Method and system for joint training sequences design for correlated channel and frequency offsets estimation

Abstract

In distributed communication networks, the signal received at the destination is characterized by unknown multiple carrier frequency offsets (MCFOs) and improper channel state information (CSI). The knowledge of offsets and channel gains are required for coherent deployment of distributed systems. Hence, joint training sequence (TS) design method is proposed for joint estimation of MCFOs and channel estimation over spatially correlated channel. Thus, the present invention provides a method of providing joint estimation for distributed communication systems with multiple antennas at the nodes over spatial correlated channels. The designed optimal training sequences are short length and spectrally efficient. The designed training sequence produces zero cross-correlation, facilitating channel estimation without matrix inversion, significantly lowers the complexity of the estimation algorithm.

Claims

1. A method of generation and utilization of optimal training sequences (TSs) for joint channel and frequency offset estimation in distributed multiple-input multiple-output (DMIMO) orthogonal frequency division multiplexing (OFDM) system over spatially correlated channel in a wireless communication network, wherein said method comprising: sending, by a common central unit (CCU), a predefined TSs to a plurality of source nodes provided with a plurality of antennas; transmitting by the plurality of source nodes, said predefined TSs to a plurality of destination nodes, forming source-destination pair links, and the plurality of destination nodes send a measured received signal strength indicators (RSSI) to said CCU; wherein, said CCU is configured to optimize or allocate power budgets for each transmit-receive antenna pair in each source-destination pair link according to said RSSI, and said CCU selects said optimal training sequences (TSs); wherein said source nodes are configured to transmit OFDM packets to a destination according to said optimal training sequences (TSs).

2. The method as claimed in claim 1, wherein after receiving said predefined TSs, said plurality of destination nodes are configured to estimate channel, calculates channel covariance, noise covariance matrix and measures received signal power (RSSI).

3. The method as claimed in claim 2, wherein said plurality of destination nodes sends RSSI, received signal, channel and noise covariance matrices to the CCU.

4. The method as claimed in claim 1, wherein said CCU defines a threshold on said power budget.

5. The method as claimed in claim 4, wherein said CCU configured to shut down a source-destination pair link if said power budget is less than said threshold.

6. The method as claimed in claim 4, wherein if said power budget is more than said threshold, said CCU configured to generates M.sub.tR numbers of said optimal training sequences (TSs), where M.sub.t defines the number of transmitting antennas and R is the number of source nodes.

7. The method as claimed in claim 6, wherein the CCU broadcasts a look-up table (LUT) containing the updated optimal training sequences, to said source-destination pair and multicast row number of the LUT for next transmission.

8. The method as claimed in claim 6, wherein said CCU multicasts row number of said LUT, node identification number, antenna number and threshold of MSE of channel estimation to each source-destination pair.

9. The method as claimed in claim 8, wherein said source node transmits said OFDM packets to said destination node by using said optimal TSs selected as per said row number as instructed by said CCU.

10. The method as claimed in claim 9, wherein said destination node computes mean square error (MSE) of channel estimation.

11. The method as claimed in claim 10, wherein if said MSE is greater than threshold, said destination node sends RSSI, received signal to the CCU.

12. The method as claimed in claim 1, wherein for the last packet transmission, said destination node configured to update said CCU about a last training sequence used, noise and channel covariance matrices.

13. The method as claimed in claim 1, wherein for generation of said optimal TSs, the CCU computes hybrid Cramer-Rao bound (HCRB) for channel and frequency offset estimation.

14. The method as claimed in claim 13, wherein said HCRB for channel estimation is obtained by computing hybrid information matrix (HIM).

15. The method as claimed in claim 14, wherein said HIM is obtained by taking the addition of expected value of Fisher information matrix (FIM) and prior information matrix (PIM).

16. The method in claim 15, wherein said PIM is obtained from precomputed channel covariance matrix in the destination node which is feedback to said CCU.

17. The method as claimed in claim 14, wherein said HCRB for channel offset estimation is computed by taking the inverse of HIM.sub.hh.

18. The method as claimed in claim 13, wherein said HCRB for frequency offset estimation is obtained from HIM.sub.ee.

19. The method as claimed in claim 13, wherein said CCU computes singular values of the HCRB of channel offset estimation matrix by eigen value decomposition.

20. The method as claimed in claim 13, wherein said CCU computes singular values of HCRB of frequency offset estimation matrix by eigen value decomposition.

21. The method as claimed in claim 13, wherein said CCU computes singular values of channel covariance matrix by eigen value decomposition.

22. The method as claimed in claim 19, wherein the singular values of training sequences are optimized and the optimized singular value of training sequence for channel offset estimation is obtained by minimizing the singular value of HCRB of channel estimation summation over all the antennas according to total power constraint (P) and allocated power constraint for the source-destination link.

23. The method as claimed in claim 22, wherein said optimized singular value of training sequence is obtained from ground and ceiling power levels for each source-destination link, calculated in the CCU.

24. The method as claimed in claim 23, wherein said ground power levels for each link is obtained by of inverse of singular values of the channel covariance matrix.

25. The method as claimed in claim 23, wherein said ceiling power level for each link is obtained by addition of of inverse of singular values of the channel covariance matrix and allotted power budget of the source-destination pair link computed by said CCU.

26. The method as claimed in claim 23, wherein said source-destination link (M.sub.k) is selected for transmission from the set of M.sub.tR (M.sub.kM.sub.tR) such that summation of ground power levels over M.sub.k is less than or equal to the ceiling level of the link.

27. The method as claimed in claim 23, wherein said CCU calculates expected power level by computing: (ceiling power level of k.sup.th path-summation of ground levels over M.sub.k)(ceiling power level of k.sup.th path-summation of ceiling levels over all paths).

