Title of Invention  "A METHOD OF CALIBRATING DOWNLINK AND UPLINK CHANNELS IN A WIRELESS MULTIPLEINPUT MULTIPLEOUTPUT (MIMO) COMMUNICATION SYSTEM" 

Abstract  A method of calibrating downlink and uplink channels in a wireless multipleinput multipleoutput (MIMO) communication system, comprising deriving a first transmit matrix based on a first pilot received via a MIMO channel between a transmitting entity and a receiving entity deriving a second transmit matrix based on a MIMO channel response estimate and first and second calibration error matrices, the MIMO channel response estimate being an estimate of a response of the MIMO channel and derived based on a second pilot received via the MIMO channel, the first calibration error matrix containing estimates of errors in a first correction matrix used to account for responses of transmit and receive chains at the transmitting entity, and the second calibration error matrix containing estimates of errors in a second correction matrix used to account for responses of transmit and receive chains at the receiving entity and revising the first and second calibration error matrices based on the first and second transmit matrices. Fig. 2 
Full Text  The present invention relates to a method of calibrating downlink and uplink channels in a wireless multipleinput multipleoutput (mimo) communication system. Background [0002] A MIMO system employs multiple (NT) transmit antennas and. multiple (NR) receive antennas for data transmission. A MIMO channel formed by the NT transmit antennas and NR receive antennas may be decomposed into Ns spatial channels, where Ns ≤ min {NT, NR}. The Ns spatial channels may be used to transmit data in parallel to achieve higher overall throughput or redundantly to achieve greater reliability. [0003] To achieve high performance, it is often necessary to know the response of the MIMO channel. For example, an access point may need to know the response of a downlink channel in order to perform spatial processing for a downlink transmission to a user terrninal. In one conventional channel estimation technique, the access point transmits a pilot on the downlink, and the user terminal estimates the downlink channel response based on the pilot and sends the downlink channel response estimate back to the access point. This channel estimation technique utilizes uplink resources and further incurs a delay to send back the channel response estimate, both of which are undesirable. [0004] A TDD system uses a single frequency band for bom the downlink and uplink, with the downlink being allocated a portion of the time and the uplink being allocated the remaining portion of the time. For a TDD system, the downlink and uplmk channel responses may be assumed to be reciprocal of one another. That is, if H represents a channel response matrix from antenna array A to antenna array B, then a reciprocal channel implies that the coupling from array B to array' A is given by HT, where HT denotes the transpose of H. With a reciprocal channel, the channel response for one JF link (e.g., the downlink) may be estimated based on a pilot received via the other link (e.g., the uplink). [0005] The access point and user terminal both utilize transmit and receive chains for transmission and reception, respectively. A downlink transmission would then observe an "effective" downlink channel response that includes the responses of the transmit chain at the access point and the receive chain at the user terminal. Correspondingly, an uplink transmission would observe an effective uplink channel response that includes the responses of the transmit chain at the user terminal and the receive chain at the access point. The responses of the transmit and receive chains at the access point are typically different from the responses of the transmit and receive chains at the user terminal. As a result, the effective downlink and uplink channel responses are typically not reciprocal of one another. If the channel response estimate obtained for one link is used for spatial processing for the other link, then any difference in the responses of the transmit/receive chains at the access point and user terminal would represent error that, if not determined and accounted for, may degrade performance. [0006] There is, therefore, a need in the art for techniques to calibrate the downlink and uplink channel responses in a TDD MMO system. SUMMARY [0007] Techniques to calibrate the downlink and uplink channel responses to account for differences in the responses of the transmit and receive chains at the access point and user terminal are described herein. After calibration, a channel response estimate obtained for one link may be used as a channel response estimate for the other link. This can simplify channel estimation and spatial processing. [0008] The calibration may be separated into two parts — initial calibration and follow on calibration. For the initial calibration, the access point and user terminal transmit MMO pilots (described below) on the downlink and uplink, respectively. The MIMO pilots are used to derive "effective" downlink and uplink channel response estimates, H^ and Hup, which include the responses of the applicable transmit/receive chains. The channel estimates H^ and Hup are used to derive correction matrices Kap and Kut, which are thereafter used by the access point and user terminal, respectively, to account for the responses of their transmit/receive chains, as described below. For the followon calibration, one entity (e.g., the access point) transmits a MIMO pilot and a steered reference (described below). The other entity (e.g., the user terminal) derives (1) an "actual received" transmit matrix Va based on the steered reference and (2) a "hypothesized" transmit matrix Vhyp based on the MIMO pilot and calibration error matrices Q and Q . The matrices Q and Q contain guesses or estimates of the errors in the correction matrices Kap and Kut, respectively. The difference between the transmit matrices Va and Vhyp are indicative of the accuracy of the estimates of the errors in the correction matrices. The matrices Qa and Qut maybe adjusted based on an adaptive procedure to minimize the error between Va and Vhyp. Several adaptive procedures to iteratively adjust the matrices Qa and Q are described below. The correction matrices Kap and Kut may thereafter be updated by the calibration error matrices Qa and Qu(, respectively. % [0010] Various aspects and embodiments of the invention are described in further detail below. BRIEF DESCRIPTION OF THE DRAWINGS [0011] FIG. 1 shows the transmit and receive portions at the access point and user terminal in the TDD MIMO system; [0012] FIG. 2 shows the use of the correction matrices at the access point and user terminal to account for their transmit/receive chains; [0013] FIG. 3 shows a process performed by the access point and user terminal for initial calibration, normal operation, and followon calibration; [0014] FIG. 4 shows a minimum mean square error (MMSE) adaptive procedure; [0015] FIG. 5 shows a steepest descent adaptive procedure; and [0016] FIG. 6 shows a block diagram of the access point and user terminal. DETAILED DESCRIPTION [0017] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration," Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. [OC§I] The calibration techniques described herein may be used for singlecarrier as well as multicarrier TDD MMO systems. For clarity, these techniques are described for a singlecarrier TDD MEMO system. [0019] FIG. 1 shows a block diagram of the transmit and receive portions at an access point 110 and a user terminal 150 in a TDD MDVIO system 100. For the downlink, at access point 110, transmit symbols (denoted by a vector Xdn) are processed by a transmit chain 114 and transmitted from Nap antennas 116 and over a wireless MIMO channel having a response of H. At user terminal 150, the Nap downlink signals are received by Nut antennas 152 and processed by a receive chain 154 to obtain received symbols (denoted by a vector r^). The processing by transmit chain 114 typically includes digitaltoanalog conversion, amplification, filtering, frequency upconversion, and so on. The processing by receive chain 154 typically includes frequency downconversion, amplification, filtering, analogtodigital conversion, and so