Channel tracking with scattered pilots using a kalman filter

Channel tracking method and apparatus with distributed pilots using Kalman filter

<p>This application is filed in 35 USC 119(e) with respect to a U.S. Provisional Patent Application with Application No. 60/588,599, filed July 16, 2004, entitled "Channel Tracking with Scattered Pilots," which is hereby incorporated by reference. claim priority on the basis of </p><p>The present invention relates to wireless digital communication systems, and to estimating channel characteristics and interference level in such systems. </p>

<p>There is an increasing demand for wireless digital communication and data processing systems. Errors inherent in most digital communication channels occur when transferring frames, packets, or cells that contain data. These errors are often caused by electrical interference or thermal noise. Data transmission error rates depend in part on the medium carrying the data. Typical bit error rates for copper-based data transmission systems are 10<sp>-6</sp>exists in the order of Fiber optics are<sp>-9</sp> or less typical bit error rates. On the other hand, wireless communication systems<sp>-3</sp> or higher error rates. The relatively high bit error rates of wireless communication systems cause some difficulties in encoding and decoding data transmitted over these systems. The additive white Gaussian noise (AWGN) model characterizes the noise in most communication channels due in part to its mathematical tractability and in part due to its applicability to a wide variety of physical communication channels. is often used to</p><p>Data is often encoded at the transmitter in a controlled manner to include redundancy. This redundancy is then used by the receiver to overcome noise and interference generated in the data while it is being transmitted over the channel. For example, the transmitter may encode k bits into n bits according to some coding scheme, where n is greater than k. The amount of redundancy provided by the encoding of data is determined by a ratio of n/k, the reciprocal of the ratio n/k being referred to as the code rate. Codewords representing n-bit sequences are generated by an encoder and passed to a modulator that interfaces with a communication channel. A modulator maps each received sequence to a symbol. In M-ary signaling, the modulator maps each n-bit sequence to one of M=2n symbols. Data that is not in binary form may be encoded, but typically data may be represented by a sequence of binary numbers. To perform operations such as channel equalization and channel-sensitive signaling, estimating and tracking a channel is required. </p><p>Orthogonal Frequency Division Modulation (OFDM) is sensitive to time-frequency synchronization. The use of pilot tones allows channel estimation to characterize transmission paths. Keeping the transmitters and receivers synchronized reduces the error rates of the transmission.</p>

<p>In one embodiment, the present invention provides a system configured to estimate and track a channel for radio orthogonal frequency division modulation (OFDM) communications. The system includes first and second modules. The first module is configured to receive a plurality of pilot symbols arbitrarily distributed among a plurality of data symbols transmitted via the at least one transmit antenna. Multiple pilot symbols are received over multiple taps indicating delay and multipath effects of the channel. The second module is configured to estimate a channel value using the plurality of received pilot symbols and according to an iterative correlation of the channel taps over time. The second module performs link scheduling using a channel value.</p><p>In another embodiment, the present invention provides a method for estimating and tracking a channel in a wireless OFDM communication system. In one step, pilot symbols distributed among data symbols transmitted through at least one transmit antenna are received. The pilot symbols are received over multiple taps indicating delay and multipath effects of the channel. The pilot symbols are randomly distributed among at least one temporal or OFDM sub-carrier. The channel value is estimated using a number of received pilot symbols and according to the correlation of the channel taps over time.