28. The method as claimed in claim 23, wherein if expected power level is equal to overall power (P) of the system, said CCU computes the power depth () by the ceiling power level.

29. The method as claimed in claim 19, wherein the optimized singular value of training sequence for frequency offset estimation is obtained by minimizing the singular value of HCRB of MCFO (multiple carrier frequency offsets) estimation summation over all the antennas according to total power constraint (P) and allocated power constraint for the source-destination link.

30. The method as claimed in claim 1, is non-linear, wherein the CCU initializes j and kj to zero.

31. The method as claimed in claim 26, wherein each source-destination link (M.sub.k) is selected such that such that summation of allotted power level for each link over M.sub.k is less than overall power P.

32. The method as claimed in claim 31, wherein the CCU computes two power levels (WL1 and WL2) or each transmit-receive link.

33. The method as claimed in claim 32, wherein one power level (WL1) computed by taking summation of X over t where kj+1tM.sub.k, X is obtained as multiplication of power allotted for each link (p.sub.i) with square root of singular value of channel covariance matrix.

34. The method as claimed in claim 33, wherein second power level (WL2) is computed by following manner (total overall system power-summation of pi over kj+1)(summation of square root of singular value of channel covariance matrix over all links).

35. The method as claimed in claim 32, wherein if WL1 is greater than WL2, the CCU calculates optimal singular value of the training sequence .sub.C,i of TS.

36. The method as claimed in claim 32, wherein if WL1 is less than WL2, the CCU sets kj+1=t and calculates optimal singular value of the training sequence .sub.C,i of TS.

37. The method as claimed in claim 30, wherein if kj+1 is equal to M.sub.k, increase kj to kj+1 and the CCU calculates optimal singular value of the training sequence .sub.C,i of TS.

38. The method as claimed in claim 13, wherein the optimal TS is designed by arranging the computed values diagonally with other entries of matrix zero, wherein the computed values are optimal singular.

39. The method as claimed in claim 13, wherein the generated optimal training sequences are of short length and requires a total transmission time which is twice the transmission time of a single optimal transmission sequence.

40. The method as claimed in claim 1, wherein said optimal training sequence is generated by using a frequency-flat channel.

41. The method as claimed in claim 30, wherein a length of said optimal training sequence is equal to number of transmit antennas which have maximum power content.

42. The method as claimed in claim 1, wherein said optimal training sequence is designed by using each channel path individually for frequency-selective channel.

43. The method as claimed in claim 32, wherein length of said optimal training sequences are equal to number of transmit antennas which have maximum power content multiplied with number of channel paths resulting in minimum length of optimal training sequences.

44. The method as claimed in claim 1, wherein said optimal training sequences of frequency offsets and channel estimation are diagonal which ensures the orthogonality among the training symbols of different transmit antennas.

45. A system for generation and utilization of optimal training sequences (TSs) for joint channel and frequency offset estimation in distributed multiple-input multiple-output (DMIMO) orthogonal frequency division multiplexing (OFDM) system with plurality of antennas over spatially correlated channel in a wireless communication network, wherein said system comprising: a plurality of source nodes, a common central unit (CCU), and a plurality of destination nodes; wherein, said CCU configured to generate a look-up-table (LUT) containing the optimal TSs and broadcast the LUT to said plurality of source nodes and multicast row number of the LUT to source-destination link pair.

46. The system as claimed in claim 45, wherein after receiving information from the CCU, the plurality source nodes adapted to use the sequence of the corresponding row number sent by said CCU.

47. The system as claimed in claim 46, wherein said plurality of source nodes transmit OFDM data payloads along with training sequence to the plurality of destination nodes and said plurality of destination nodes estimate the frequency offset and channel characteristics from the received optimal training sequences.

Description

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

(1) The above and other aspects, features, and advantages of certain exemplary embodiments of the present invention will be more apparent from the following description taken in conjunction with the accompanying drawings in which:

(2) FIG. 1 shows the block diagram of DMIMO communication system, according to one embodiment of present invention.

(3) FIG. 2 shows the structure of packet transmitted with multiple OFDM symbols, according to one embodiment of present invention.

(4) FIG. 3 shows the optimal Training Sequence information multicasted by CCU, according to one embodiment of present invention.

(5) FIG. 4(a) illustration the process flow diagram of the use generated optimal TSs for estimating channel and frequency offsets, and the FIG. 4(b) shows the process flow diagram of training sequence generation, according to one embodiment of present invention.

(6) FIGS. 5A, 5B and 5C show the process flow diagram of the training sequence design method for channel estimation, according to one embodiment of present invention.

(7) FIG. 6 shows process flow diagram of the training sequence design method for frequency synchronization, according to one embodiment of present invention.

(8) FIG. 7 shows the block diagram of channel estimation method, according to one embodiment of present invention.

(9) FIG. 8 shows (a) MSE performance vs. SNR for different TSs for MCFOs estimation, (b) MSE performance vs. SNR for different TSs for channel estimation, according to one embodiment of present invention.

(10) FIG. 9 shows bit error rate vs. SNR for various methods of TSs design, according to one embodiment of present invention.

(11) Persons skilled in the art will appreciate that elements in the figures are illustrated for simplicity and clarity and may have not been drawn to scale. For example, the dimensions of some of the elements in the figure may be exaggerated relative to other elements to help to improve understanding of various exemplary embodiments of the present disclosure. Throughout the drawings, it should be noted that like reference numbers are used to depict the same or similar elements, features, and structures.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

(12) The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of exemplary embodiments of the invention. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary.

(13) Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope of the invention. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness.

(14) The terms and words used in the following description and claims are not limited to the bibliographical meanings, but, are merely used by the inventor to enable a clear and consistent understanding of the invention. Accordingly, it should be apparent to those skilled in the art that the following description of exemplary embodiments of the present invention are provided for illustration purpose only and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.