on. [0020] For the uplink, at user terminal 150, transmit symbols (denoted by a vector xup) are processed by a transmit chain 164 and transmitted from Nut antennas 152 and over the MIMO channel. At access point 110, the Nut uplink signals are received by Nap antennas 116 and processed by a receive chain 124 to obtain received symbols (denoted by a vector r^). [0021] For the downlink, the receive vector at the user terminal may be expressed as: rdnRutHTapxdn, Eq(l) where x^ is the vector with Nap transmit symbols sent from Nap access point antennas; r a,, is the vector with Nut received symbols obtained via Nut user terminal antennas; Tap is an Nap x Nap diagonal matrix with Nap complex gains for the access point transmit chain, one complex gain for each access point antenna; Rut is an Nut x Nut diagonal matrix with Nut complex gains for the user terminal receive chain, one complex gain for each user terminal antenna; and H is the Nut x Nap channel response matrix for the downlink. The responses of the transmit/receive chains and the MIMO channel are typically a function of frequency. For simplicity, a flatfading channel with a flat frequency response is assumed. For the uplink, the receive vector at the access point may be expressed as: rup=EapHrTutxup , Eq(2) where x is the vector with Nut transmit symbols sent from Nut user terminal antennas; r^ is the vector with Nap received symbols obtained via Nap access point antennas; Tut is an Nut x Nut diagonal matrix with Nut complex gains for the user terminal transmit chain, one complex gain for each user terminal antenna; Rut is an Nap x Nap diagonal matrix with Nap complex gains for the access point receive chain, one complex gain for each access point antenna; and Hr is the Nap x Nut channel response matrix for the uplink. [0023] From equations (1) and (2), the "effective" downlink and uplink channel responses, H^ and H^ , which include the responses of the applicable transmit and receive chains, may be expressed as: H^BtfSX* and Hup=RapHrTut. Eq(3) Combining the two equations in equation set (3), the following may be obtained: Hup = lut Rut Hdn Tap Rap = Kut H^ Kap or H^ = (K H Kap ) , Eq (4) where K^TR,,, and Kut=T~Rllt. Kap is an NapxNap diagonal matrix for the access point and obtained by a ratio of the receive chain response Rap to the transmit chain response Tap , where the ratio is taken elementbyelement. Similarly, Kut is an Nm xNut diagonal matrix for the user terminal and obtained by a ratio of the receive chain response Rut to the transmit chain response Tut . [0024] Equation (4) may also be expressed as: Hcup = Hup Kut = (HdnKap) = Hcdn > Eq (5) where Hcup denotes the calibrated channel response for the uplink; and Hcdn denotes the calibrated channel response for the downlink. The matrices Kap and Kut include values that account for differences in the transmit/receive chains at the access point and user terminal. The application of the diagonal matrices, Kap and Kut, to the effective downlink and uplink channel responses, as shown in equation (5), allows the calibrated channel response for one link to be expressed by the calibrated channel response for the other link. [0025] Initial calibration may be performed to determine the matrices Kap and Kut. Typically, the true channel response H and the transmit/receive chain responses are not known nor can they be exactly or easily ascertained. Instead, the effective downlink and uplink channel responses, H^ and H^, may be estimated based on MIMO pilots sent on the downlink and uplink, respectively. A MIMO pilot is a pilot comprised of NT pilot transmissions sent from NT transmit antennas, where the pilot transmission from each transmit antenna is identifiable by the receiving entity. This can be achieved, for example, by using a different orthogonal sequence for the pilot transmission from each transmit antenna. Estimates of the matrices Kap and Kut (which are called correction matrices Kap and Kut) may then be derived based on the effective downlink and uplink channel response estimates, H^ and H^, as described below. The matrices Kap and Kut include correction factors that can account for differences in the transmit/receive chains at the access point and user terminal. [0026] FIG. 2 shows the use of the correction matrices Kap and Kut at access point 110 and user terminal 150. On the downlink, the transmit vector x^, is first multiplied with the correction matrix Kap by a unit 112. The subsequent processing by transmit chain 114 and receive chain 154 for the downlink is as described in FIG. 1. Similarly, on the uplink, the transmit vector x^ is first multiplied with the correction matrix Kut by a unit 162. The subsequent processing by transmit chain 164 and a receive chain 124 for the uplink is also as described in FIG. 1. [0027] For a MIMO system, data may be transmitted on NS eigenmodes of a MIMO channel. These eigenmodes may be viewed as orthogonal spatial channels of the MIMO channel. The channel response matrix H may be "diagonalized" to obtain the NS eigenmodes of the MIMO channel. This diagonalization may be achieved by performing either singular value decomposition of H or eigenvalue decomposition of a correlation matrix of H, which is R = HHH, where H" denotes the conjugate transpose of H . [0028] Table 1 shows the effective and calibrated channel responses for the downlink and uplink as well as the singular value decomposition of the calibrated downlink and uplink channel response matrices. Table 1  Singular Value Decomposition (Table Removed) (( In Table 1, Uap is an Nap x Nap unitary matrix of left eigenvectors of Houp, E is an Nap x Nut diagonal matrix of singular values of Hcup, Vut is an Nut x Nut unitary matrix of right eigenvectors of Hcup, and denotes the complex conjugate. A unitary matrix M is characterized by the property M^M = I, where I is the identity matrix. The matrices V*t and U*p are also matrices of left and right eigenvectors, respectively, of HC()n . The matrices V, V, Vr and V" &Q different forms of the matrix V. For simplicity, reference to the matrices Uap and Vut in the following description may also refer to their other forms. The matrices Uap and Vut (which are also called transmit matrices) may be used by the access point and user terminal, respectively, for spatial processing and are denoted as such by their subscripts. The singular value decomposition is described in further detail by Gilbert Strang entitled "Linear Algebra and Its Applications," Second Edition, Academic Press, 1980, which is incorporated herein by reference. [0030] In a practical system, the matrices Hcdn and Hcup are not available. Instead, the user terminal can estimate the calibrated downlink channel response based on a MIMO pilot transmitted by the access point. The user terminal can then perform singular value* decomposition of the calibrated downlink channel response estimate, Hcdn, to obtain a» diagonal matrix E and a matrix Vut of left eigenvectors of Hcdn, where the hat (" A ") above each matrix indicates that it is an estimate of the actual matrix. Similarly, the access point can estimate the calibrated uplink channel response based on a MIMO pilot transmitted by the user terminal. The access point can then perform singular value decomposition of the calibrated uplink channel response estimate, Hcup, to obtain the diagonal matrix 2 and a matrix Uap of left eigenvectors of Hcup. [0031] Because of the reciprocal channel and the calibration, the singular value decomposition only needs to be performed by either the user terminal or the access point to obtain both matrices Vut and Uap. For clarity, the following description is for an implementation whereby the user terminal obtains the calibrated downlink channel response estimate, Hcdn, performs decomposition of Hcdn, uses the matrix Vut for spatial processing, and sends the matrix Uap back to the access point using a steered reference, as described below. A steered reference (or steered pilot) is a pilot that is transmitted from all antennas and on the eigenmodes of the MIMO channel. [0032] The user terminal may transmit an uplink steered reference, as follows: xap,m=Kutvutjmjpm , Eq(6) where pm is a pilot symbol transmitted on eigenmode m for the steered reference; xupm is a transmit vector for the uplink steered reference for eigenmode m; and yutjm is the mth eigenvector