</p><p>In another embodiment, the present invention provides a system configured to estimate and track a channel for a wireless OFDM communication system. The system comprises receiving means and estimating means. The receiving means receives a plurality of pilot symbols arbitrarily distributed among a plurality of data symbols transmitted via at least one transmit antenna. The pilot symbols are received via taps indicating the delay and multipath effects of the channel. The estimating means estimates the channel value using a plurality of received pilot symbols and according to an iterative correlation of the channel taps over time. A channel includes multiple OFDM sub-channels.</p><p>Additional areas to which the present invention may be applied will become apparent from the detailed description presented hereinafter. The detailed description and specific examples, which provide various embodiments of the invention, are presented for purposes of explanation only and are not necessarily intended to limit the scope of the invention.</p>

<p>The following description presents only the preferred exemplary embodiment(s) and is not intended to limit the scope, applicability or configuration of the present invention. Rather, the following description of the preferred exemplary embodiment(s) will provide those skilled in the art with a description for implementing the preferred exemplary embodiment of the present invention. It should be understood that various modifications may be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims.</p><p>Specific details are set forth in the following description to provide a thorough understanding of these embodiments. However, it will be understood by one of ordinary skill in the art that such embodiments may be practiced without these specific details. For example, circuits may be shown in block diagrams in order not to obscure the embodiments in unnecessary details. In other instances, well-known circuits, processes, algorithms, structures, and techniques will be presented without reference to unnecessary details in order to avoid obscuring the embodiments.</p><p>Further, these embodiments may be described as a process presented as a flowchart, flow diagram, data flow diagram, structure diagram, or block diagram. Although the flowchart describes the operations as a sequential process, many of the operations may be performed in parallel or concurrently. Also, the order of the operations may be rearranged. The process is terminated when the operations of the process are completed, but may include additional steps not included in the figure. A process may correspond to a method, function, procedure, subroutine, subprogram, or the like. If a process corresponds to a function, then the termination of the process corresponds to the return of the function to the calling function or main function.</p><p>Further, embodiments may be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware or microcode, the program code or code segments for performing necessary tasks may be stored in a machine-readable medium such as a storage medium. The processor(s) may perform the necessary tasks. A code segment or computer-executable instructions may represent a procedure, function, subprogram, program, routine, subroutine, module, software package, class, any combination of instructions, data structures, or program statements. A code segment may be coupled to another code segment or a hardware circuit by passing and/or receiving information, data, arguments, parameters, or memory contents. Information, arguments, parameters, data, etc. may be communicated, forwarded, or transmitted via any suitable means including memory sharing, message passing, token passing, network transport, and the like. </p><p>Estimation and tracking of time-varying frequency-selective channels in multi-carrier systems are arbitrary, random, and pseudo-LAN is according to an algorithm using distributed pilot tones in an and/or substantially random time-frequency pattern. is carried out Pilot tones have a known modulation and coding scheme from which the time at which they were transmitted can be determined. The algorithm is based on a linear model that recursively estimates the channel value at any time instance using a previous estimate of the channel along with the received values of the pilot symbols. The channel value is an indicator of a channel, such as a channel quality indicator (CQI), signal-to-noise ratio, signal strength or any other measure of channel sensitive signaling including spatial-selective channel conditions. The algorithm uses a number of parameters representing the channel loading, the ratio of the pilot symbols to the received noise level, and the covariance matrix of the channel estimation error. The algorithm modifies these parameter values and channel estimates until they converge to meet predefined conditions. The channel value is used for link scheduling in one embodiment.