(15) It is to be understood that the singular forms a, an, and the include plural referents unless the context clearly dictates otherwise.

(16) By the term substantially it is meant that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.

(17) Features that are described and/or illustrated with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments.

(18) It should be emphasized that the term comprises/comprising when used in this specification is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.

(19) The present invention is related to the development of a system and method for joint optimal training sequences design for spatially correlated channel estimation and frequency synchronization in Distributed multi-input multi-output (DMIMO)-OFDM systems.

(20) Distributed multi-input multi-output (DMIMO) OFDM communication systems have a key enabler of small-cell deployment, capacity enhancement. In such network, the signal received at the destination node is characterized by multiple carrier frequency offsets (MCFOs) due to independent oscillators of the transmitting nodes and improper channel state information (CSI) as receiver does not know the channel. Hence, the knowledge of offsets and channel gains are required for coherent deployment of DMIMO-OFDM systems. In this patent, joint training sequence (TSs) design method is proposed for joint estimation of MCFOs and channel estimation over spatially correlated channel. The proposed TSs are short length, hence spectrally efficient.

(21) In one implementation, FIG. 1 shows block diagram of a DMIMO communication system. The transmission system includes transmitting nodes having OFDM modulator with multiple transmit antennas. The receiving system includes synchronizer, equalizer units and OFDM demodulator. The transmitted symbols traverse over multiple paths of the wireless channels and received by the receiving antennas. The received symbols are synchronized, equalized and demodulated to retrieve the original transmitted signal at the receiver end.

(22) In one implementation, FIG. 2 shows the structure of transmitted packet, which consists of preamble, data payloads and guard symbols. The preamble contains training sequence, which helps the receiver to synchronize and equalize the received symbols. Data payload contains the information to be transmitted. Guard symbols may be padded at the end of data payload in order to distinguish between the transmitted packets.

(23) In one implementation, FIG. 3 illustrates the pattern of the optimal TS information multicasted by CCU.

(24) In one implementation, FIGS. 4(a) and (b) shows the method of training sequence generation for training sequence generation. At the beginning of transmission, common central unit (CCU) sends the predefined training sequence (TS) to source. In the next timing instant, source transmits using predefined TS to destination. Destination received the TS, starts estimating channel, calculates channel covariance, noise covariance matrix and measures received signal power (RSSI). In the next time instant, it feeds back RSSI, received signal, channel and noise covariance matrices to CCU. According to the RSSI, CCU determines how much power is assigned on transmit-receive antenna pair in each source-destination link. Considering each source node has same M.sub.t number of transmitting antennas, CCU generates M.sub.tR numbers of training sequences, where R is the number of source nodes. It prepares a look-up-table (LUT) which contains all the generated optimal TSs (initial LUT is prepared with high density of source-destination pair). It broadcast the LUT to all nodes. It multicast node identification number, antenna number corresponding row number of LUT, threshold for mean square error (MSE) of channel estimation to source antenna-destination pair.

(25) In the implementation, the source nodes choose optimally designed TS as the preamble according to the LUT, add data payloads, guard symbols to produce OFDM packet as shown in the FIG. 2 and transmit those packets to the destination node. Destination computes mean square error (MSE) of channel estimation. If computed MSE is greater than predefined threshold received from CCU, then destination again sends RSSI, received signal, channel and noise covariance matrices to CCU. CCU reallocates the power budget for the said source-destination pair. If the computed power budget is less than some threshold, then CCU shuts down the corresponding source-destination path and informs related node about the updated row number and other source-destination pairs, if necessary. After selecting source nodes, OFDM packets transmission starts with the help of optimal training sequences. If the received OFDM packet is last one, then destination updates the CCU about last training sequence used, noise and channel covariance matrices.

(26) (1) Training Sequence Design Method:

(27) In one implementation, FIG. 5 and FIG. 6 shows the TS design method for channel estimation and frequency synchronization. A wireless network with R number of randomly spaced nodes and one destination is considered. Destination has M.sub.r number of antennas. The nodes have M.sub.t number of antennas. Spatial correlation among M.sub.t number of antennas is considered. The proposed DMIMO model is half duplex, i.e. can not transmit and receive simultaneously. The channels between nodes to destination are assumed to be quasi-static Rayleigh faded and constant for N consecutive OFDM training symbols. Each symbol has K number of subcarriers. The correlated channel for r.sup.th node may be modeled as
g.sub.rl=R.sub.rl.sup.1/2g.sub.rwl(R.sub.tl.sup.1/2).sup.T1
where, the elements of g.sub.rwlC.sup.MrMt are uncorrelated independent and identically distributed as CN(0, I). R.sub.rlC.sup.MrMr and R.sup.tlC.sup.MtMt are receive and transmit correlation matrices, respectively. The vector of channel coefficients from r.sup.th node to destination may be represented as h.sub.r=[vec(g.sub.r0), vec(g.sub.r1), . . . , vec(g.sub.r(Lh1))].sup.C.sup.LhMtMr, where, L.sub.h is the length of channel. .sub.r is the frequency offset corresponding to r.sup.th node. Let, for K number of subcarriers, the training sequence is s(k), k=0, 1, . . . , (K1) or equivalently,
S.sub.r=[S(0),S(1), . . . ,S(K1)].sup.TC.sup.KM.sup.t2
S=[S.sub.1. . . S.sub.R]3
Let, M.sub.r(S(k))=[W.sub.K.sup.k,0S.sub.r.sup.T(k) W.sub.K.sup.k,1S.sub.r.sup.T(k) . . . W.sub.K.sup.k, (L.sup.h.sup.1)S.sub.r.sup.T(k)], For K number of subcarriers, the received signal at the destination