or column of Vut, where Vm = [vuU yuu ... yut]Njt ]. [0033] The received uplink steered reference at the access point may be expressed as: Iup,m = Su Eq(7) where r, is a received vector for the uplink steered reference for eigenmode m; crm is the with diagonal element of £ ; and «aP,m is the mth eigenvector or column of Uap , where Uap = [uapi, uap.2 ... uap,Nip] . Equation (7) shows that the received uplink steered reference at the access point, in the absence of noise, is approximately equal to uapm terminal using various estimation techniques. [0034] hi one embodiment, to obtain an estimate of uap m , the received vector r^ m is first multiplied with the complex conjugate of the pilot symbol, or p"m , and then integrated over multiple received steered reference symbols for each eigenmode to obtain a vector f upm , which is an estimate of uap)mom for eigenmode m. Since the eigenvectors have unit power, the singular value am for each eigenmode may be estimated based on the received power of the uplink steered reference for that ** i eigenmode, which is crm =rupm  ). Each of the Nap elements of the estimate of uapm ^ is obtained by dividing a corresponding one of the Nap elements of r^ by am . [0035] In another embodiment, an estimate of uapm is obtained based on the received vector r ^ m and using an MMSE technique. Since the pilot symbols pm are known, the access point can derive the estimate of uap>m such that the mean square error between a received pilot symbol pm (which is obtained after performing the matched filtering on the received vector with vuUl) and the transmitted pilot symbol pm is minimized. [0036] The access point may perform additional processing on the estimates of uap m , for m = 1 .. Ns . For example, since these estimates are obtained for one eigenvector at a time, the Ns eigenvector estimates may not be orthogonal to one another due to, for example, noise in the received steered reference, changes in the MIMO channel response, and so on. The access point may then perform GramSchmidt orthogonalization on the NS eigenvector estimates to obtain orthogonal transmit vectors. A hi any case, the access point obtains a transmit matrix Uap, which is an estimate of Uap, which in turn is derived by the user terminal based on Hcdn. The access point uses the A A transmit matrix Uap to perform spatial processing for downlink transmission. 1. Followon Calibration [0037] The correction matrices Kap and Kut obtained from the initial calibration may contain errors due to various sources such as (1) imperfect channel estimates H^ and Hup used for the initial calibration, (2) changes in the transmit/receive chains at the access point and user terminal, and so on. Errors in the correction matrices cause errors A in both (1) the transmit matrix Vut used by the user terminal for spatial processing and derived from Hcdn and (2) the transmit matrix Uap used by the access point for spatial processing and derived from the uplink steered reference sent using Vut. Improved performance may be obtained if the errors in the correction matrices can be estimated and removed. [0038] The access point and/or the user terminal can perform followon calibration to estimate the errors in the correction matrices Kap and Kut. For clarity, the following description is for followon calibration by the user terminal. For followon calibration by the user terminal, the access point transmits a MMO pilot on the downlink using the correction matrix Kap and also transmits a steered reference on the downlink using thetransmit matrix Uap and the correction matrix Kap. The downlink steered reference may be expressed as: = Kapuap,mjpm, where Uap =[uap1l uap12 ... uap,NJ. The user terminal can obtain an estimate of Y^S7^ based on the received downlink steered reference, similar to that described above for the uplink steered reference. For simplicity, the estimate of V^Z7" derived from the downlink steered reference is called an "actual received" transmit matrix Va, which is an unnormalized matrix that includes an estimate of Vut as well as an estimate of I,. (For clarity, the "~" above a matrix 1 indicates that it is an unnormalized matrix.) The user terminal also obtains another version of Hcdn from the MIMO pilot sent by the access point. •"* A [0039] The errors in the correction matrices Kap and Kut may be represented by diagonal calibration error matrices Qa and Q, respectively. The correction matrices Kap and Kut may then be expressed as: Kap=KapQ:ap and Kut=KutQ_'ut. Eq(8) If the errors in the correction matrices are small, then the diagonal elements of Qa and Qut are complex values close to 1 + y'0. The calibrated downlink channel response estimate, Hcdn, may then be expressed as:  [0040] The matrices Q and Qut contain the "true" errors in Kap and Kut, respectively. A guess or estimate of Q[a and Q^ut may be denoted as Qa and Qut, respectively. A "hypothesized" downlink channel may be defined as: Eq (10) A hypothesized downlink channel is a guess of H^K^ and is derived under the A assumption that the error in the applied correct correction matrix Kap is Qa . If Qa is a perfect guess of Q^a in equation (10) and H is a perfect estimate of Hto in equation (9), then Hhyp =Hcdn and H =Hcup. [0041] The spatial processing at the access point may be expressed as: US = HV=HKV=HKO'V EqCll) where Vut is obtained from the singular value decomposition of Hcdn, which is obtained from the downlink MIMO pilot. The user terminal does not have the value for Q^ap, but only its guess Qa . The user terminal thus computes an unnormalized transmit matrix U^ that hypothetically would have been obtained by the access point if the calibration error matrices were Q and Q . as follows: Equation (12) is equal to equation (11) if Q is a perfect guess of Q' and Q is a perfect guess of Q[M. If this is the case, then Hhyp = HK. [0042] The user terminal then performs processing on Ura in the same manner that the access point would have performed on a received uplink steered reference and obtains a "generated" transmit matrix Ug, which is a normalized transmit matrix that resembles Uap. For example, the access point may perform GramSchmidt orthogonalization of A the received eigenvectors uapm in order to improve the performance of its transmit steering vectors. In this case, the user terminal would perform the same orthogonalization on the eigenvectors in Ura. The user terminal simply emulates the processing that is normally performed by both the access point and the user terminal, albeit under an assumption of calibration errors represented by Qa and Qut. The matrix Ug would have been used by the access point to transmit the downlink steered reference and for spatial processing of downlink transmission. [0043] The spatial processing at the user terminal may be expressed as: V,£j =HcdnUg fiJUH, =SUKapO:apH8 • Eq (13) Again, the user terminal does not have Q , but only its guess Qa . The user terminal thus computes a hypothesized transmit matrix Vhyp for itself as follows: Yhyp=HhypQapUg. Eq(14) 13 Equation (14) is equal to equation (13) if Hhyp is a perfect guess of H^K^ and Qa is a perfect guess of Q . The matrix Vhy is an unnormalized matrix that includes a user terminal transmit matrix Vg (which corresponds to the access point transmit matrix Ug) as well as a diagonal matrix Sg (which resembles S). The matrix Vhyp is hypothesized to have been received by the user terminal with (1) the user terminal transmitting an uplink steered reference using Vut , (2) the access point performing its normal processing on the received uplink steered reference to derive its transmit matrix Ug , (3) the access point transmitting a downlink steered reference using Ug , (4) the correction matrices Kap and Kut having the errors indicated by the matrices Qa and Qut, respectively, and (5) assuming no channel estimation error in Hcdn from the downlink MMO pilot. [0044] Equations (12) and (14) are correct if the calibration error matrices Qa and Qut correctly indicate the true errors in the correction matrices Kap and Kut , respectively. The difference between the actual received transmit matrix Va obtained from the downlink steered reference and the hypothesized transmit matrix Vhyp obtained from the downlink MMO pilot may be computed as follows: where E is an Nut x Nap matrix of errors between Va and Vhyp . The