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UT EE 381K - Channel Estimation for Wired MIMO Communication Systems

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1Channel Estimation for Wired MIMO Communication Systems Literature Survey Multidimensional DSP Project, Spring 2005 Daifeng Wang Abstract This report investigates channel modeling and estimation for a wired multiuser multicarrier communications system. The special case of a multiple-input multiple-output (MIMO) channel is considered where the different users transmit at the same time and over the same bandwidth. In the report, I will introduce data transmission and training systems. The report also will present a MIMO channel model and Multicarrier Modulations. Then, three typical channel estimation methods are presented and analyzed. I. Introduction Communication systems that use multiple transmitters and receivers are often called multiple-input multiple-output (MIMO) systems. MIMO systems can provide both high data reliability and high data rates for a home network. The bonded Asymmetric Digital Subscriber Line (ADSL) is a wired MIMO communication system. By taking multiple ADSL connections and combining them (bonding) into a single 'virtual' connection you can achieve a high speed, resilient connection using a cost effective medium. The current challenges for MIMO systems are still the transmission power, bandwidth, and computational complexity and channel capacity. To estimate an unknown channel is a very important and necessary work before transmitting the real signals since the channel is commonly time-varying. The channel estimation can be performed by either sending a known training/pilot sequence or using cyclic statistics of the received signal.2In this survey, section II introduces some key techniques and describes the multicarrier data transmission and reception for MIMO systems. Section III describes MIMO channel models and provides the Shannon capacity of MIMO channels. Section IV presents and analyzes three channel estimation methods which are based on the simplified estimation, linear interpolation and linear precoding respectively. Section V discusses and compares these methods. Section VI concludes and summarizes this report. II. Background All transmission channels are fundamentally analog and thus may exhibit a wide variety of transmission effects. The modulation is to convert a stream of input bits into equivalent analog signals that are suitable for the transmission line. A primary impairment in communications is inter-symbol interference (ISI) which is caused by the memory in the channel. To combat ISI, a receiver usually uses an equalizer to compensate for the spreading in time and distortion in frequency caused by the channel. One technique to avoid ISI, without sacrificing the transmission rate, is Multicarrier Modulation (MCM). In order to obtain the MCM, we can divide broadband channel into narrowband subchannels which have their own center carrier frequencies. There is no ISI in subchannels if each subchannel has the ideal sampling and constant gain. Because of its robustness to multipath, and the ease of implementating it using the fast Fourier transform (FFT), the MCM concept is growing rapidly in practical importance. It has been implemented in several wireline and wireless high-speed data communications standards (ADSL, IEEE 802.11). The discrete multitone modulation (DMT) is a MCM application in the wired communication system. And another increasingly popular multicarrier modulation technique in wireless communications is orthogonal frequency division multiplexing (OFDM).3A Multicarrier Modulation transmitter is shown below: Figure 1 Multicarrier Modulation Transmission The receiver is the mirror image of the transmitter. The input of the S/P converter is a sequence of symbols of B bits each; the output for each symbol is Ncar groups of b(n) bit each. That is B=()carnNbn≤∑. The groups of b(n) are then constellation-encoded, perhaps filtered, and then modulated onto Ncar subcarriers. III. MIMO Channel Modeling Figure 2 MIMO with M transmitters and N receivers The relation between the input and output signals of a Multiple-Input Multiple-Output (MIMO) link is represented in the equivalent discrete time base-band model by the complex vector notation rHsn=+ where s is the ( 1M×) complex transmitted signal4vector, r is the ( 1N × ) complex received signal vector, H is the ( NM× ) complex channel matrix, and n is the (1N × ) complex noise vector. Further, σ2 denotes the average transmission power; M and N are the number of transmitters and receivers, respectively. IV. MIMO Channel Estimation Althought ISI can be avoided by MCM, the phase and gain of each subchannel is needed for coherent symbol detection. An estimate of these parameters can be obtained with pilot/training symbols at the expense of bandwidth. Another way called blind channel estimation to take into account cyclic statistics of the received signal or subspace decomposition of the correlation matrix of the pre-FFT received blocks. 1. Simplified Channel Estimation for OFDM systems [1] Considering an OFDM system with two transmitters and two receivers, at time n , a data block {b[n,k]:k=0,1,…,} is transformed into two different signals {ti[n,k]: k=0,…, K-1 and i=1,2.} at the transmit diversity processor, where K, k, and i are the number of subchannels of the OFDM systems, subchannel (or tone) index, and antenna index, respectively. The signal from each receiver can be expressed as 21[, ] [, ][, ] [, ]iiirnk H nkt nk wnk==+∑ (1) where Hi[n,k] is the frequency response at the kth tone of the nth block corresponding to the ith transmitter which can be expressed as 010[, ] [,]KkliiKlHnk hnlW−==∑, K0 is the number of nonzero taps of the channel impulse response. w[n,k] denotes the additive complex Gaussian noise and is assumed to be zero mean with variance 2nσ. Hence, to obtain Hi[n,k], we only need to estimate hi[n,l]. if the transmitted5signals ti[n,k]’s, for i=1,2 are known, [,]ihnl, the temporal estimation of hi[n,l], can be found by [7] 11 21 1 112 22 22[] [] [] [][] [] [][]Qn Qn hn pnQn Qn pnhn⎛⎞⎛⎞⎛⎞=⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠ (2) where []ihn is the temporal estimation of channel parameter vector, defined as 0[] ( [,0], , [, 1])Tii ihn hn hnK−  (3) and [,], [], [,]ij ij iqnlQnpnl and pi[n] are defined as 0121*0112,01*00[,] [, ][, ][] ( [, ])[,] [, ][, ][] ( [,0], , [, 1])Kklij i j KkKij ij l


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UT EE 381K - Channel Estimation for Wired MIMO Communication Systems

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