in Table 5.2. We can observe that, the simulated symbol error rate differs from the theoretical one. Therefore, the interpolation error can not be considered Gaussian noise. 41.

(103) Fig. 5.3 shows the result of different interpolations in MSE and SER senses. Out of our expection, as shown in the figure, the linear interpolation has a better performace than the others. That might be owing to the lack of pilot carriers. That is, the carrier spacing is too large for we to use the pilot carriers which outside the two adjacent ones. There are also error floors in all the three interpolations. As we discussed in the previous chapter, the pilot carriers are insuffecient of this six taps channel. There is a great improvement in the 2-D interpolation simulation in this aspect. Since we have almost four times the number of pilot carriers in the 2-D interpolation simulation. The second-order interpolation outperforms the linear one. And the larger the. . is, the better the. second-order interpolation performs than the linear one. The detail and the result will be discussed also in the section of the subsection 5.1.5.. 5.3.2 Result of moving averaging Because there is no parameter needed to be adjudged in this scheme. We put the result and the the analysis in the section 5.2.6.. 5.3.3 Comparison of different weightings in exponential averaging In this simulation, we use only linear interpolation because of the result of the former section. For the linear interpolation performs better than the second-order one with limited pilot carriers number.. . We can see from Fig. 5.4, the MSE gets smaller when increases from 0 to 0.9. But , thus the best choise of is 0.9. There is a gain about 8 the MSE gets larger when compared with using only linear interpolation. In the circuit realization dB when. . concern, we might chose. . /. . . . . as . which can easily done by right shift the data.. 42.

(104) Linear Interpolation Second−Order Interpolation Cubic Spline Interpolation. −1.5. MSE. 10. −1.6. 10. −1.7. 10. 15. 10. 30. 25. 20. E /N b. 35. 40. 0. (a) 0. 10. SER. Linear Interpolation Second−Order Interpolation Cubic Spline Interpolation. −1. 10. −2. 10. 10. 15. 20. 25. 30. 35. 40. Eb/N0. (b) Fig. 5.3: The (a) MSE and (b) SER of diffrent interpolation schemes.. 43.

(105) omega=0 omega=0.2 omega=0.5 omega=0.8 omega=0.9 omega=0.99 omega=0.999. −1.6. 10. −1.7. MSE. 10. −1.8. 10. −1.9. 10. 10. 15. 20. 25. 30. 35. 40. Eb/N0. (a) 0. 10. omega=0 omega=0.2 omega=0.5 omega=0.8 omega=0.9 omega=0.99 omega=0.999 −1. SER. 10. −2. 10. −3. 10. 10. 15. 20. 25. 30. 35. 40. Eb/N0. (b) Fig. 5.4: The (a) MSE and (b) SER of using different weightings in exponential averaging.. 44.

(106) 5.3.4 Comparison of different weightings in LMS adaptation method of the LMS algorithm [20], [21]:. Obeying the criterion of the step-size parameter.

(107) . &. (5.2). where tr[R] is the sum of the powers of the signal samples at the filter tap inputs, which , is the powers of the channel impulse response in our case. And the tr[R] equals thus we choice to be 0.05 and 0.005. Recalling the adaptive equation 4 3 , the X(n) here is obtained by the decision output which is . " #. . #. . . . decided by the receive data over estimated channel, which X(n)= . . . And this. is based on the assumption that our decision is correct. We also compare the different weighting. . of the LMS filter output and the interpolated data. The result is shown in Fig.. 5.5.. 5.3.5 Comparison of the sets of variable location pilots taken in the 2-D interpolation Because we need to use the information of previous seven symbols. We do the 2-D interpolation after the th symbol. The previous seven symbols are estimated simply with 1-D interpolation. The result of the 2-D interpolation with using different sets of variable location pilots is shown in Fig. 5.6. We can observe that, the second-order interpolation performs better than the linear one while the variable location pilots and the. . increase. For exam-. ple, with four sets of variable location pilots are taken, there is a better performance in the second-order interpolation when. . . 4

(108). dB. This observation also provides the. reason why the linear interpolation has a better performance than the second-order and cubic spline ones. It is because the lack of pilot carriers which is allocated and arranged with the IEEE 802.16a specifications. Note that there are also error floors in these simulations. That is because we use 1-D interpolation at the first seven symbols. The summation of the symbol errors of the seven 45.

(109) −1. 10. u=0.05,alpha=1 u=0.05,alpha=0.9 u=0.05,alpha=0.8 u=0.05,alpha=0.5 u=0.005,alpha=1 u=0.005,alpha=0.9 u=0.005,alpha=0.8 u=0.005,alpha=0.5 −2. MSE. 10. −3. 10. −4. 10. 10. 15. 20. 25. 30. 35. 40. Eb/N0. (a) −1. 10. SER. u=0.05,alpha=1 u=0.05,alpha=0.9 u=0.05,alpha=0.8 u=0.05,alpha=0.5 u=0.005,alpha=1 u=0.005,alpha=0.9 u=0.005,alpha=0.8 u=0.005,alpha=0.5. −2. 10. −3. 10. 10. 15. 20. 25 Eb/N0. 30. 35. 40. (b) Fig. 5.5: The (a) MSE and (b) SER for different weightings and different step-size parameters in LMS method.. 46.