error matrix E gives an indication of the accuracy of the guess for Qa and Qu( . Various adaptive procedures may be used to adjust the matrices Qa and Qut to drive the error matrix E toward zero. Such adaptive procedures include an MMSE adaptive procedure and a steepest descent adaptive procedure. The diagonal elements of Qa and Qut may be initialized to 1 + 7'0 for the adaptive procedures. [0045] For the MMSE adaptive procedure, approximate partial derivatives of the elements of E are computed with respect to the elements of Qa and Q . If the "lead" A element (which is the upper leftmost element) of Kap is set to 1 + jQ by the initial calibration, then this element does not need to be adjusted. In addition, the error matrix E is not affected by the magnitude of the elements in Q . Thus, Qut may be normalized, for example, by defining the real component of the lead element of Q to be 1.0. Furthermore, an eigenvector may be scaled by any unitmagnitude complex number (or rotated by any phase) without affecting its performance. Thus, a set of phases may be selected to make Vhyp close to Va without any loss in generality. This property allows for scaling of Q^ by an arbitrary unitmagnitude factor, so the imaginary component of the lead element of Qut may be defined to be 0.0. [00461 The MMSE adaptive procedure may be performed as follows. Let q be a real vector of length 2(Nap +Nut 2) and made up of the real and imaginary components of the diagonal elements of Qa and Qut , except for the lead elements which are set to 1 .0. The vector q may be defined as: where q is the zth element of q ; Qap 0' 0 IB me z"m diagonal element of Qa ; and Qut(i,f) is the zth diagonal element of Qm . The oddindexed elements of q are for the real component of the diagonal elements of Qa and Qu( , and the evenindexed elements of q are for the imaginary component of the diagonal elements of Qa and Qut . The first 2Nap  2 elements of q are for the Nap —1 diagonal elements other than the lead element of Qo , and the last 2Nut 2 elements of q are for the Nut  1 diagonal elements other than the lead element of Qut . [0047] Let e be a real vector of length 2NapNut and made up of the real and imaginary components of the elements of E . The vector e may be defined as: where ei is the zth element of e; and E(i, j) is the element in the zth row andy'th column of E. The oddindexed elements of e are for the real component of the elements of E, and the evenindexed elements of e are for the imaginary component of the elements of E. The error vector e can be obtained by evaluating equations (10), (12), (14), and (15) with the vector q. [0048] For the MMSE adaptive procedure, the partial derivative of a real or imaginary component of an element in E with respect to a real or imaginary component of an element in Qa or Qut may be generated by perturbing the component of the element in Qa or Qut and computing the function defined by equations (10), (12), (14), and (15). As part of the computation for Vhyp, a single ej* term may be selected such that I Ya ~ ejx" Xhyp \2 ig minimized. This is done to normalize the phase of the lead element ofQ . —but [0049] Approximate partial derivatives of the elements of e with respect to the elements of q may be expressed as: for ; = 1...2(Nap+Nul2) dg, ' and j = 1 ... 2NopN Eq(16) where A ^ is a vector of length 2(Nap + Nut  2) and containing a small real value of 6 for the 7th element and zeros elsewhere; and Aji is the approximate partial derivative of thejth element of e with respect to the zth element of q . The approximate partial derivative Aijt maybe obtained as follows. A vector q; is first computed as q. = q + A, . The function defined by equations (10), (12), and (14) is then evaluated for q. (which contains Qa . and QuU) to obtain a new (or "revised") hypothesized transmit matrix Vhyp,. Vhyp,. is then subtracted from Va to obtain a new error matrix E, = Va  Vhyp,., which is used to form a new error vector e,.. The 7th element of e, which is denoted as ^.(q) in equation (16), is then subtracted from the 7th element of e,., which is denoted as e;(q + A,.) in equation (16). The result of the subtraction is divided by £to obtain A^. [0050] The computation for equations (10), (12), (14), and (15) is performed for each of the 2(Nap + Nut 2) elements of q to obtain a corresponding new error vector e,. For each new error vector e., the 2NapNut elements of e are subtracted from the 2NapNut elements of e,, on an elementbyelement basis, to obtain 2NapNut approximate partial derivatives of the 2NapNut elements of e with respect to the ith element of q. A matrix A of dimension 2NapNut by 2(Nap + Nut  2) may be formed with all of the partial derivatives for all of the elements of e and q. Each column of A contains 2NopNut approximate partial derivatives for the 2NapNut elements of e with respect to one element of q. The 2(Nap + Nut 2) columns of A are for the 2(Nap +NBt2) elements q. [0051] If the relationships in equations (10), (12), (14), and (15) are approximately linear, then an estimate of the difference between the guess of the calibration errors in q and the actual calibration errors may be expressed as: y = A~'e, Eq(17) where y is an update vector for the estimated difference between q and the actual calibration errors. The update vector y has the same format and dimension as the vector q, which is a real vector made up of the real and imaginary components of the diagonal elements of Qa and Qut other than the lead elements. [0052] If A is not a square matrix, which is typically the case, then the simple matrix inverse does not exist. The MoorePenrose pseudoinverse of A may then be used for equation (17). This pseudoinverse is simply a matrix that satisfies the equations AA"1 A = A and A"1 AA"1 = A"1. The pseudoinverse may be generated by performing singular value decomposition of A , which is A = U0DVf , and computing the pseudoinverse as A"1 = U^D"1 Va , where D"1 is a diagonal matrix made up of the inverses of the corresponding nonzero diagonal elements of D . [0053] The matrix A of partial derivatives is computed under an assumption that the function defined by equations (10) through (13) is approximately linear for calibration errors of the size being evaluated. Since the linearity assumption is not completely accurate, the procedure may be iterated multiple times to determine the correct calibration errors. For some cases, the procedure does not converge. However, convergence can generally be achieved by simply selecting a different initial guess for the calibration errors. If convergence is not obtained, the user terminal can also obtain another version of Va and Hcdn based on another estimate of the downlink steered reference and downlink MIMO pilot and perform the MMSE adaptive procedure using these new matrices. [0054] If equations (10), (12), (14), and (15) are linear, then y + q would minimize the mean square of the elements of e . However, since these equations are not linear, q is replaced with y + q and the procedure is repeated. The calibration error vector may then be updated as follows: where n is an index for the iteration number; q (n) is the calibration error vector for the nth iteration; Umntse v ' y(/i) is the update vector obtained for the nth iteration; and q (n + 1) is the calibration error vector for the (n + 1) th iteration. Jmmie ' ' [0055] The computation described above may be repeated for any number of iterations. Each iteration uses the updated calibration error vector q (n + 1) obtained from the r immse v ' prior iteration. The procedure can terminate when the update vector y («) is sufficiently small. For example, the termination condition may be j y (») j 2 = y y, is the zth element of y(n) and ylh2 is another threshold value. After all iterations have been completed, the matrices for the final estimates of calibration errors are denoted as Q , , and Q ~ap,Jinal 2zut,J!nal [00561 For the steepest descent adaptive procedure, an aggregate error may be defined as: The aggregate error, z, is obtained by summing the squares of the magnitude of the elements of E . The partial derivatives of z with respect to the elements of q may be computed as follows: where g. is the approximate partial derivative of z with respect to the zth element of q and A, is a vector of length 2(Nap + Nut  2) and containing a small real