(28) $\begin{array}{cc}y={{\left[\left({}_1\right)M_1\left(S_1\right)\mathrm{.Math.}\left({}_R\right)M_R\left(S_R\right)\right]}_{K{L}_h{M}_{t}R}\left[\begin{array}{c}{h}_1\\ \mathrm{.Math.}\\ h_R\end{array}\right]}_{L_h{M}_{t}R1}+n& 4\end{array}$
where, y=[y(0) y(1) . . . y(K1)].sup.T .sup.KM.sup.r, the additive white Gaussian noise (AWGN) noise n=[n(0) . . . n(K1)].sup.T .sup.KM.sup.r with variance .sub.n.sup.2I.sub.KK,
M.sub.r(S.sub.r)=[M.sub.r(s(0))M.sub.r(s(1)) . . . M.sub.r(s(K1))].sup.T=[F.sub.0s F.sub.1s . . . F.sub.L1s].Math.I.sub.M.sub.r.sup.KM.sup.r.sup.L.sup.h.sup.M.sup.t.sup.M.sup.r, F.sub.l=diag{W.sub.K.sup.kl}.sub.k=0,1, . . . , (K1), l=0,1, . . . , (L.sub.h.sub.1) and
(.sub.r)=diag{e.sup.(j2.sup.r.sup.)(0)/K, . . . , e.sup.(j2.sup.r.sup.)(K1)/K}.Math.I.sub.M.sub.r .sup.KM.sup.r.sup.KM.sup.r.

(29) Rewriting Eq. (3) as
y=h+n5
where, =[(.sub.1)M.sub.1(S) . . . (.sub.R)M.sub.R(S)] and h=[h.sub.1 . . . h.sub.R].sup.T. The received signal vector y is circularly symmetric complex Gaussian random variable, i.e., yCN(.sub.y, .sub.y), with mean .sub.y h and covariance matrix .sub.y=.sub.n.sup.2I.sub.K. The parameter vector of interest for joint estimation of frequency offset and frequency-selective complex channel gains is given by
=[Re{h},Im{h}].sup.T6
where, =[.sub.1, . . . , .sub.R].sup.T. The elements of Fisher information matrix (FIM) (Step III in FIG. 5) can be easily obtained by simple manipulation

(30) $\begin{array}{cc}\mathrm{FIM}=\frac{2}{{}_n^2}\left[\begin{array}{ccc}\mathrm{.Math.e}\left({}^H\right)& -\mathrm{��}m\left({}^H\right)& \mathrm{��}m\left({}^H\mathrm{Xh}\right)\\ \mathrm{��}m\left({}^H\right)& \mathrm{.Math.}e\left({}^H\right)& \mathrm{��}m\left({}^H\mathrm{Xh}\right)\\ -\mathrm{��}m\left({}^H\mathrm{Xh}\right)& \mathrm{.Math.}e\left({}^H\mathrm{Xh}\right)& \mathrm{.Math.}e\left(h^H{X}^H\mathrm{Xh}\right)\end{array}\right]& 7\end{array}$
and X are obtained by taking the derivative of y with respect to h and . The hybrid Cramer-Raobound (HCRB) is a lower bound on the joint estimation of random and deterministic parameters and not a function of the random parameters. To ensure generality, frequency offset is assumed to be deterministic and unknown parameters that can assume any value within the specified range. Channel is assumed to be random with zero mean and covariance matrix R.sub.h Gaussian distribution. The first step in determining the HCRB is to formulate the parameter vector of interest [.sub.r .sub.d]. The hybrid information matrix (HIM) (Step VII in FIG. 5) for estimation of the parameter of interest
HIM=E.sub..sub.r.sub.|.sub.d[FIM]+PIM(8)
where, PIM is the prior information matrix of random variable. The expected value of all the elements of FIM w.Math.r.Math.t.sub.r (Step IV in FIG. 5) are found, which results in terms,
E.sub..sub.r{e[h.sup.HX.sup.HXh]}=e[X.sup.HXE(hh.sup.H)]=e[X.sup.HXR.sub.h](9)
and
E.sub..sub.r{m[.sup.HXh]}=E.sub..sub.r[e(.sup.HXh)]=0(10)
Hence,

(31) $\begin{array}{cc}{\mathrm{FIM}}_{\mathrm{ex}}=E_{{}_r|{}_d}\left[\mathrm{FIM}\right]=\left[\begin{array}{ccc}\mathrm{.Math.}e\left({}^H\right)& -\mathrm{��}m\left({}^H\right)& 0\\ \mathrm{��}m\left({}^H\right)& \mathrm{.Math.}e\left({}^H\right)& 0\\ 0& 0& \mathrm{.Math.}e\left(X^H{\mathrm{XR}}_h\right)\end{array}\right]& \left(11\right)\end{array}$
The FIM.sub.ex for the real and imaginary part of channel coefficients are correlated with each other. So,

(32) $\begin{array}{cc}=\left[\begin{array}{cc}2{}^H& 0\\ 0& \mathrm{.Math.}e\left[X^H{\mathrm{XR}}_h\right]\end{array}\right]\left(\mathrm{Step}V\mathrm{in}\mathrm{FIG}.5\right)& \left(12\right)\\ \mathrm{PIM}=\left[\begin{array}{cc}{R}_h^{-1}& 0\\ 0& 0\end{array}\right]\left(\mathrm{Step}\mathrm{VI}\mathrm{in}\mathrm{FIG}.5\right)& \left(13\right)\end{array}$
where, channel correlation matrix

(33) $\begin{array}{cc}{R}_h={\left[\begin{array}{ccc}{R}_{h1}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& R_{\mathrm{hR}}\end{array}\right]}_{L_h{M}_t{\mathrm{RM}}_r{L}_h{M}_t{\mathrm{RM}}_r}& \left(14\right)\end{array}$
Also the correlation matrix of the channel vector h.sub.r corresponding to the r.sup.th node is