</p><p>Pilot tones have a known modulation and coding scheme in which receivers do not necessarily need to know when the pilot tones are being transmitted in order to recognize themselves as pilot tones. Receivers are geographically dispersed throughout the wireless space such that they operate as taps with varying propagation delay and multipath effects from the transmitter. The channel estimate may be iteratively determined based on analysis of taps on the pilot tones. Channel estimation may be used for link scheduling in one embodiment.</p><p>In one embodiment of the present invention, estimation and tracking of a time-varying frequency-selective channel in a multi-carrier system is performed using distributed pilot tones having an arbitrary time-frequency pattern. This channel estimate is an unbiased estimate of the channel, and the covariance matrix of the estimation error defined as the difference between the actual value and the estimated value of the channel has a minimum variance. However, it should be understood that there may be non-substantial variations in these estimates.</p><p>To estimate and track the channel, a linear model is presented, according to which a previous estimate of the channel along with the received values of the pilot symbols at any time instance is used to estimate a new value for the channel. The pilot symbols may be part of a transport protocol that the wireless communication system is configured to conform to, and thus may, for example, be part of a signal field. Alternatively, the pilot symbols may be residual symbols inserted between data symbols for the purpose of estimating the channel.</p><p>In one embodiment, the system may be an OFDMA system, and an initial value assigned to a channel may have a value of 0. The estimation/tracking algorithm is, in part, a first parameter that represents the channel loading and is applied to balance the contribution of the received pilot symbols with a previous estimate of the channel, representing the ratio of the pilot symbols to the received noise. A third parameter obtained by performing a trace operation on the covariance matrix of the estimation error as well as the second parameter is used.</p><p>According to the algorithm of the present invention, the first parameter value and the channel are updated cyclically to arrive at new estimated values. The third parameter value is also updated to reflect the modified value of the first parameter. These modifications continue cyclically until the first parameter, the channel estimate and the third parameter converge to satisfy predefined conditions.</p><p>The algorithm underlying channel estimation/tracking assumes finite support of the time-domain response of the channel and uses a time-domain correlation or approximation of the channel response relative to the known Doppler spectrum of channel changes. The algorithm also accounts for singularities that arise in the initial phase of channel estimation/tracking due to the limited number of pilot symbols used. The algorithm provides a best-effort estimate of channel state information over a limited number of pilot symbols available over the control channels of the OFDMA reverse link. The algorithm may be used for channel sensitive scheduling, such as forward link beamforming, or for frequency sensitive scheduling.</p><p>According to the present invention, estimation and tracking of a time-varying frequency-sensitive channel in a multi-carrier system is performed using distributed pilot tones having an arbitrary time-frequency pattern. Distributed pilots appear in different tones over time and are substantially distributed throughout the band. The channel estimate is substantially an unbiased estimate. Also, the covariance matrix of the estimation error defined as the difference between the actual value and the estimated value of the channel has substantially the smallest variance.</p><p>The algorithms and methods described above may be performed on a per-antenna basis. Accordingly, a channel can be estimated for each antenna. These estimates can be used to obtain a spatial signature or a space-time signature of the channel. The estimates can then be used to provide beamforming, beam steering or other spatial functions.