value of 8 for the zth element and zeros elsewhere. The approximate partial derivative gt may be obtained as follows. A vector q. is first computed as q. = q + A; . The function defined by equations (10), (12), (14), and (15) is evaluated for q. to obtain a new error vector e, . The aggregate error z, is then computed for the new error vector e, , as shown in equation (19). The aggregate error z obtained with q, which is denoted as z(q) in equation (20), is then subtracted from the aggregate error z, obtained with q. , which is denoted as z(q + A:.) in equation (20). The result of the subtraction is divided by S to obtain g, . The computation is repeated for each of the 2(Nap + Nut  2) elements of q. A vector g of dimension 2(Nap + Nut  2) may be formed with the approximate partial derivates obtained for the 2(Nap +Nut 2) elements of q. Each element of g is the slope of the aggregate error evaluated at a corresponding element of q . [0057] The calibration error vector may then be updated as follows: where g(n) is the slope vector obtained for the iteration, and q (n) and q (n + 1) are the calibration error vectors for the nth and (n + 1) th iterations, respectively, for the steepest descent procedure. The computation described above may be repeated for any number of iterations. Each iteration uses the updated calibration error vector qjrf (n + 1) obtained from the prior iteration. The procedure can terminate when the aggregate error z is sufficiently small, e.g., less then a zth threshold value. [0058] Two adaptive procedures have been described above for deriving estimates of the actual calibration errors. Other adaptive and nonadaptive procedures may also be used, and this is within the scope of the invention. [0059] The user terminal can update its correction matrix to account for the calibration errors, as follows: Eq(22) The user terminal uses the new correction matrix Kutjnew , instead of the prior correction matrix Kut , for spatial processing for uplink transmission, as shown in FIG. 2. The user terminal may send the calibration error matrix Qa to the access point, which may then update its correction matrix as Kapjnev, = KapQ . To reduce the amount of signaling, the user terminal may only send back the calibration error matrix 0" na/ if the matrix meets some predetermined threshold. [0060] FIG. 3 shows a process 300 performed by the access point and user terminal for initial calibration, normal operation, and followon calibration. The access point and user terminal perform initial calibration to calibrate their transmit and receive chains and derive correction matrices Kap and ]£ut (block 310). The initial calibration is described below. [0061] Thereafter, for normal operation, the access point transmits a downlink MTMO pilot using its correction matrix Kap (block 322). The user terminal obtains a calibrated downlink channel response estimate, Hcdn , based on the downlink MDVIO pilot (block 324) and performs singular value decomposition of Hcdn to obtain its transmit matrix Vut (block 326). The user terminal then transmits an uplink steered reference using Vut and Kut, as shown in equation (6) (block 328). The access point receives the uplink steered reference and derives its transmit matrix Uap, as described above (block 330). The access point and user terminal use the transmit matrices Uap and Vut, respectively, for spatial processing. [0062] For the followon calibration, the access point transmits a downlink steered reference using Uap and Kap, and further transmits a downlink MIMO pilot using Kap (block 342). The user terminal derives the actual unnormalized transmit matrix Va based on the downlink steered reference, as described above (block 344). The user terminal also computes the unnormalized transmit matrix TJ^ based on its transmit matrix Vut, the calibrated downlink channel response estimate Hcdn, and the calibration error matrices Qa and Qut, as shown in equations (10) and (12), or Uw =(HcdnCT1)rQutVw (block 346). The user terminal further processes Ura in the same manner as would have been performed by the access point (e.g., perform orthogonalization) to obtain the normalized transmit matrix Ug (block 348). The user terminal then computes the hypothesized unnormalized transmit matrix Vhyp based on the transmit matrix Ug and the calibrated downlink channel response estimate Hcdn, as shown in equations (10) and (14), which is Vhyp =HcdnUg (block 350). The matrix Vhyp is the unnormalized transmit matrix that the user terminal would have received if the access point transmits a downlink steered reference using Ug. The user terminal then revises the calibration error matrices Qa and Qut based on the transmit matrices Va and Vhyp (block 352). Blocks 346 through 352 may be performed using an adaptive procedure. The user terminal may thereafter update its correction matrix Kut with the calibration error matrix Qut (block 354), and the access point may thereafter update its correction matrix Kap with the calibration error matrix Qap (block 356). [0063] FIG. 4 shows an MMSE adaptive procedure 400, which may be used for blocks 346 through 352 in FIG. 3. The hypothesized transmit matrix Vhyp is first computed based on Hcdn and Qa and Qut (block 410). Block 410 corresponds to blocks 346 through 350 in FIG. 3, The error matrix E is next computed as the difference between the transmit matrices Va and Yhyp, as shown in equation (15) (block 412). Partial derivatives for each of the elements in the error matrix E with respect to each of selected ones of the elements (e.g., all diagonal elements except for the lead elements) in the calibration error matrices Q and Q are then derived, as shown in equation Jsap iut * (16) (block 414). The matrix E and the matrices Qa and Qw may be placed in the form of vectors for ease of computation, as described above. The partial derivatives may be derived separately for the real and imaginary components of the elements in the matrices, as also described above. The update vector y is then computed based on the matrix A of partial derivatives and the error matrix E, as shown in equation (17) (block 416). The calibration error matrices Qa and Qut are then updated with the update vector y, as shown in equation (18) (block 418). A determination is next made whether or not the update vector y satisfies a termination condition (block 420). If the answer is 'yes', then process 400 terminates. Otherwise, the process returns to block 410 and performs another iteration. [0064] FIG. 5 shows a steepest descent adaptive procedure 500, which may also be used for blocks 346 through 352 in FIG. 3. The hypothesized transmit matrix Vhyp is first computed based on Hcdn and Qn and Qut (block 510). The aggregate error z is next computed as z Va Vhyp 2, as shown in equation (19) (block 512). Partial derivatives for the aggregate error with respect to each of selected ones of the elements in the calibration error matrices Q and Q are then derived, as shown in equation (20) (block 514). The matrices Qa and Qm may be placed in the form of a vector, and the partial derivatives may be derived separately for the real and imaginary components of the elements in the matrices. The calibration error matrices Qa and Qut are then updated with the partial derivatives, as shown in equation (21) (block 516). A determination is next made whether or not the aggregate error z satisfies a termination condition (block 518). If the answer is 'yes', then process 500 terminates. Otherwise, the process returns to block 510 and performs another iteration. [0065] hi the above description, the user terminal estimates the calibration errors in both the correction matrices Kap and Kut. To simplify the followon calibration, the user terminal can assume that the correction matrix Kap contains no errors and only estimate the errors in the correction matrix Kut. This is equivalent to setting the calibration error matrix Qa to the identity matrix. By omitting Q , the dimensions of the vectors q, y, and g and the matrix A are reduced, which may then greatly reduce the computation. [0066] For clarity, the description above is for the case in which the user terminal performs followon calibration. The access point may also perform the followon calibration. La this case, the access point and user terminal switches role in FIG. 3. The user terminal would then