(34) $\begin{array}{cc}{R}_{\mathrm{hr}}={\left[\begin{array}{ccc}{R}_{t0}.Math.R_{r0}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& R_{t\left(L_h-1\right)}.Math.R_{r\left(L_h-1\right)}\end{array}\right]}_{L_h{M}_t{M}_r{L}_h{M}_t{M}_r}& \left(15\right)\end{array}$
Hence, HIM is obtained as

(35) $\begin{array}{cc}\mathrm{HIM}=\left[\begin{array}{cc}{\mathrm{HIM}}_{\mathrm{hh}}& 0\\ 0& {\mathrm{HIM}}_{\mathrm{ee}}\end{array}\right]=\left[\begin{array}{cc}2{}^H+R_h^{-1}& 0\\ 0& \mathrm{.Math.}e\left(X^H{\mathrm{XR}}_h\right)\end{array}\right]& \left(16\right)\end{array}$
HCRB for frequency offset (Step VIII in FIG. 5)

(36) $\begin{array}{cc}\mathrm{HCRB}\left(\right)=\frac{{}_n^2}{2}\left[\mathrm{tr}{\left\{\mathrm{.Math.}e\left[X^H{\mathrm{XR}}_h\right]\right\}}^{-1}\right]& \left(17\right)\end{array}$
HCRB for complex channel gains (Step VIII in FIG. 5)

(37) 0$\begin{array}{cc}\mathrm{HCRB}\left(h\right)=\frac{{}_n^2}{2}\left[\mathrm{tr}{\left\{2{}^H+R_h^{-1}\right\}}^{-1}\right]& \left(18\right)\end{array}$
Optimization Framework for Training Sequence Design of Channel Estimation:

(38) In one implementation, optimization framework for training sequence design of channel estimation is disclosed. It is desirable to generate FDM training sequence such that cross correlation between any two training sequences is essentially zero, i.e. S.sup.H F.sub.l.sup.HF.sub.mS=0 when 0lmL.sub.h1. The optimal training sequence design is to find S.sup.KM.sup.t.sup.R that minimizes the objective function HCRB(h), subject to the individual and total power constraint.

(39) Case 1: For frequency-flat channel L.sub.h=1. Suppose, eigenvalue decomposition (Step XII in FIG. 5) of R.sub.t and R.sub.r are R.sub.t=UU.sup.H, R.sub.r=V{tilde over ()}V.sup.H, where, U and V are unitary matrices and =diag(.sub.1, . . . , .sub.M.sub.t.sub.R), {tilde over ()}=diag(v.sub.1, . . . , v.sub.M.sub.r), respectively. Suppose,

(40) $a_i=\frac{1}{M_r}{}_i\underset{i=1}{\overset{M_{}}{.Math.}}{v}_j.$
For any positive definite matrix .sup.H, the diagonal elements are considered. diag{.sup.H}=diag(.sub.C,1, .sub.C,2, . . . , .sub.C,M.sub.t.sub.R). Hence, the optimization problem is equivalent to

(41) $\begin{array}{cc}P1\text{:}{}_{{}_{C,i}}^{\min }\underset{i=1}{\overset{M_{t}R}{.Math.}}\frac{1}{\frac{1}{a_i}+2{}_{c,i}}\mathrm{Subject}\mathrm{to}\underset{m_t=0}{\overset{M_t}{.Math.}}{}_{C,i}P,o{}_{C,i}{p}_i\left(\mathrm{Step}\mathrm{IX}\mathrm{in}\mathrm{FIG}.5\right)& \left(19\right)\end{array}$

(42) Case II: For frequency selective channel, the diagonal elements of R.sub.t,l, R.sub.r,l for l.sup.th channel path are .sub.l=diag(.sub.l1, . . . , .sub.lM.sub.t.sub.R) and {tilde over ()}=diag(v.sub.l1, . . . , v.sub.lM.sub.r), respectively. Suppose,

(43) $a_{\mathrm{li}}=\frac{1}{M_r}{}_i\underset{j=1}{\overset{M_r}{.Math.}}{v}_j.$
For l.sup.th channel path and the positive definite matrix .sup.H, the optimal solution is obtained when the singular values are diagonally aligned. i.e. {tilde over (Z)}=diag (.sub.C,1, .sub.C,2, . . . , .sub.C,M.sub.t.sub.RM.sub.r). Hence, the optimization problem is equivalent to

(44) $\begin{array}{cc}P2\text{:}{}_{{}_{C,i}}^{\min }\underset{l=0}{\overset{L_h-1}{.Math.}}\underset{i=1}{\overset{M_{t}R}{.Math.}}\frac{1}{\frac{1}{{\mathrm{al}}_i}+2{}_{C,i}}\mathrm{Subject}\mathrm{to}\underset{m_t=0}{\overset{M_t}{.Math.}}{}_{C,i}P,o{}_{C,i}{p}_i\left(\mathrm{Step}X\mathrm{in}\mathrm{FIG}.5\right)& \left(20\right)\end{array}$
A method of generating the training sequence for frequency-selective channel can be obtained from Eq. (19). Therefore, the CCU calculates the ground, ceiling power level, and .sub.C,k for each l.sup.th channel coefficients according to the algorithm stated below. Repeat the algorithm for l.sub.h number of times.
Obtained Training Sequence for Channel Estimation:

(45) In one implementation, the process of generating training sequence is described in FIG. 5. A method of generating and using the training sequence can be obtained from the Eq. (18). The CCU first calculates ground level of power already present in each node-to-destination path