</p><p>The algorithm underlying channel estimation/tracking assumes finite support of the time-domain response of the channel and uses a time-domain correlation or approximation of the channel response relative to the known Doppler spectrum of channel changes. The algorithm also accounts for singularities that arise in the initial phase of channel estimation/tracking due to the limited number of pilot symbols used. The algorithm provides a best-effort estimate of channel state information over a limited number of pilot symbols available over the control channels of the OFDMA reverse link. The algorithm may be used for channel sensitive scheduling, such as forward link beamforming, or for frequency sensitive scheduling.</p><p>1 shows an example of a wireless network 10 used for communication between transmitters/receivers 12, 14 and transmitters/receivers 16, 18 as indicated. Each of the transmitters/receivers 12 , 14 , 16 , 18 may have one or multiple transmit/receive antennas (not shown). Although separate transmit and receive antennas are shown, the antennas may be used for both transmitting and receiving signals. The free space medium forming the transmitted channel of signals is often noisy and affects the received signal. Estimates of the interference level and characteristics of the transmission channel due to noise are often made at the receiver, which exhibits taps. The geographic location in radio space causes the delays for the taps to vary.</p><p>2 is a simplified block diagram of an example of a transmit end of a wireless transmission system 100 . The wireless transmission system is shown to include, in part, an encoder 110 , a space-frequency interleaver 120 , modulators 130 , 160 , OFDM blocks 140 , 170 , and transmit antennas 150 , 180 . has been The modulator 130 , the OFDM block 140 and the transmit antenna 150 are disposed in the first transmit path 115 ; The modulator 160 , the OFDM block 170 and the transmit antenna 180 are disposed in the second transmit path 125 . Although the exemplary embodiment 100 of the wireless transmission system is shown to include only two transmission paths, it is to be understood that the wireless transmission system 100 may include two or more transmission paths. Data transmitted by transmit antennas 150 and 180 are received by one or more receive antennas of a wireless receive system. For example, pilot symbols and data symbols are transmitted on various sub-carriers of an OFDM channel. </p><p>3 is a simplified block diagram of an example of a receiving end of a wireless receiving system P200. The wireless receiving system 200 includes, in part, receive antennas 205 and 255 , front-end blocks 210 , 260 , demodulators 215 , 265 , space-frequency deinterleavers 220 , 270 . and decoders 225 and 285 . Although the wireless reception system 200 is illustrated to include a pair of reception transmission paths, it should be understood that the wireless reception system 200 may include two or more transmission paths. The pilot symbols and data symbols are received by a wireless receiving system 200 . Each transmission path is associated with a specific sub-carrier. Analyzing the pilot symbols repeatedly over time allows to characterize the channel.</p><p>In addition, the estimates may be iteratively performed for each receive chain, e.g., separate estimates for reception at antennas 205 and 255. This allows the channel to be estimated for each spatial channel between the transmitter and receiver. The estimates may be used, eg, combined, to obtain a spatial or temporal signature of a channel from different channels for each antenna. The estimates may then be used to provide beamforming, beam steering, or other spatial functions.</p><p>f<sb>s</sb>Assume OFDM or OFDMA transmission having N orthogonal tones arranged at intervals of . Also, it is assumed that the transmitter transmits the pilot symbols in a specific time frequency pattern known to the receiver as shown in FIG. It is then assumed that the total number N of different pilot tones in the time-frequency pattern is equal to or greater than the number of taps L of the channel, ie, N&gt;=L. This pilot pattern enables baseband channel response estimation with up to L taps. In the following analysis, it is assumed that the effect of excess delay is negligible. In addition, OFDMA symbol interval T<sb>s</sb>=1/f<sb>s</sb> Channel changes during the period are negligible, and the noise is assumed to be AWGN. channel<b>h</b><sb>k</sb>can be expressed by the following equation:</p><p><img file="KR20080098553A_D0001.tif" /></p><p>channel <b>h</b><sb>k</sb>is thus any given time instance t<sb>k</sb>Relative delays for l<sb>1</sb>,...,l<sb>L</sb><sb>-1</sb>It is an L×1 vector of channel taps with . A time instance may represent a channel update phase, one OFDMA symbol interval, a slot or frame interval, and the like. Also, assume that the channel is a time-varying channel with a scalar complex Gaussian first-order channel process, as shown in Equation (1) below:</p><p><maths num="1"><df><img file="KR20080098553A_D0002.tif" /></df></maths></p><p>In Equation (1), <img file="KR20080098553A_D0003.tif" />denotes a complex cyclic Gaussian vector specified by its mean and covariance matrices, respectively, <img file="KR20080098553A_D0004.tif" />Is <img file="KR20080098553A_D0005.tif" /> is the identity matrix. Also, the process r<sb>k</sb>=r(t<sb>k</sb>-t<sb>k-1</sb>) defined as r<sb>k</sb>is stationary during the tracking interval so that α can be obtained from a channel change model, eg, its Doppler spectrum. r<sb>k</sb>is assumed to be known. </p><p>signal x received in step k<sb>k</sb>can thus be defined by the following equation (2):</p><p><maths num="2"><df><img file="KR20080098553A_D0006.tif" /></df></maths></p><p>here, <img file="KR20080098553A_D0007.tif" />denotes the pilot-to-noise ratio, and H[m<sb>k</sb>] is the index m<sb>k</sb>represents the channel frequency response corresponding to the pilot tone with<sb>k</sb>&lt;N), η<sb>k</sb>is the observation noise. The channel frequency response can be re-expressed as:</p><p><maths num="3"><df><img file="KR20080098553A_D0008.tif" /></df></maths></p><p><img file="KR20080098553A_D0009.tif" /></p><p><img file="KR20080098553A_D0010.tif" /></p><p>here, <b>w</b><sb>k</sb>is the index m<sb>k</sb>indicates the direction of the pilot tone with . </p><p>Above, assuming there is one tone per step, then the channel estimate can be updated with only one pilot observation per step, which reduces the complexity of channel estimation/tracking. However, if multiple tones are observed at once, then the same time instance t (eg, t<sb>k</sb>=t<sb>k-1</sb>=...) to be understood that there may be multiple steps corresponding to . Channel Estimation at Step K<img file="KR20080098553A_D0011.tif" />is defined by the following equation:</p><p><img file="KR20080098553A_D0012.tif" /></p><p>Since the channel is assumed to be Gaussian, the channel estimation <img file="KR20080098553A_D0013.tif" />is also Gaussian. According to the present algorithm, the channel estimator is unbiased and has minimal variance. In the most common case, this<img file="KR20080098553A_D0014.tif" />Directions of the pilot tones where the expected value of is used in estimation/tracking through step k <b>w</b><sb>k</sb>The real channel in the subspace expanded to <b>h</b><sb>k</sb>to be consistent with the projection of In the starting stage, this condition ensures that there is no noise in the subspace where there is no channel information available. At steady state, if the present/past pilots are extended to the entire L-order space, this condition gives the following equation:</p><p><img file="KR20080098553A_D0015.tif" /></p><p>Accordingly, the channel estimate can be defined as:</p><p><maths num="4"><df><img file="KR20080098553A_D0016.tif" /></df></maths></p><p>here, <b>P</b><sb>k</sb>is the projection through the subspace magnified in the available pilot directions, as shown below:</p><p><img file="KR20080098553A_D0017.tif" /></p><p><img file="KR20080098553A_D0018.tif" />is the estimation error <img file="KR20080098553A_D0019.tif" />is the covariance matrix of </p><p><img file="KR20080098553A_D0020.tif" />corresponding to and the data tones mΩ<sb>D</sb>The variance of the estimate of the channel response H[m] evaluated at <img file="KR20080098553A_D0021.tif" />is expressed below, and this algorithm is <img file="KR20080098553A_D0022.tif" />Attempts to minimize the mean variance of The following equation (5) applies to a multicarrier system:</p><p><maths num="5"><df><img file="KR20080098553A_D0023.tif" /></df></maths></p><p>The exact equation in equation (5) is the set of data tones Ω<sb>D</sb>A full set of tones Ω<sb>D</sb>={1,...,N}. The asymptotic equivalent of Equation (5) holds when data tones are uniformly distributed over the entire spectrum. Assuming a static channel process in a broad sense with proper design of the time-frequency pilot pattern, estimation/tracking is a stationary step covariance matrix equal to the scaled identity.