transmit an uplink steered reference and an uplink MIMO pilot, and the access point would perform the computation to derive Qa and Qut. [0067J Also for clarity, the followon calibration is described for a. singlecarrier MIMO system. The followon calibration may also be performed for a multicarrier MIMO system, which may utilize orthogonal frequency division multiplexing (OFDM) or some other multicarrier modulation technique. OFDM effectively partitions the overall system bandwidth into multiple (Np) orthogonal subbands, which are also called tones, subcarriers, bins, and frequency channels. With OFDM, each subband is associated with a respective subcarrier that may be modulated with data. For a MIMO system that utilizes OFDM (an MIMOOFDM system), the computation described above may be performed for each of multiple subbands. Since a high degree of correlation may exist between nearby subbands, the calibration may be performed in a manner to take advantage of this correlation, for example, to reduce the number of subbands to perform followon calibration, to speed up convergence, and so on. 2. Initial Calibration [0068] For the initial calibration to derive the correction matrices Kap and Kut, one entity (either the user terminal or access point) obtains both the effective downlink channel response estimate, VLto, and the effective uplink channel response estimate, H,,,, . The channel estimates H^ and H^ may be obtained based on downlink and uplink MBVIO pilots, respectively. The correction matrices may be computed from H^ and H^ and using matrixratio computation or MMSE computation. [0069] For the matrixratio computation, an Nut xNap matrix C is first computed as: where the ratio is taken elementbyelement. __ ^ [0070] The diagonal elements in the correction matrix Kap for the access point are set equal to the mean of the normalized rows of C . Each row of C is first normalized by scaling each of the Nap elements in that row with the first element in the row. The mean of the normalized rows (denoted by a vector £row ) is then computed as the sum of the Nut normalized rows divided by Nut. The Nap diagonal elements of Kap are then set equal to the Nap elements of jcrow . Because of the normalization, the lead element of Kap is equal to unity. [0071] The diagonal elements in the correction matrix Kut for the user terminal are set equal to the mean of the inverses of the normalized columns of C . Theyth column of C , for j = 1 ... Nap , is first normalized by scaling each element in that column with the _/th diagonal element of Kap . The mean of the inverses of the normalized columns (denoted by a vector £col ) is then computed by (1) taking the inverse of each normalized column, where the inversion is performed elementwise, (2) summing the Nap inverse normalized columns, and (3) dividing each element in the resultant column by Nap to obtain cco, . The Nut diagonal elements of Kut are set equal to the Nut elements of c_col . [0072] For the MMSE computation, the correction matrices Kap and Kut are derived from the effective downlink and uplink channel response estimates, H^ and H^ , such that the mean square error (MSB) between the calibrated downlink and uplink channel responses is minimized. This condition may be expressed as: min (lUlLp)7 "MupKut , which may also be written as: min KapHdn Hup I£ut where Kap = Kap since Kap is a diagonal matrix. A [0073] Equation (24) is subject to the constraint that the lead element of Kap is set equal to unity. Without this constraint, the trivial solution would be obtained with all elements of the matrices Kap and Kut set equal to zero. In equation (24), a matrix Y is first obtained as Y = KapHdnHupKut. The square of the absolute value is next obtained for each of the NapNut elements of Y. The mean square error (or the square error since a divide by NapNut is omitted) is then equal to the sum of all squared values. [0074] The MMSE computation is performed as follows. For simplicity, the elements of Hj,, are denoted as {a..}, the elements of H^ are denoted as {by}, the diagonal elements of Kap are denoted as {».}, and the diagonal elements of Kut are denoted as {Vj}, where f = 1 ... Nap and j = 1 ... Nm. The mean square error may be rewritten from equation (24), as follows: again subject to the constraint . The minimum mean square error may be obtained by taking the partial derivatives of equation (25) with respect to u and v and setting the partial derivatives to zero. The results of these operations are the following equations: Li equation (26a), u, = 1 so there is no partial derivative for this case, and the index i runs from 2 through Nap. [0075] The set of Nap + Nut  1 equations in equation sets (26a) and (26b) may be more conveniently expressed in matrix form, as follows: where (Table Removed) [0076] The matrix B includes Nap+NMl rows, with the first Napl rows corresponding to the Nap 1 equations from equation set (26a) and the last Nut rows corresponding to the Nut equations from equation set (26b). The elements of the matrix B and the vector z may be obtained based on the elements of H and H. The diagonal elements of Kap and Kut are included in the vector k, which may be obtained as: k = B'z . Eq(28) The results of the MMSE computation are correction matrices Kap and Kut that minimize the mean square error in the calibrated downlink and uplink channel responses, as shown in equation (24). 3. Spatial Processing [0077] Table 2 summarizes the spatial processing performed by the user terminal and access point for data transmission and reception on the eigenmodes of the MDVIO channel. (Table Re moved) known a priori by both the access point and user terminal. A TX spatial processor 620 receives the data symbols from TX data processor 610, performs spatial processing on the data symbols, multiplexes in pilot symbols as appropriate (e.g., for channel estimation, calibration, and so on), and provides Nap streams of transmit symbols to Nap modulators (MOD) 622a through 622ap. Each modulator 622 receives and processes a respective transmit symbol stream to obtain a corresponding stream of OFDM symbols, which is further processed by a transmit chain within the modulator to obtain a corresponding downlink modulated signal. Nap downlink modulated signals from modulator 622a through 622ap are then transmitted from Nap antennas 624a through 624ap, respectively. [0079] At user terminal 150, Nut antennas 652a through 652ut receive the transmitted downlink modulated signals, and each antenna provides a received signal to a respective demodulator (DEMOD) 654. Each demodulator 654 (which includes a receive chain) performs processing complementary to that performed at modulator 622 and provides received symbols. A receive (RX) spatial processor 660 then performs receiver spatial processing on the received symbols from all Nut demodulators 654 to obtain detected symbols, which are estimates of the data symbols sent by the access point. For followon calibration, RX spatial processor 660 provides (1) a calibrated downlink channel response estimate, Hcdn, obtained from a downlink MEMO pilot transmitted by the access point and (2) received symbols for a downlink steered reference transmitted by the access point. An RX data processor 670 processes (e.g., symbol demaps, deinterleaves, and decodes) the detected symbols and provides decoded data. The decoded data may include recovered traffic data, signaling, and so on, which are provided to a data sink 672 for storage and/or a controller 680 for further processing. [0080] The processing for the uplink may be the same or different from the processing for the downlink. Data and signaling are processed (e.g., coded, interleaved, and modulated) by a TX data processor 690, and further spatially processed and multiplexed with pilot symbols by TX spatial processor 692 to obtain transmit symbols. The transmit symbols are further processed by modulators 654a through 654ut to obtain Nut uplink modulated signals, which are then transmitted via Nut antennas 652a through 652ut to the access point. User terminal 150 sends back the correction Kap for the initial calibration and may send back the calibration error matrix Q . , for the follow on calibration, for the implementation described above. At access point 1 10, the uplink modulated signals are received by antennas 624, demodulated