(46) $\frac{1}{a_1}\mathrm{.Math.}\frac{1}{2a_{M_{t}R}}$
(Step XIII in FIG. 5). Again, it calculates ceiling power level

(47) $\left(\frac{1}{2a_k}+p_k\right)$
of k.sup.th patch (step XIV in FIG. 5). Then, it calculates the expected power level (Step XVII in FIG. 5) as

(48) $\begin{array}{cc}{E}_k=\underset{i=1}{\overset{M_k}{.Math.}}\left(\frac{1}{2a_k}+p_k-\frac{1}{2a_i}\right)-\underset{i=1}{\overset{k-1}{.Math.}}\left(\left(\frac{1}{2a_k}+p_k\right)-\left(\frac{1}{2a_i}+p_i\right)\right)& \left(21\right)\end{array}$
where, M.sub.k is such that

(49) $\frac{1}{2a_M}\frac{1}{2a_k}+p_k$
(Step XVI in FIG. 5). If E.sub.k=P, it calculates

(50) $=\frac{1}{2a_k}+p_k$
(Step XVIII in FIG. 5). The power level required for transmission k.sup.th patch is =

(51) 0$\frac{1}{}.$
If E.sub.k=P, calculate using,

(52) $\begin{array}{cc}\underset{i=k}{\overset{M_k}{.Math.}}\max \left\{0,-\frac{1}{\sqrt{2}{a}_i}\right\}=P-\underset{i=1}{\overset{k-1}{.Math.}}{p}_i\left(\mathrm{Step}\mathrm{XX}\mathrm{in}\mathrm{figure}5\right)& \left(22\right)\end{array}$
If the ceiling level is less than , then the corresponding k.sup.th patch is saturated (Step XXI in FIG. 5). No more power can be poured in that patch. The particular patch is shut down from data transmission for that time instance. Otherwise, the remaining amount of power will be distributed with a depth of into the other patches (Step XXII in FIG. 5). The diagonal elements of training sequence can be calculated using the value of as

(53) $\begin{array}{cc}{}_{c,k}=-\frac{1}{2a_k}\left(\mathrm{Step}\mathrm{XXIII}\mathrm{in}\mathrm{figure}5\right)& \left(23\right)\end{array}$
If E.sub.k<P, calculate the optimum M.sub.k for k=(k+1).sup.th patch. Repeat the above stated algorithm to get the optimum training sequences.
Optimization Framework for Training Sequence Design of Frequency Synchronization:

(54) Case I: For frequency-flat channel L.sub.h=1. Suppose, eigenvalue decomposition (Step XXVII in FIG. 5) of R.sub.t and R.sub.r are R.sub.t=UU.sup.H, R.sub.r=V{tilde over ()}V.sup.H, where, U and V are unitary matrices and =diag(.sub.1, . . . , .sub.M.sub.t.sub.R), {tilde over ()}=diag(v.sub.1, . . . , V.sub.M.sub.r), respectively. Suppose,

(55) $a_i=\frac{1}{M_r}{}_i\underset{j=1}{\overset{M_r}{.Math.}}{v}_{\mathrm{ji}}.$
For any positive definite matrix .sup.H, the diagonal elements are considered. Diag{.sup.H}=diag(.sub.C,1, .sub.C,2, . . . , .sub.C,MtR). Optimal .sub.C,i (Step VIII in FIG. 5) can be found from

(56) $\begin{array}{cc}P1\text{:}\underset{{}_{C,i}}{\min }\underset{i=1}{\overset{M_{t}R}{.Math.}}\frac{1}{{}_{C,i}{a}_i}\mathrm{Subject}\mathrm{to}\underset{i=1}{\overset{M_{t}R}{.Math.}}{}_{C,i}P,o{}_{C,i}{p}_{i}i=1,\mathrm{.Math.},M_{t}R\left(\mathrm{Step}\mathrm{IX}\mathrm{in}\mathrm{figure}5\right)& \left(24\right)\end{array}$

(57) Case II: For frequency selective channel, the diagonal elements of R.sub.t,l, R.sub.r,l for l.sup.th channel path are .sub.l=diag(.sub.l1, . . . , .sub.lM.sub.t.sub.R), {tilde over ()}=diag(v.sub.l1, . . . , v.sub.lM.sub.r), respectively. Suppose,

(58) $a_{l,i}=\frac{1}{M_r}{}_i\underset{j=1}{\overset{M_r}{.Math.}}{v}_j.$
For l.sup.th channel path and the positive definite matrix .sup.H, the optimal solution is obtained when the singular values are diagonally aligned. i.e. {tilde over (Z)}=diag(.sub.C,1, .sub.C,2, . . . , .sub.C,M.sub.t.sub.R). Hence, the optimization problem is equivalent to

(59) $\begin{array}{cc}P2\text{:}\underset{{}_{C,i}}{\min }\underset{l=0}{\overset{L_h-1}{.Math.}}\underset{i=1}{\overset{M_{t}R}{.Math.}}\frac{1}{{}_{C,i}{a}_{\mathrm{li}}}\mathrm{Subject}\mathrm{to}\underset{i=1}{\overset{M_{t}R}{.Math.}}{}_{C,i}Po{}_{C,i}{p}_{i}i=1,\mathrm{.Math.},M_{t}R\left(\mathrm{Step}X\mathrm{in}\mathrm{figure}5\right)& \left(25\right)\end{array}$
Obtained Training Sequence for Frequency Synchronization:
In one implementation, the process of generating training sequence for frequency synchronization is described as shown in FIG. 6. The CCU first initialize the values of j, k.sub.j to 0 (Step XXVIII in FIG. 6). For k.sub.j+1tM.sub.k calculate two power levels WL.sub.1=.sub.i=k.sub.j.sub.+1.sup.tp.sub.i{square root over (a.sub.i)} (Step XXIX in FIG. 6) and WL.sub.2=(P.sub.i=1.sup.k.sup.jp.sub.i) (.sub.i=k.sub.j.sub.+1.sup.M.sup.t.sup.R{square root over (a.sub.i)}) (Step XXX in FIG. 6). If the power level WL.sub.2 is lowest, CCU calculates .sub.C,k (Step XXXIV in FIG. 6) using

(60) $\begin{array}{cc}{}_{C,k}=\frac{1}{\sqrt{a_k}}\left(P-\underset{i=1}{\overset{k_j}{.Math.}}{p}_i\right)\left(\underset{i=k_j+1}{\overset{M_k}{.Math.}}\sqrt{a_i}\right)\mathrm{for}{k}_j+1k{M}_t& \left(26\right)\end{array}$
Otherwise, if WL.sub.1 gives the lowest power level, set k.sub.j+1=t (Step XXXI in FIG. 6), and Calculate

(61) $\begin{array}{cc}{}_{C,k}=\frac{1}{\sqrt{a_k}}\left(P-\underset{i=k_j+1}{\overset{k_{j+1}}{.Math.}}{p}_i\sqrt{a_i}\right)\mathrm{for}{k}_j+1k{k}_{j+1}\left(\mathrm{Step}\mathrm{XXXII}\mathrm{in}\mathrm{figure}6\right)& \left(27\right)\end{array}$
If k.sub.j+1=M.sub.t then set j=j+1, and again CCU calculates .sub.C,k using Eq. (25). Otherwise set j=j+1, and repeat the training sequence generation process again (Step XXXIII in FIG. 6). There are M.sub.tR number of paths with a depth of

(62) $\frac{1}{a_k}.$
A total P amount of power has been poured into all paths. The power levels of all paths will increase simultaneously. If the power level of any path reaches its maximum value, then no power has poured into this path. The remaining amount of power will be distributed into other paths. The final power level of each path is described by the value of .sub.C,k.
After generating the singular values .sub.C,k, the training sequence can be recovered back from Z by

(63) 0$\begin{array}{cc}S=Q_K\left[\begin{array}{c}{Z}^{\frac{1}{2}}\\ 0_{\left(K-M_{t}R\right)M_{t}R}\end{array}\right]\left(\mathrm{Step}\mathrm{XXIV}\mathrm{in}\mathrm{figure}5\right)\mathrm{and}\left(\mathrm{Step}\mathrm{XXXV}\mathrm{in}\mathrm{figure}6\right)& \left(28\right)\end{array}$
with unitary matrix Q.sub.K.sup.KK. A further advantage in designing training sequences according above stated technique is that, S.sup.HF.sub.l.sup.HF.sub.mS=0 when 0lmL.sub.h1. This ensures the orthogonality between the training sequences. A joint estimator estimating various impairments (MCFOs and channel gains) using these training sequences and can effectively attain theoretical lower bound. Accordingly, such sets of training symbols can enable estimator in achieving theoretical bound.

(64) In one implementation, a system for estimation of channel and frequency offsets, after getting the optimum training sequence is disclosed. CCU prepares a look-up-table (LUT) which contains all the generated optimal TSs. CCU broadcast the LUT to all nodes and multicast row number of LUT to source antenna-destination pair. After receiving that information from CCU, source nodes use the sequence of the corresponding row number, which is sent by CCU. Node antennas transmit OFDM data payloads along with training sequence. The receiver estimates the frequency offset and channel characteristics from the received training sequences.

(65) After getting the optimum training sequence, the receiver uses those sequences to estimate the channel and frequency offsets. FIG. 7 describes the block diagram of MCFOs and channel estimation. Hence, the parameters to be estimated are =[, h]. The RF section transform RF waves to baseband signal, which in turn fed to Inverse fast Fourier transform (IFFT) block. It converts the frequency domain signal to time domain signal, which is termed as incomplete data set. The complete data set is also generated by using the received optimal training sequence and the estimated channel characteristics obtained from previous time instance in the block named as complete data set generator. The complete data set for r.sup.th transmitting node is described by
z.sub.r=(.sub.r)M.sub.r(S.sub.r)h.sub.r+w.sub.r(29)
The log-likelihood generator generates a log-likelihood function (LLF) which in turn fed to expectation block. The expectation of the LLF given the parameters to be estimated, is given as
N(|{circumflex over ()}.sup.[m])E{log f(z|)|y,{circumflex over ()}.sup.[m]}(30)

(66) The maximization block provides an output of at the (m+1).sup.th step, which can be written as

(67) $\begin{array}{cc}{\hat{}}^{\left[m+1\right]}=\arg \underset{}{\min }{.Math.{\hat{z}}^{\left[m\right]}-\underset{r=1}{\overset{R}{.Math.}}\left({}_r\right)M_r\left(S_r\right)h_r.Math.}^2& \left(31\right)\end{array}$
The updated MCFOs {circumflex over ()}.sup.[m+1] is obtained as

(68) $\begin{array}{cc}{\hat{}}_r^{\left[m+1\right]}=\arg \underset{}{\max }\left[z_r^H{h\left({}^H\right)}^{-1}{}^H{h}^H{z}_r\right]& \left(32\right)\end{array}$
where, =.sub.r=1.sup.R(.sub.r)M.sub.r(S.sub.r) The updated channel coefficient .sup.[m+1] is obtained as
.sub.r.sup.[m+1]=(.sup.H).sup.1.sup.Hz.sub.r(33)

(69) Destination calculates MSE for frequency offset and channel gains. If computed MSE for channel estimation is greater than predefined threshold received from CCU, then destination again sends RSSI and received signal. CCU reallocates the power budget for the said source-destination pair. If the computed power budget is less than some threshold, then CCU shuts down the corresponding source-destination path and informs related node about the updated row number and other source destination pairs, if necessary.

(70) Performance Analysis

(71) In one exemplary implementation, simulation results are presented in order to evaluate the performance of proposed system and methods. Without loss of generality, it is assumed that

(72) ${}_w^2=\frac{1}{\mathrm{SNR}}.$
Normalized frequency offset at the destination, .sub.m.sub.t.sup.RD is assumed to be uniformly distributed over the range of (0.5, 0.5). Assuming uniform antenna array, the Kronecker correlation matrix model is adopted. A channel with a length of L.sub.h=5 is considered. Performance metric of the proposed estimators is evaluated by means of their respective MSE and BER. Three transmitting nodes each equipped with two antennas following the DF protocol send decoded data to the destination. Other simulation parameters are listed in the Table 1.

(73) TABLE-US-00001 TABLE 1 Zadoff-Chu Orthogonal Training sequences sequence Length of orthogonal TS 64 Channel Length (L.sub.h) 5 Threshold () 0.001 Fr. Offset range (u: Unif. distn.) u (0.5, 0.5) LTE Band Number 23 Bandwidth 20 MHz Centre Frequency 2190 MHz No. of OFDM symbols 7 FFT Size 2048 No. of data Subcarriers/OFDM 1200 CP Length 144 Subcarrier Spacing 15 KHz

(74) In one implementation, the MSE for the estimation of a parameter, timing offset, is defined as the average MSE over 1000 simulations, i.e. .sub.frane=1.sup.100.sub.ro=1.sup.10({circumflex over ()}.sub.r).sup.2/1000. FIG. 8 shows the performance of the proposed TS. The HCRBs for frequency offsets and channel gains estimation with proposed optimum designed TSs results in 1.5 dB and 5 dB SNR improvement when compared with the HCRBs with orthogonal TSs (like Zadoff-Chu sequence), respectively as shown in FIGS. 8a and 8b respectively. The SAGE estimator performance for joint estimation of MCFOs and channel gains with designed optimum TSs closely match with the HCRBs of optimum TSs. Further, the BER performance of the DMIMO-OFDM system with proposed optimal TSs is estimated. Quadrature phase shift keying (QPSK) constellation is used for the transmission of information.

(75) In one implementation, FIG. 9 shows BER performance with optimum sequence. For comparison, BER for perfect channel and MCFOs estimation is provided. The BER performance of DMIMO-OFDM system with optimum TSs improves by 2 dB SNR gain than that of orthogonal TSs.

(76) Some of the noteworthy features of the present invention are: A method of providing joint estimation for DMIMO-OFDM system with multiple antennas at the nodes over spatial correlated channels. The training sequence design depends on optimal selection of two power constraints, (a) total power of the whole system, (b) individual power constraint over each transmitting nodes. These two power budgets are controlled by one common central unit (CCU). The designed optimal training sequences are of short length and require two second transmission time only, hence they are spectrally efficient. In one aspect, training sequence is designed by considering the frequency-flat channel. The length of said training sequence is equal to number of transmit antennas which have maximum power content. In other aspect, training sequence is designed by considering each channel path individually for frequency-selective channel. The length of said training sequence is equal to number of transmit antennas which have maximum power content multiplied with number of channel paths. The designed training sequence invokes zero cross-correlation as a property resulting in estimation of channel without any matrix inversion, which significantly lowers the complexity of the estimation algorithm. The optimal training sequences of frequency offsets and channel estimation are diagonal which preserves the orthogonality between all transmit antennas in order to avoid false estimation. The designed optimal training sequences are applicable for collocated as well as distributed antenna system. A Method of generating optimal training sequences for joint estimation of MCFOs and channel estimation in DMIMO systems with OFDM modulation over spatially correlated channel with individual and overall power constraint is presented in this patent. The optimal training sequence is short length, hence spectrally efficient. Low complexity in hardware is required in generation of TSs. The constraints on the power in generation further ensures its applicability in energy efficient communication systems. The training sequences are diagonal which ensures the orthogonality among the training symbols of different transmit antennas resulting in reduced false estimation. This results in proper estimation following perfect equalization and detection steps.

(77) Some of the non-limiting advantages of the present invention are: The method of training sequence design is optimal for joint frequency offset and channel estimation over spatially correlated channel. The method of training sequence design is optimal for collocated and distributed communication systems with multiple antenna node structure. The intelligent DMIMO system employing distributed antenna system (DAS) indicates a leap to large scale antenna system (LSAS) if the number of nodes can be made scalable. This method of TS design may also applicable to LSAS. The optimal training sequence is of short length. The developed training sequence design method requires less power consumption. Proposed sequence is power efficient in terms of hardware implementation at the receiver. The method of optimal TS generation disclosed in the present invention enables fast update of TSs based on dynamic change in networks. The developed method of optimal TS generation is equally logically applicable for highly mobile environment, i.e. nodes of the system are mobile. Time domain training sequence design method, disclosed in the present invention, effectively reduces the interference between training sequence and information bearing signal. The common central unit (CCU) has a control over the power budget of the DMIMO-OFDM systems. The method of generating training sequences ensures the cross-correlation between any two set of training sequences is essentially zero. The zero cross-correlation ensures the orthogonality between any set of training sequences that reduces false estimation.

(78) Although a system and a method for optimal training sequence generation for joint channel and frequency offsets estimation in DMIMO-OFDM systems have been described in language specific to structural features, it is to be understood that the embodiments disclosed in the above section are not necessarily limited to the specific methods or devices described herein. Rather, the specific features are disclosed as examples of implementations of the system and method for optimal training sequence generation for joint channel and frequency offsets estimation in DMIMO-OFDM systems.