<img file="KR20080098553A_D0024.tif" />, thus ensuring that the worst-case variance in the normal phase is minimized. </p><p><b>h</b><sb>k</sb>linear estimation of <img file="KR20080098553A_D0025.tif" />is the pilot observation x<sb>k</sb>as well as the estimates obtained in the previous step <img file="KR20080098553A_D0026.tif" />, and is defined by Equation (6) as follows</p><p><maths num="6"><df><img file="KR20080098553A_D0027.tif" /></df></maths></p><p>Using equations (1)-(4), linear estimation <img file="KR20080098553A_D0028.tif" />can be expressed as:</p><p><maths num="7"><df><img file="KR20080098553A_D0029.tif" /></df></maths></p><p>The linear estimate (7) is shown to include equations representing mean and error values. without losing generality<b>A</b><sb>k</sb>is assumed to be full rank. Accordingly<b>A</b><sb>k</sb>can also be defined as:</p><p><maths num="8"><df><img file="KR20080098553A_D0030.tif" /></df></maths></p><p>here, <img file="KR20080098553A_D0031.tif" />denotes the Moore-Penrose pseudo-inverse operator. To further simplify the estimation algorithm, we assume that the class of linear estimators is defined as:</p><p><maths num="9"><df><img file="KR20080098553A_D0032.tif" /></df></maths></p><p>Here, the loading parameters <img file="KR20080098553A_D0033.tif" />is the previous channel estimate <img file="KR20080098553A_D0034.tif" />It is a non-negative scalar that balances the contribution by , and the contribution by the current pilot. This simplification avoids computational complexity. linear estimator<img file="KR20080098553A_D0035.tif" />can thus be expressed as:</p><p><maths num="10"><df><img file="KR20080098553A_D0036.tif" /></df></maths></p><p><img file="KR20080098553A_D0037.tif" />Wow <img file="KR20080098553A_D0038.tif" />The update rules for the resulting estimate accuracy measured by <img file="KR20080098553A_D0039.tif" />is the covariance matrix of the error term in Equation (7), and Tr is the tracking operator. Using equations (1), (2), (4), (7), (9) and (10), the following cycle is obtained:</p><p><maths num="11"><df><img file="KR20080098553A_D0040.tif" /></df></maths></p><p><maths num="12"><df><img file="KR20080098553A_D0041.tif" /></df></maths></p><p>during the starting phase <img file="KR20080098553A_D0042.tif" />To determine the value for , in equation (11) <img file="KR20080098553A_D0043.tif" />Assume that Also, in the starting phase, every pilot tone contributes to a new direction for channel estimation; This requires the following conditions:</p><p><img file="KR20080098553A_D0044.tif" /></p><p><img file="KR20080098553A_D0045.tif" /></p><p>Thus, it leads to the following result:</p><p><maths num="13"><df><img file="KR20080098553A_D0046.tif" /></df></maths></p><p>Equation (13) is the loading parameter <img file="KR20080098553A_D0047.tif" />does not change in relation to single observation (e.g., x<sb>k</sb>) can provide an estimate of a single degree of freedom. In the starting phase, adding additional pilots is an inclusion relationship.<img file="KR20080098553A_D0048.tif" />, which adds an additional direction to the channel estimation. In other words, x<sb>k</sb>The value of is for the entire space <b>P</b><sb>k-1</sb>On a subspace that is the orthogonal complement of <b>w</b><sb>k</sb>is transformed into an estimate of the scaling applied to the orthographic projection of the normalized version of . previous estimate<img file="KR20080098553A_D0049.tif" />go <b>P</b><sb>k</sb><sb>-1</sb>Since it is within the range of , the balance between the contribution of the new pilot and the previous estimate is not affected. this is the loading factor<img file="KR20080098553A_D0050.tif" />to be arbitrarily selected in the starting stage. Especially,<img file="KR20080098553A_D0051.tif" />may be selected to have a relatively small value. <img file="KR20080098553A_D0052.tif" />The advantage of these values for f is the elimination of pseudo-inverse operations, as shown below:</p><p><img file="KR20080098553A_D0053.tif" /></p><p>linear estimator <img file="KR20080098553A_D0054.tif" />can thus be expressed as:</p><p><maths num="14"><df><img file="KR20080098553A_D0055.tif" /></df></maths></p><p>here, loading <img file="KR20080098553A_D0056.tif" />is set to a small value in the starting stage, K=1,...,L. </p><p>The matrix inverse operation of Equation (14) can be efficiently performed due to the matrix inverse transform theorem (lemma). estimator<img file="KR20080098553A_D0057.tif" />The resulting simplified update of m is expressed by the following equation (15), which is used to provide an estimate of the channel and to track the channel:</p><p><maths num="15"><df><img file="KR20080098553A_D0058.tif" /></df></maths></p><p>here, <img file="KR20080098553A_D0059.tif" />am. During the normal phase K&gt;L, the loading factor<img file="KR20080098553A_D0060.tif" /> or equivalent <img file="KR20080098553A_D0061.tif" />The selection of is explained first. After performing the relevant algebra, the analog of equation (13) in the normal phase gives the following cycles:</p><p><maths num="16"><df><img file="KR20080098553A_D0062.tif" /></df></maths></p><p>here,</p><p><maths num="17"><df><img file="KR20080098553A_D0063.tif" /></df></maths></p><p>parameter <img file="KR20080098553A_D0064.tif" />in relation to <img file="KR20080098553A_D0065.tif" />The exact minimization of <img file="KR20080098553A_D0066.tif" />unique structure and projections of <img file="KR20080098553A_D0067.tif" /> and <img file="KR20080098553A_D0068.tif" />complicated by the non-trivial relationship between the structures of As described above, in normal mode,<img file="KR20080098553A_D0069.tif" />should converge to the scaled identity matrix based on the assumptions about the time-frequency structure of the pilot and the static channel process. Through any substantial number of steps, the pilot tones are evenly distributed throughout the signal bandwidth. Specifically, any k<sb>0</sb>For =1,2,... the following conditions apply:</p><p><maths num="18"><df><img file="KR20080098553A_D0070.tif" /></df></maths></p><p>Condition (18) is statistically satisfied when a pseudo-random pilot pattern is used (ie, probability 1). With respect to the channel process, r<sb>k</sb>is fixed as k increases <img file="KR20080098553A_D0071.tif" />It is assumed that convergence to In many cases, r<sb>k</sb>is a constant, i.e. r<sb>k</sb>=r can be assumed. In other cases, for example, in variable update times, r<sb>k</sb>may be variable. </p><p>sequence <img file="KR20080098553A_D0072.tif" />Assume that is a process with a unitary covariance matrix. According to the minimum tracking criterion and update rule (15), any quadratic equation form<img file="KR20080098553A_D0073.tif" />(here, <img file="KR20080098553A_D0074.tif" />=1) can be shown to be a monotonic (non-increasing) sequence with a lower bound of 0. therefore,<img file="KR20080098553A_D0075.tif" />converges to a certain limit. These limits are different<img file="KR20080098553A_D0076.tif" />the same for Two different observations are made. First, a normal stage in the form of<img file="KR20080098553A_D0077.tif" />can be considered for:</p><p><maths num="19"><df><img file="KR20080098553A_D0078.tif" /></df></maths></p><p>This is as shown below <img file="KR20080098553A_D0079.tif" />As an approximate cycle with respect to <img file="KR20080098553A_D0080.tif" />Let it be possible to express the cycle (16) for</p><p><maths num="20"><df><img file="KR20080098553A_D0081.tif" /></df></maths></p><p>or equivalently,</p><p><maths num="21"><df><img file="KR20080098553A_D0082.tif" /></df></maths></p><p>Here, the approximation is required to be accurate at the normal stage. </p><p>so that Equation (21) is a minimum, defined in Equation (17) <img file="KR20080098553A_D0083.tif" />corresponding to <img file="KR20080098553A_D0084.tif" />It is preferable to find almost optimal<img file="KR20080098553A_D0085.tif" />corresponding with <img file="KR20080098553A_D0086.tif" />can be obtained as shown below:</p><p><maths num="22"><df><img file="KR20080098553A_D0087.tif" /></df></maths></p><p><maths num="23"><df><img file="KR20080098553A_D0088.tif" /></df></maths></p><p>The cycles defined by (22)-(23) are factors <img file="KR20080098553A_D0089.tif" />used to update Together with equation (15), this cycle provides estimation and tracking for the channel. Normal phase estimation error<img file="KR20080098553A_D0090.tif" />can be determined by replacing cycle (22) with (23), resulting in:</p><p><maths num="24"><df><img file="KR20080098553A_D0091.tif" /></df></maths></p><p><img file="KR20080098553A_D0092.tif" />Equation (24), which is a quadratic equation for , may have one positive root. A closed form solution to equation (24) may exist. Table I provides a summary of the channel estimation/tracking procedure described above in pseudo-code form:</p><p> table I</p><p><img file="KR20080098553A_D0093.tif" /></p><p>The two parameters specified are <img file="KR20080098553A_D0094.tif" /> and <img file="KR20080098553A_D0095.tif" />am. While ensuring a numerically stable algorithm, relatively large values<img file="KR20080098553A_D0096.tif" />can be selected for<img file="KR20080098553A_D0097.tif" />for a relatively small value). <img file="KR20080098553A_D0098.tif" />The value of α reflects the magnitude of the estimation error at the end of the starting phase. covariance matrix<img file="KR20080098553A_D0099.tif" />may differ from the identity matrix at the end of the starting phase, so that <img file="KR20080098553A_D0100.tif" />the choice of <img file="KR20080098553A_D0101.tif" />are orthogonal and will always be approximate except in some special cases, such as the case where the channel changes in the starting phase can be neglected. For very slow variable channels, the magnitude of the error is<img file="KR20080098553A_D0102.tif" />will be proportional to </p><p>In addition, <img file="KR20080098553A_D0103.tif" />By setting =1, it is possible to select the initial error at the same level as the actual channel. Estimation accuracy at the end of the starting phase depends on the specific sequence of pilots in the starting phase.<img file="KR20080098553A_D0104.tif" />This choice is generally more reliable because it can vary depending on the <img file="KR20080098553A_D0105.tif" />A relatively large value for α will cause the tracking procedure to converge somewhat slowly, and it should be understood that the convergence speed may not be the overriding factor for best-effort acquisition of channel state information. But,<img file="KR20080098553A_D0106.tif" />The optimal choice of a given set <img file="KR20080098553A_D0107.tif" />to understand that it can be provided in </p><p>Table II is a more simplified pseudo-code of Table I. Table II uses normal initialization and does not distinguish between the starting phase and the normal phase. This simplification does not affect the normal phase.</p><p> table II</p><p><img file="KR20080098553A_D0108.tif" /></p><p>A proper characterization of the channel process, shown in equation (24), depends on the Doppler spectrum of the channel changes. Specifically, it is as follows:</p><p><maths num="25"><df><img file="KR20080098553A_D0109.tif" /></df></maths></p><p>here, <img file="KR20080098553A_D0110.tif" />is the power spectral density of channel changes that typically depend on the propagation environment as well as the speed of the mobile terminal. The existing model assumes that it has a uniform azimuth distribution, has a fixed velocity, and is sufficiently distributed near the mobile terminal. The corresponding Doppler spectrum, known as the U-shaped spectrum, is defined as:</p><p><maths num="26"><df><img file="KR20080098553A_D0111.tif" /></df></maths></p><p>here, <img file="KR20080098553A_D0112.tif" />and f<sb>c</sb>is the carrier frequency, v<sb>m</sb>is the mobile speed, c=3·10<sp>8</sp>is m/s. </p><p>Other existing models take a uniform spectrum defined as follows:</p><p><maths num="27"><df><img file="KR20080098553A_D0113.tif" /></df></maths></p><p>The time-frequency pilot pattern used herein is defined by the expression:</p><p><maths num="28"><df><img file="KR20080098553A_D0114.tif" /></df></maths></p><p>This pattern ensures uniform coverage over the entire bandwidth for any finite period of time, thus enabling estimation and tracking for fast variable channels. </p><p>Channel estimation and tracking uses various codes of one or more software modules forming a program, for example executed as instructions/data by a central processing unit, or specifically configured and used exclusively for determining the channel and interference level. This can be done using hardware modules. Alternatively, channel estimation may be performed using a combination of software and hardware modules.</p><p>The foregoing embodiments of the present invention are for illustrative purposes only and are not intended to limit the present invention. Various alternatives and equivalents may exist. The present invention is not limited by the type of encoding, decoding, modulation, demodulation, combining, eigenbeamforming, etc. performed. The invention is not limited by the number of transmitters or receivers. The invention is not limited by the type of integrated circuit in which the invention may be deployed. The present invention is not limited to any particular type of process technology that may be used to fabricate the present invention, such as CMOS, Bipolar or BICMOS. Other additions, subtractions or modifications are obvious in light of the invention and are intended to be made within the scope of the appended claims.</p>