by demodulators 622, and processed by an RX spatial processor 640 and an RX dataprocessor 642 in a complementary to that performed at the user terminal. RX data processor 642 provides the matrices Kap and Qap to controller 630. [0081] For the initial calibration, the access point and user terminal transmit MIMO pilots on the downlink and uplink, respectively. Each entity derives the effective channel response estimate for its link. One entity (e.g., the access point) sends the channel estimate to the other entity (e.g., the user terminal) for computation of the correction matrices Kap and Kut for both entities. The entity that derives the correction matrices uses its correction matrix and sends the other correction matrix back to the other entity. For the followon calibration, one entity (e.g., the access point) transmits both the steered reference and MEMO pilot. The other derives the calibration error matrices Q .. , and Q . , for both entities based on the received pilots, as described above. The entity that derives the calibration error matrices uses its calibration error matrix and may send the other calibration error matrix back to the other entity (e.g., if the errors are sufficiently large). [0082] Controllers 630 and 680 control the operation of various processing units at the access point and user terminal, respectively. Controllers 630 and/or 680 may also perform processing for the initial and followon calibration (e.g., the computation for the correction matrices Kan and K... and the calibration error matrices Q andQu ). Memory units 632 and 682 store data and program codes used by controllers 630 and 680, respectively. [0083] The calibration techniques described herein may be implemented by various means. For example, these techniques may be implemented in hardware, software, or a combination thereof. For a hardware implementation, the processing units used to perform the initial and/or followon calibration may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, other electronic units designed to perform the functions described herein, or a combination thereof. [008?j For a software implementation, the calibration techniques may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes may be stored in a memory unit (e.g., memory unit 632 or 682 in FIG. 6) and executed by a processor (e.g., controller 630 or 680). The memory unit may be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art. [0085] Headings are included herein for reference and to aid in locating certain sections. These headings are not intended to limit the scope of the concepts described therein under, and these concepts may have applicability in other sections throughout the entire specification. [0086] The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein. We claim: 1. A method of calibrating downlink and uplink, channels in a wireless multiple input multipleoutput (MIMO) communication system, comprising: deriving a first transmit matrix based on a first pilot received via a MIMO channel between a transmitting entity and a receiving entity; deriving a second transmit matrix based on a MIMO channel response estimate and first and second calibration error matrices, the MIMO channel response estimate being an estimate of a response of the MIMO channel and derived based on a second pilot received via the MIMO channel, the first calibration error matrix containing estimates of errors in a first correction matrix used to account for responses of transmit and receive chains at the transmitting entity, and the second calibration error matrix containing estimates of errors in a second correction matrix used to account for responses of transmit and receive chains at the receiving entity; and revising the first and second calibration error matrices based on the first and second transmit matrices. 2. The method of claim 1, wherein the first pilot is a steered pilot received via a plurality of eigenmodes of the MIMO channel. 3. The method of claim 1, wherein the second pilot is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas at the transmitting entity, where the pilot transmission from each transmit antenna is identifiable by the receiving entity. 4. The method of claim 1, wherein the deriving the second transmit matrix comprises decomposing the MIMO channel response estimate to obtain a first matrix of eigenvectors for the MIMO channel, computing a second matrix of eigenvectors for the MIMO channel based on the MIMO channel response estimate and the first and second calibration error matrices, and computing the second transmit matrix based on the second matrix of eigenvectors and the MIMO channel response estimate. 5. The method of claim 4, wherein the deriving the second transmit matrix further comprises processing the second matrix of eigenvectors to obtain a third matrix of eigenvectors, wherein the processing on the second matrix of eigenvectors matches processing performed by the transmitting entity to generate a transmit matrix based on a steered pilot received by the transmitting entity from the receiving entity, and wherein the second transmit matrix is computed based on the third matrix of eigenvectors and the MIMO channel response estimate. 6. The method of claim 5, wherein the processing the second matrix of eigenvectors comprises performing orthogonal ization on the eigenvectors in the second matrix to derive orthogonal eigenvectors for the third matrix. 7. The method of claim 1, wherein the first and second calibration error matrices are revised based on a minimum mean square error (MMSE) adaptive procedure. 8. The method of claim 1, wherein the revising the first and second calibration error matrices comprises computing an error matrix as a difference between the first and second transmit matrices, deriving partial derivatives for elements in the error matrix with respect to selected ones of elements in the first and second calibration error matrices, computing an update vector based on the partial derivatives and the error matrix, and updating the first and second calibration error matrices with the update vector. 9. The method of claim 8, wherein the deriving the partial derivatives comprises deriving a revised second transmit matrix based on the MIMO channel response estimate, the first and second calibration error matrices, and an error vector, computing a revised error matrix as a difference between the first transmit matrix and the revised second transmit matrix, and computing the partial derivatives based on the error matrix and the revised error matrix. 10. The method of claim 8, wherein the error matrix and the first and second calibration error matrices contain complexvalued elements, each complexvalued element having a real component and an imaginary component, and wherein the partial derivatives are derived separately for the real and imaginary components. 11. The method of claim 8, wherein the revising the first and second calibration error matrices further comprises forming a matrix with the partial derivatives, and wherein the update vector is computed based on the error matrix and an inverse of the matrix of the partial derivatives. 12. The method of claim 8, wherein the selected ones of the elements in the first and second calibration error matrices include all diagonal elements, except for upper leftmost elements, in the first and second calibration error matrices. 13. The method of claim 8, wherein the revising the first and second calibration error matrices further comprises repeating the computing the error matrix, deriving the partial derivatives, computing the update vector, and updating the first and second calibration error matrices for a plurality of times until the update vector satisfies a termination condition. 14. The method of claim 1, wherein the first and second calibration error matrices are revised based on a steepest descent adaptive procedure. 15. The method of claim 1, wherein the revising the first and second calibration error matrices comprises computing an error matrix as a difference between the first and second transmit matrices, computing an aggregate error based on the error matrix, deriving partial derivatives for the aggregate error with respect to selected ones of elements in the first and second calibration error matrices, and updating the first and second calibration error matrices with the partial derivatives. 16. The method of claim 15, wherein the aggregate error is computed as a sum of squares of magnitude of elements in the error matrix. 17. The method of claim 15, wherein the revising the first and second calibration error matrices further comprises repeating the computing the error matrix, computing the aggregate error, deriving the partial derivatives, and updating the first and second calibration error matrices for a plurality of times until the aggregate error satisfies a termination condition. 18. The method of claim 1, further comprising: updating the second correction matrix with the second calibration error matrix. 19. The method of claim 1, wherein the first correction matrix is updated with the first calibration error matrix. 20. The method of claim 1, wherein the receiving entity is a user terminal and the transmitting entity is an access point in a time division duplex (TDD) MIMO system. 21. The method of claim 1, wherein the system utilizes orthogonal frequency division multiplexing (OFDM), and wherein a set of first and second calibration error matrices is derived for each of a plurality of subbands based on the first and second pilots received on the subbands. 22. An apparatus in a wireless multipleinput multipleoutput (MIMO) communication system, comprising: means for deriving a first transmit matrix based on a first pilot received via a MIMO channel between a transmitting entity and a receiving entity; means for deriving a second transmit matrix based on a MIMO channel response estimate and first and second calibration error matrices, the MIMO channel response estimate being an estimate of a response of the MIMO channel and derived based on a second pilot received via the MIMO channel, the first calibration error matrix containing estimates of errors in a first correction matrix used to account for responses of transmit and receive chains at the transmitting entity, and the second calibration error matrix containing estimates of errors in a second correction matrix used to account for responses of transmit and receive chains at the receiving entity; and means for revising the first and second calibration error matrices based on the first and second transmit matrices. 23. The apparatus of claim 22, wherein the first pilot is a steered pilot received via a plurality of eigenmodes of the MIMO channel, and wherein the second pilot is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas at the transmitting entity, where the pilot transmission from each transmit antenna is identifiable by the receiving entity. 24. The apparatus of claim 22, further comprising: means for decomposing the MIMO channel response estimate to obtain a first matrix of eigenvectors for the MIMO channel; means for computing a second matrix of eigenvectors for the MIMO channel based on the MIMO channel response estimate and the first and second calibration error matrices; and means for computing the second transmit matrix based on the second matrix of eigenvectors and the MIMO channel response estimate. 25. The apparatus of claim 22, further comprising: means for computing an error matrix as a difference between the first and second transmit matrices; means for deriving partial derivatives for elements in the error matrix with respect to selected ones of elements in the first and second calibration error matrices; means for computing an update vector based on the partial derivatives and the error matrix; means for updating the first and second calibration error matrices with the update vector; and means for repeating the computation of the error matrix, derivation of the partial derivatives, computation of the update vector, and updating of the first and second calibration error matrices for a plurality of times until the update vector satisfies a termination condition. 26. The apparatus of claim 22, further comprising: means for computing an error matrix as a difference between the first and second transmit matrices; means for computing an aggregate error based on the error matrix; means for deriving partial derivatives for the aggregate error with respect to selected ones of elements in the first and second calibration error matrices; means for updating the first and second calibration error matrices with the partial derivatives; and means for repeating the computation of the error matrix, computation of the aggregate error, derivation of the partial derivatives, and updating of the first and second calibration error matrices for a plurality of times until the aggregate error satisfies a termination condition. 27. The method of claim 1, further comprising: performing a first calibration based on downlink and uplink channel response estimates for [[a]] the MIMO channel between a transmitting entity and a receiving entity to obtain the first and second correction matrices and performing a second calibration based on the first and second pilots received via the MIMO channel to obtain the first and second calibration error matrices. 28. The method of claim 27, further comprising: updating the second correction matrix with the second calibration error matrix. 29. The method of claim 27, wherein the first pilot is a steered pilot received via a plurality of eigenmodes of the MIMO channel, and wherein the second pilot is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas at the transmitting entity, where the pilot transmission from each transmit antenna is identifiable by the receiving entity. 30. The method of claim 27, wherein the performing the second calibration comprises deriving the first transmit matrix based on the first pilot, deriving the second transmit matrix based on [[a]] the MIMO channel response estimate obtained from the second pilot, and revising the first and second calibration error matrices based on the first and second transmit matrices. 31. The method of claim 30, wherein the first and second calibration error matrices are revised using an adaptive procedure that iteratively adjusts the first and second calibration error matrices to reduce error between the first and second transmit matrices. 32. The apparatus of claim 22 further comprising: means for performing a first calibration based on downlink and uplink channel response estimates for the MIMO channel between a transmitting entity and a receiving entity to obtain the first and second correction matrices, and means for performing a second calibration based on the first and second pilots received via the MIMO channel to obtain the first and second calibration error matrices. 33. The apparatus of claim 32, wherein the means for performing the second calibration comprises means for deriving the first transmit matrix based on the first pilot, means for deriving the second transmit matrix based on the MIMO channel response estimate obtained from the second pilot, and means for revising the first and second calibration error matrices based on the first and second transmit matrices. 34. The apparatus of claim 33, wherein the first and second calibration error matrices are revised using an adaptive procedure that iteratively adjusts the first and second calibration error matrices to reduce error between the first and second transmit matrices. 

4831DELNP2006Abstract (02032010).pdf
4831DELNP2006Claims (02032010).pdf
4831DELNP2006CorrespondenceOthers (02032010).pdf
4831DELNP2006CorrespondenceOthers (14012010).pdf
4831delnp2006correspondenceothers.pdf
4831DELNP2006Description (Complete) (02032010).pdf
4831delnp2006description (complete).pdf
4831DELNP2006Drawings (02032010).pdf
4831DELNP2006Form1 (02032010).pdf
4831DELNP2006Form16(05122011).pdf
4831DELNP2006Form2 (02032010).pdf
4831DELNP2006Form3 (14012010).pdf
4831DELNP2006GPA (02032010).pdf
4831DELNP2006GPA(05122011).pdf
Patent Number  240318  

Indian Patent Application Number  4831/DELNP/2006  
PG Journal Number  20/2010  
Publication Date  14May2010  
Grant Date  04May2010  
Date of Filing  23Aug2006  
Name of Patentee  QUALCOMM INCORPORATED, a Delaware corporation of 5775 Morehouse Drive, San Diego, California 921211714, United States of America  
Applicant Address  5775 MOREHOUSE DRIVE, SAN DIEGO, CALIFORNIA 921211714, USA.  
Inventors:


PCT International Classification Number  H04L 25/03  
PCT International Application Number  PCT/US2005/005262  
PCT International Filing date  20050218  
PCT Conventions:
