Title of Invention  A METHOD TO DETECT DATA TRANSMITTED FROM MULTIPLE ANTENNAS AND SYSTEM THEREOF 

Abstract  A method to detect data transmitted from multiple antennas, said method comprising steps of: selecting a starting data block and calling it as previous data block; defining a set of indices of bits to be checked for possible flip in the previous data block as a check candidate set; applying update rule to obtain updated data block using the previous data block and the check candidate set, wherein the update is made in such a manner that change in likelihood is positive; checking if the updated data block and several consecutive previous data blocks are the same; if yes, declare the updated data block as the detected data block; if no, make updated data block as previous data block and repeat updation of data block. Figure 14 
Full Text  FIELD OF INVENTION The present invention relates to large Multipleinput multipleoutput (MIMO) systems, where by 'large' we mean large number of transmit and receive antennas of the order of tens to thousands. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. For example, in a VBLAST system, increased number of transmit antennas means increased data rate without bandwidth increase. However, two major bottlenecks in realizing such large MIMO systems are i) physical placement of such a large number of antennas in communication terminals; for small terminal sizes, this would require a high carrier frequency operation, i.e., small carrier wavelengths for A/2 separation to ensure independence between antennas, and ii) lack of practical lowcomplexity detectors for such large systems. The latter problem is addressed in this invention. BACKGROUND OF PRESENT INVENTION AND PRIOR ART Multipleinput multipleoutput (MIMO) systems with multiple antennas at both transmitter and receiver sides have become very popular owing to the several advantages they promise to offer, including transmit diversity and spatial multiplexing [l][3]. It is known that the MIMO channels have a capacity that grows linearly with the minimum of the number of antennas on the transmitter and receiver sides [4][6], A key component of a MIMO system is the MIMO detector at the receiver, whose job is to recover the symbols that are transmitted simultaneously from multiple transmitting antennas. In practical applications, the MIMO detector is often the bottleneck for both performance and complexity. MIMO detectors including sphere decoder and several of its variants [8][13] achieve nearML performance at the cost of high complexity. Other well known detectors including ZF (zero forcing), MMSE (minimum mean square error), and ZF/MMSESIC (ZF/MMSE with successive interference cancellation) detectors [14] are attractive from a complexity view point, but achieve relatively poor performance. Maximum number of transmit and receive antennas for which the performance of MIMO detectors have been reported in the literature so far is only in the range of 10 to 20 (e.g., 16 antennas for sphere decoder [8] and 12 antennas for ZFSIC [15]). The ZFLAS detector for VBLAST is shown to achieve the following gains compared to the well known VBLAST detector (i.e., the ZFSIC detector with ordering) under signal tonoise ratios (SNR) and bit error rates (BER) of interest: i) for moderate number of antennas (e.g., about 30 antennas), ZFLAS achieves complexity gain compared to ZF SIC, and ii) for large number of antennas, ZFLAS achieves both complexity gain as well as bit error performance gain compared to ZFSIC. The achieved complexity gain significantly increases with increasing number of antennas due to the average perbit complexity of 0(NtNr) for ZFLAS versus perbit complexity of 0(N2t Nr) for ZFSIC. The fact that we could show the simulation points of uncoded BER up to 105 in V BLAST systems with several hundreds of antennas demonstrates the ZFLAS detector's fantastic lowcomplexity attribute (which other known detectors have not been shown to possess). For large Nt, ZFLAS not only has lesser complexity but also achieves much better diversity than ZFSIC, which is a significant and interesting result. This practical detection feasibility could potentially trigger wide interest in the theory and implementation of large MIMO systems. Interestingly, even for a nearterm practical system like 8> References [1] A. Paulraj, R. Nabar, and D. Gore, Introduction to SpaceTime Wireless Communications, Cambridge University Press, 2003. [2] H. Jafarkhani, SpaceTime Coding: Theory and Practice, Cambridge University Press, 2005. [3] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005. [4] G. J. Foschini, "Layered spacetime architecture for wireless communication in a fading environment when using multielement antennas," Bell Labs Tech. Jl., vol. 1, pp. 4159, August 1996. [5] G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Pers. Commun., vol. 6, pp. 311335, March 1998. [6] E. Teletar, "Capacity of multiantenna Gaussian channels," Eur. Trans. Telecomm., vol. 10, no. 6, pp. 585595, November 1999. [7] G. J. Foschini, "Layered spacetime architecture for wireless communication in a fading environment when using multielement antennas," Bell Labs Tech. Jl., vol. 1, pp. 4159, 1996. [8] E. Viterbo and J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 16391242, July 1999. [9] B. Hassibi and H. Vikalo, "On the spheredecoding algorithm I. Expected complexity," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 28062818, August 2005. [10] H. Vikalo and B. Hassibi, "On the spheredecoding algorithm II. Generalizations, secondorder statistics, and applications to communications," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 28192834, August 2005. [11] W. Zhao and G. Giannakis, "Sphere decoding algorithms with improved radius search," IEEE Trans. Commun, vol. 53, no. 7, pp. 11041109, July 2005. [12] H. D. Zhu, B. FarhangBoroujeny, and R.R. Chen, "On the performance of sphere decoding and Markov chain Monte Carlo detection methods," IEEE Signal Proc. Letters, vol. 12, no. 10, pp. 669672, October 2005. [13] L. Azzam and E. Ayanoglu, "Reduced complexity sphere decoding for square QAM via a new lattice representation," arXiv:0705.2435vl [cs.IT] 16 May 2007. [14] S. Verdu, Multiuser Detection, Cambridge University Press, 1998. [15] P. W. Woliniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, "VBLAST: An architecture for realizing very high data rates over the richscattering wireless channel," Proc. ISSSE, pp. 295300, SeptemberOctober 1998. [16] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky, "Detection algorithm and initial laboratory results using VBLAST spacetime communication architecture," Electron. Lett., vol. 35, no. 1, pp. 1416, January 1999. [17] Y.T. Zhou, R. Chellappa, A. Vaid, and B. K. Jenkins, "Image restoration using a neural network," IEEE Trans, on Acoust., Speech, Signal Process., vol. 36, no. 7, pp. 11411151, July 1988. [18] Y. Sun, J.G. Li, and S.Y. Yu, Improvement on performance of modified Hopfield neural network for image restoration," IEEE Trans, on Image Process., vol. 4, no. 5, pp. 688692, May 1995. [19] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction  Part I: Algorithms and simulations," IEEE Trans, on Signal Process., vol. 48, no. 7, pp. 21052118, July 2000. [20] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction  Part II: Performance analysis," IEEE Trans, on Signal Process., vol. 48, no. 7, pp. 21192131, July 2000. [21] Y. Sun, "Eliminatinghighesterror and fastestmetricdescent criteria and iterative algorithms for bit synchronous CDMA multiuser detection," Proc. IEEE ICC'98, pp. 15761580, June, 1998. [22] Y. Sun, "A family of linear complexity likelihood ascent search detectors for CDMA multiuser detection," Proc. IEEE 6th Intl. Symp. on Spread Spectrum Tech. & App., September 2000. [23] L. Hanzo, LL. Yang, EL. Kuan, and K. Yen, Single and Multicarrier DSCDMA: Multiuser Detection, SpaceTime Spreading, Synchronization and Standards, IEEE Press, 2003. [24] S. Manohar, V. Tikiya, R. Annavajjala, and A. Chockalingam, "BERoptimal linear parallel interference cancellation for multicarrier DSCDMA in Rayleigh fading," IEEE Trans. Commun., to appear in June 2007 issue. [25] B. FarhangBoroujeny, H. D. Zhu, and Z. Shi, "Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems," IEEE Trans, on Sig. Process., vol. 54, no. 5, pp. 18961908,May 2006. [26] B. A. Sethuraman, B. Sundar Rajan and V. Shashidhar, "Fulldiversity, highrate spacetime block codes from division algebras," IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2596 2616, October 2003. [27] IEEE C802.16e04/532r3, Pilot allocations for 5, 6, 7, and 8 BS antennas, IEEE 802.16 Broadband Wireless Access Working Group, 20041112. OBJECTS OF INVENTION The principle objective of the present invention is to develop a method to detect data transmitted from multiple antennas. Another objective of the invention is selecting a starting data block and calling it as previous data block; Another objective of the invention is defining a set of indices of bits to be checked for possible flip in the previous data block as a check candidate set; Another objective of the invention is applying update rule to obtain updated data block using the previous data block and the check candidate set, wherein the update is made in such a manner that change in likelihood is positive; Another objective of the invention is checking if the updated data block and several consecutive previous data blocks are the same; if yes, declare the updated data block as the detected data block; if no, make updated data block as previous data block and repeat updation of previous data block. Another main objective of the present invention is to develop a MIMO system. Another objective of the invention is to develop multiple transmit antennas for data transmission. Another objective of the invention is to develop multiple receive antennas for data reception. Another objective of the invention is to develop a data detector using ZF/MF/MMSE/RVLAS (zeroforcing/matched filter/minimum mean square error/random vector likelihood ascent search) to detect transmitted data, and Another objective of the invention is to develop a data detector which uses output data block from any known detector as the starting data block. STATEMENT OF INVENTION Accordingly the invention provides a method to detect data transmitted from multiple antennas, said method comprising steps of: (i) selecting a starting data block and calling it as previous data block; (ii) defining a set of indices of bits to be checked for possible flip in the previous data block as a check candidate set; (iii) applying update rule to obtain updated data block using the previous data block and the check candidate set, wherein the update is made in such a manner that change in likelihood is positive; (iv) checking if the updated data block and several consecutive previous data blocks are the same; if yes, declare the updated data block as the detected data block; if no, make updated data block as previous data block and go to step (ii). There is also provided a MIMO system comprising: multiple transmit antennas for data transmission, multiple receive antennas for data reception, a data detector using ZF/MF/MMSE/RVLAS (zero forcing/matched filter/minimum mean square error/random vector likelihood ascent search) to detect transmitted data, and a data detector which uses output data block from any known detector as the starting data block. BRIEF DESCRIPTION OF ACCOMPANYING DRAWINGS Figure 1: shows uncoded BER performance for ZFLAS detector for i) 10 x 10, ii) 10 x 11, and iii) 10x12 VBLAST systems. 10 bps/Hz spectral efficiency. Figure 2: shows uncoded BER performance of ZFLAS detector as a function of number of transmit/receive antennas (Nt = Nr) for VBLAST at an average SNR = 20 dB. jV, bps/Hz spectral efficiency. Figure 3: shows uncoded BER performance of ZFLAS versus ZFSIC as a function of average SNR for a 200 x 200 VBLAST system. 200 bps/Hz spectral efficiency. ZFLAS achieves higher order diversity than ZFSIC at a much lesser complexity. Figure 4: shows uncoded BER performance of ZFLAS for VBLAST as a function of average SNR for different values of N=Nr . Bps/Hz spectral efficiency. Figure 5: shows average SNR required to achieve a target uncoded BER of 10~3 in V BLAST for different values of Nt = Nr. ZFLAS versus ZFSIC. Figure 6: shows coded BER performance of ZFLAS as a function of Eb/No for a 8x 8 V BLAST system with rate1/2 turbo code and 4QAM. Spectral efficiency: 8 bps/Hz for coded system and 16 bps/Hz for uncoded system. Number of turbo decoding iterations = 1,2,3. Figure 7: shoes coded BER performance of ZFLAS as a function of Eb/NO for a 15 x 15 V BLAST system with rate1/3 turbo code and 4QAM. Spectral efficiency: 10 bps/Hz for coded system and 30 bps/Hz for uncoded system. Number of turbo decoding iterations = 1,2,3. Figure 8: shows coded BER performance of ZFLAS for a 4 x 4 highrate spacetime block code from Division Algebra. Rate4 STBC, rate1/3 turbo code, 4QAM. Number of turbo decoding iterations = 1,2,3. Figure 9: shows BER performance of ZFLAS and MFLAS detectors as a function of average SNR for single carrier CDMA in Rayleigh fading. M = 1, K = 200, N = 300, i.e., a = 2/3. Figure 10: shows BER performance of ZFLAS and MFLAS detectors as a function of number of users, K, for single carrier CDMA (M = 1) in Rayleigh fading for a fixed a = 2/3 and average SNR = 15 dB. N varied from 15 to 1500. Figure 11: shows BER performance of ZFLAS and MFLAS detectors as a function of average SNR for multicarrier CDMA in Rayleigh fading. M = 1,2,4, a = 1, K = 100, MN= 100. Figure 12: shows BER performance of ZFLAS and MFLAS detectors as a function of loading fading factor, a , for multicarrier CDMA in Rayleigh fading. M = 4, K = 30, N varied from 300 to 5, average SNR = 8 dB. Figure 13: shows bit flip rate of LAS operation as a function of number of users, K, for different values of average SNR and a for M = 1. Figure 14: shows a MIMO system DETAILED DESCRIPTION OF THE INVENTION ZFLAS Detector for VBLAST [We adopt the following notation throughout the document. Vectors are denoted by boldface lowercase letters, and matrices are denoted by boldface uppercase letters. [,]T, * , and [,]H denote transpose, conjugate, and conjugate transpose operations, respectively. !R{a} and 3{a} denote the real and imaginary parts of a] The primary embodiment of the invention is a method to detect data transmitted from multiple antennas, said method comprising steps of: i. selecting a starting data block and calling it as previous data block; ii. defining a set of indices of bits to be checked for possible flip in the previous data block as a check candidate set; iii. applying update rule to obtain updated data block using the previous data block and the check candidate set, wherein the update is made in such a manner that change in likelihood is positive; iv. checking if the updated data block and several consecutive previous data blocks are the same; if yes, declare the updated data block as the detected data block; if no, make updated data block as previous data block and go to step ii. In yet another embodiment of the present invention the starting data block is either a random data block or an output data block from known detectors. In still another embodiment of the present invention the sequence of check candidate set is chosen such that the bits are checked for possible flip in an order. In still another embodiment of the present invention the order is circular or random. In still another embodiment of the present invention the method provides for checking of multiple bits for possible flip. In still another embodiment of the present invention the method of defining update rule comprise steps of; i. making kth bit +1 in (n+1 )th step data block if kth bit of the nth step data block is 1 and gradient of likelihood function corresponding to the kth bit in the nth step data block is greater than a threshold corresponding to the kth bit in the nth step data block; ii. making kth bit 1 in (n+l)th step data block if kth bit of the nth step data block is +1 and gradient of likelihood function corresponding to the kth bit in the nth step data block is less than a threshold corresponding to the kth bit in the nth step; and iii. if conditions in (i) and (ii) are not satisfied the kth bit in (n+l)th step data block is kept same as kth bit value in the nth step data block. In still another embodiment of the present invention the antennas in range of tens to thousands are used to transmit and to receive the data. In still another embodiment of the present invention signals transmitted from the antennas occupy same transmission bandwidth using same modulation format of either BPSK or QPSK. In still another embodiment of the present invention the method provides for low complexity detection with linear or quadratic complexity in multiple number of antennas. In still another embodiment of the present invention the method provides for near maximumlikelihood (ML) performance for multiple antennas in the range of tens to thousands. In still another embodiment of the present invention the method provides for spectral efficiencies of the order of tens to thousands of bps/Hz. In still another embodiment of the present invention the method provides for spatial processing gain equal to the number of transmit antennas by exploiting the spatial dimensions without expanding the transmission bandwidth. In still another embodiment of the present invention the method provides for reduction in Eb/No (Bit energy to noise spectral density ratio) by a factor of the number of transmit antennas without expanding the transmission bandwidth. In still another embodiment of the present invention the method employs the data transmissions using higher order modulation format selected from a group comprising M ary Quadrature Amplitude Modulation (MQAM), Mary Pulse Amplitude Modulation (MPAM) and Mary Phase Shift Keying (MPSK). In still another embodiment of the present invention the method detects data symbols transmitted from multiple transmit antennas using MIMO technique selected from a group comprising SpaceTime Block Coding (STBC) and VBLAST. In still another embodiment of the present invention the method provides for detection in distributed/cooperative MIMO systems and networks with multiple number of cooperating nodes. In still another embodiment of the present invention the method provides for detection in Ultrawide band (UWB) systems with multiple users, multiple channel taps and multiple subcarriers. In still another embodiment of the present invention the method provides for detection in underwater acoustic communications with multiple nodes deployed to sense and send information. In still another embodiment of the present invention the method provides for detection in multiuser OFDM and MIMOOFDM systems with multiple subcarriers. In still another embodiment of the present invention the method provides for detection in outercoded MIMO systems with outcode selected form group comprising turbo coding, LDPC coding, convolutional coding and block coding. Another main embodiment of the present invention is a MIMO system comprising: i. multiple transmit antennas for data transmission, ii. multiple receive antennas for data reception iii. a data detector using ZF/MF/MMSE/RVLAS (zeroforcing/matched filter/minimum mean square error/random vector likelihood ascent search) to detect transmitted data, and iv. a data detector which uses output data block from any known detector as the starting data block. In yet another embodiment of the present invention the antennas are ranging from tens to thousands in number. In still another embodiment of the present invention the system employs MIMO technique selected from a group comprising SpaceTime Block Coding (STBC) and V BLAST. In still another embodiment of the present invention the system provides for low complexity detection with linear or quadratic complexity in multiple number of antennas. In still another embodiment of the present invention the system provides for near maximumlikelihood (ML) performance for multiple antennas in the range of tens to thousands. In still another embodiment of the present invention the system provides for spectral efficiencies of the order of tens to thousands of bps/Hz. In still another embodiment of the present invention the system provides spatial processing gain equal to the number of transmit antennas by exploiting the spatial dimensions without expanding the transmission bandwidth. In still another embodiment of the present invention the system provides for reduction in Eb/No (Energy per bit to noise spectral density ratio) by a factor of the number of transmit antennas without expanding the transmission bandwidth. In still another embodiment of the present invention the system employs the data transmissions using higher order modulation format selected from a group comprising M ary Quadrature Amplitude Modulation(MQAM), Mary Pulse Amplitude Modulation (MPAM) and Mary Phase Shift Keying (MPSK). In still another embodiment of the present invention the system provides for detection in outercoded MIMO systems with outercode selected from a group comprising turbo coding, LDPC coding, convolutional coding and block coding. Specifically, the invention provides for a lowcomplexity detector for large MIMO systems, including VBLAST as well as highrate, nonorthogonal spacetime block codes (STBC). We show that this detector, termed as ZFLAS (zeroforcing likelihood ascent search) MIMO detector, is much superior to other detectors in terms of both complexity as well as performance with large number of antennas. The ZFLAS MIMO detector in instant invention has its roots in past work on Hopfield neural network (HNN) based algorithms for image restoration [17][20], which are meant to handle large digital images (e.g., 512x512 image with 262144 pixels). In [21],[22], Sun applied his HNN based image restoration algorithms in [18][20] to multiuser detection (MUD) in CDMA systems on AWGN channels. This detector, referred to as the likelihood ascent search (LAS) detector, essentially searches out a sequence of bit vectors with monotonic likelihood ascent and converges to a fixed point in finite number of steps [21],[22]. The power of the LAS detector for CDMA lies in i) its linear average perbit complexity in number of users, and ii) its ability to perform very close to Maximum likelihood (ML) detector for large number of users, which other suboptimum multiuser detectors do not possess [21],[22]. Taking the cue from LAS detector's complexity and performance superiority in large systems, we, in this invention, successfully adopt the LAS detector for large MIMO systems  both for VBLAST as well as STBC systems [1],[2]  and report interesting results. While the adoption of HNN algorithms to CDMA MUD by Sun is a powerful development in MUD research, our contribution in this invention is a powerful development in MIMO detection. We also adopt the LAS detector for multicarrier (MC) CDMA in Rayleigh fading. We have carried out extensive simulations and evaluated the bit error performance and complexity of the ZFLAS detector for large i) VBLAST systems, ii) highrate, nonorthogonal STBCs, and iii) MC CDMA systems. Advantages of instant invention: • In terms of complexity and performance: The ZFLAS detector has a significant complexity advantage over the well known VBLAST detector (i.e., ZFSIC with ordering, we use the term 'ZFSIC' to always refer 'ZFSIC with ordering') Specifically, •y ZFSIC has a complexity of 0(N t Nr), whereas ZFLAS has a complexity of only 0(NtNr), where Nt and Nr denote the number of transmit and receive antennas, respectively. This complexity advantage has great impact for large Nt, i.e., ZFLAS allows practical detection of VBLAST signals even for large number of antennas (of the order of thousands). The fact that we could show the simulation points of uncoded BER up to 10~5 in VBLAST systems with several hundreds of antennas demonstrates the ZF LAS detector's fantastic lowcomplexity attribute (which other known detectors have not been shown to possess). For large Nt, ZFLAS not only has lesser complexity but also achieves much better diversity than ZFSIC, which is a significant and interesting result. This practical detection feasibility could potentially trigger wide interest in the theory and implementation of large MIMO systems. • In terms of nearterm applicability: Interestingly, even for a more nearterm practical system like 8x8 VBLAST system with 4QAM and rate1/2 outer turbo code (i.e., 8 bps/Hz spectral efficiency), ZFLAS achieves a BER of 10~4 at an Eb/No (Energy per bit to noise spectral density ratio) of 6 dB with 3 turbo decoding iterations. Likewise, a 15 x 15 VBLAST system with 4QAM and rate1/3 outer turbo code (i.e., 10 bps/Hz spectral efficiency), ZFLAS achieves a BER of 10~5 at an Eb/No of just 3 dB with 3 turbo decoding iterations. The complexity involved with achieving similar performances using the well known ZFSIC detector is comparatively very large. • We show that ZFLAS is effective in decoding highrate, nonorthogonal STBCs as well. A 4 x 4s rate4 STBC [26] (i.e., 16 symbols sent in 4 time slots using 4 transmit antennas) with rate1/3 turbo code is shown to achieve a BER of 10~4 at an Eb/No of about 5 dB using ZFLAS and just 2 turbo decoding iterations. • In MC CDMA, ZFLAS detection achieves good performance for greater than one loading factors, whereas other MUDs including ZF/MMSE, PIC/SIC achieve relatively poor performance at such loading factors. With its superiority in performance and complexity for large number of users, MFLAS can be a powerful approach to MUD implementations in practical CDMA systems. In this section, we present the ZFLAS detector for VBLAST, its complexity and performance. Consider a VBLAST system with Nt transmit antennas and Nr receive antennas, Nt > Nr, where Nt symbols are transmitted from Nt transmit antennas simultaneously. Let bkc {+1,1} be the symbol transmitted by the kth transmit antenna. Each transmitted symbol goes through the wireless channel to arrive at each of Nr receive antennas. Denote the path gain from transmit antenna j to receive antenna k by h k e l,2...,7V,.), V/ e {1,2,..., A^,}, are assumed to be i.i.d. complex Gaussian r.v's (i.e., fade amplitudes are Rayleigh distributed) with zero mean and E (h'kj )  E (hk/ j =0.5, where h and hk/ are the real and imaginary parts of hk/ . The noise sample at the kth receive antenna, nk, is assumed to be complex Gaussian with zero mean, and [nk], k = 1, 2, • • • , Nr, are assumed to be independent with E [n] J = N0 = , where Es is the average power of the transmitted symbols, X and is the average receive SNR per receive antenna. Compactly2, collecting the received signals from all receive antennas, we write y = HI) + 11. R>) where y= [^^...^A^,. ]' is the Nr length received signal vector, b = [b]b2...bNl]r is the Nr length transmitted bit vector (bit vector is also represented as data block), H denotes the NrxN, channel matrix with channel coefficients {hk/ }, and n = \n^n2...nNrJ is the N(. length noise vector. H is assumed to be known perfectly at the receiver, but not at the transmitter. ZFLAS for VBLAST: method In the following, we obtain the ZFLAS detector for the VBLAST system considered in the above. The ZFLAS detector essentially searches out a sequence of bit vectors; this sequence is decided based on an update rule, until a fixed point is reached. In the V BLAST system considered, for ML detection [14], the most likely b is taken as that b which maximizes TUpdate Criterion in the Search Procedure: Let b(n) denote the bit vector tested by the LAS procedure in the search step n. The starting vector b(0) can be either a random vector, or the output vector from any known detector. When the output vector of the ZF detector is taken as the b(0), we call the resulting LAS detector as the ZFLAS detector. We define matched filter LAS (MFLAS) detector also likewise, i.e., the MF detector output vector is taken as the b(0). Given b(n), the LAS procedure obtains b(n + 1) through an update rule until reaching a fixed point. The update is made in such a way that and i) observing that br (n) IIvreal b(n) = 2b' (n)Hveffb(n), ii) adding & subtracting the term (n)Hvrealb(n + l)to the RHS of (10), and iii) further observing that br(n)IIvrealb(n +1) = b'\n + \)Hvrcalb(n), we can simplify (10) as Now, given yveff Hveff and b(n), the objective is to obtain b(n + 1) from b(n) such that AA (b(n)) in (12) is positive. Potentially any one or several bits in b(n) can be flipped (i.e., changed from +1 to 1 or vice versa) to get b(n+l). We refer to the set of bits to be checked for possible flip in a step as a check candidate set. Let L(n) e {1,2, *, AT} denote the check candidate set at step n. With the above definitions, it can be seen that the likelihood change at step n, given by (12), can be written as A A (I > I>))  V A//T.( n ) gk ( n) + ^ :k [ji) . (14) k(EL(n) " Where bk(ri),gk{ri)and zk(n) are the kth elements of the vectors b(n), g(n), and z(n), respectively. As shown in [21],[22] for single carrier CDMA on AWGN, the following update rule can be easily shown to achieve monotonic likelihood ascent (i.e., AA (b(n)) > 0 if there is at least one bit flip) in the VBLAST system as well. LAS Update Procedure: Given L(«)c{1,2,,A:},Vh>0 and an initial bit vector (for ZFLAS detector, initial vector for the method is taken to be the ZF detector output vector) ¿>(0) e {l,+l}*, bits in b(n) are updated as per the following update rule: where tk (n) is a threshold for the kth bit in the nth step, which, similar to the threshold in [21],[22], is taken to be where (Hvrea/)k/. is the element in the kth row and jlh column of the matrix Hvrcal. It can be shown, as in [21],[22], that tk{n) in (16) is the minimum threshold that ensures monotonic likelihood ascent. It is noted that different choices can be made to specify the sequence of L(n),\/n> 0. One of the simplest sequences correspond to checking one bit in each step for a possible flip, which is termed as a sequential LAS (SLAS) algorithm with constant threshold, lk = (Hvreai)kk • sequence of L(n) in SLAS can be such that the indices of bits checked in successive steps is chosen circularly or randomly. Checking of multiple bits for possible flip is also possible. Let Lf(n) e L(n) denote the set of indices of the bits flipped according to the update rule in (15) at step n. Then the updated bit vector b(n + 1) can be written as where ej is the ith coordinate vector. Using (17) in (8), the gradient vector for the next step can be obtained as (18) where (Hvreal)i denotes the ith column of the matrix Hvreal. The LAS method keeps updating the bits in each step based on the update rule given in (15) until b{n) = bfp V« > nf for some njp > 0, in which case bf is a fixed point, and it is taken as the detected bit vector and the algorithm terminates. ZFLAS for VBLAST: Complexity In terms of complexity, given an initial vector, the LAS operation part alone has an average perbit complexity oiO(NtNr). This can be explained as follows. The complexity involved in the LAS operation is due to two components: i) initial computation of g(0) in (8), which requires 0(NtNr) complexity per bit, and ii) update of g(n) as per (18), which requires complexity whenever there is a flip in a given step. So the total average perbit complexity in ii) in the above is determined by the average number of flips per bit, referred to as the bit flip rate. From simulations (which will be shown in MC CDMA results), we find that these flip operations have constant average perbit complexity c, where the constant c depends on SNR, Nt, Nr, and the initial vector b(0). So, putting the complexities of i) and ii) in the above together, we see that the average perbit complexity of LAS operation alone in ZF/MFLAS is 0(NtNr). Also, the initial vector generation using ZF detector has a complexity of 0{NlNr), and the initial vector generation using MF detector has a complexity of 0{Nr). So, the overall average perbit complexity of ZF/MFLAS detectors for VBLAST is 0{NlNr). This is in contrast with the well known ZFSIC detector for VBLAST whose perbit complexity is 0(N?Nr). Thus, ZFLAS enjoys a clear complexity advantage over ZFSIC by an order of Nt. Thus, while the ZFSIC becomes prohibitively complex for large number of antennas of the order of hundreds, the lowcomplexity attribute makes ZFLAS practically viable. To illustrate this point, in the following subsection, we will present the simulation plots of ZFLAS for up to 400x400 VBLAST systems up to 10~5 uncoded BER (obtained within few hours of simulation run time), whereas simulation points for ZFSIC for such large number of antennas were found to require several days of simulation run time (because of which ZFSIC performance results for up to 400 antenna systems are not given). ZFLAS for VBLAST: Performance Results & Discussions In this subsection, we present the performance results of ZFLAS for VBLAST obtained through extensive simulations, and compare with those of other known detectors. The LAS procedure used is the SLAS with circular checking of bits starting from the first user's bit. The major comparison we draw is between the ZFLAS detector and the ZF SIC detector (which is the well known VBLAST detector [15],[16]). In addition, we also present the comparison with other detectors including the MF detector, ZF detector, and MFLAS detector, where ever appropriate. Since ZF and ZFSIC detectors are good representative candidates for comparison with ZFLAS, we do not present the performance comparison with other detectors like MMSE, PIC, SIC, MMSESIC explicitly. For example, a performance and complexity comparison between MMSELAS (where MMSE detector output is taken as the LAS's initial vector) and MMSESIC will be similar to that between ZFLAS and ZFSIC. Initially, in Figs. 1 to 5 we present the uncoded BER performance of various detectors, where we illustrate the superiority of ZFLAS detector in terms of both complexity and performance in large VBLAST systems. Next, in Figs. 6 to 7, we present the coded BER performance with turbo code, where we illustrate the advantage of ZFLAS in more near term practical VBLAST systems with 8x8 and 15x15 antennas. In Fig. 8, we present the coded BER performance of ZFLAS detector for highrate, nonorthogonal STBC. Uncoded BER Performance Effect of increasing Nr for a fixed TV, : In Fig. 1, we present the uncoded BER performance of ZFLAS as a function of average SNR per receive antenna, T(dB), for MF, ZF, and ZFLAS detectors for three different cases, namely, 10x10 (N,=N=\0), 10 x 11 (N=10^=11), and 10 x 12 (N =10^Vf=12) VBLAST systems with BPSK modulation. This figure illustrates the effect of increasing the number of receive antennas for a given number of transmit antennas. As expected, ZFLAS performs better than ZF and picks up the receive diversity offered by the increased number of receive antennas. ZFLAS performs increasingly better than ZFSIC for increasing N=Nr: In Fig. 2, we plot the BER performance ZFLAS and ZFSIC detectors for VBLAST as a function of N=Nr at an average SNR of 20 dB. The performance of MF, ZF, and MFLAS detectors are also plotted for comparison. From Fig. 2, we can observe that, ZFLAS performs slightly better than ZFSIC for antennas less than 4. But ZFSIC performs better than ZF LAS for antennas in the range 4 to 25. Beyond 25 antennas, however, ZFLAS performs increasingly better than ZFSIC for increasing N=Nr. We found this crossover point to be different for different SNRs. A general behavior, however, we observed is that (which is in line with the observation/results reported in [21],[22]), ZFLAS performs very well in a large system setting (large number of antennas in our case, whereas it was large number of users in [21],[22]). Another interesting behavior in Fig. 2 is that for antennas greater than 50, MFLAS performs better than ZFLAS. This behavior can be explained by observing the performance comparison between MF and ZF detectors given in the same figure. For more than 50 antennas, MF performs better than ZF. Hence, starting with a better initial vector, MFLAS performs better than ZFLAS. ZF detector's poorer performance compared to MF detector in high interference conditions (here high interference due to large Nt ) and high noise conditions (see MF vs ZF performance in Fig. 3) is well known in the literature [14], ZFLAS outperforms ZFSIC in large VBLAST systems both in complexity & diversity: In Fig. 3, we present an interesting comparison of the uncoded BER performance between ZF, ZFLAS and ZFSIC, as a function of average SNR for a 200 x 200 V BLAST system. This system being a large system, the ZFLAS has a huge complexity advantage over ZF SIC as pointed out before. In fact, although we have taken the effort to show the performance of ZFSIC at such a large number of antennas like 200, we had to obtain these simulation points for ZFSIC over days of simulation time, whereas the same simulation points for ZFLAS were obtained in just few hours. This is due to the 0(NtNr) complexity of ZFSIC versus 0(NtNr) complexity of ZFLAS, as pointed out before. More interestingly, in addition to this lesser complexity advantage, ZFLAS is able to achieve much higher order of diversity in BER performance compared to ZFSIC. This is clearly evident from the slopes of the BER curves of ZFLAS and ZFSIC. This complexity as well as diversity order advantage of ZFLAS over ZFSIC is clearly very valuable. ZFLAS performance with hundreds of antennas: As pointed out in the above, obtaining ZFSIC results for more than even 50 antennas requires very long simulation run times, which is not the case with ZFLAS. In fact, we could easily generate BER results for antennas up to 400 for ZFLAS, which are plotted in Fig. 4. The key observations here are that i) the average SNR required to achieve a certain BER performance keeps reducing for increasing number of antennas for ZFLAS, and ii) increasing the number of antennas results in increased orders of diversity achieved. Observation i) in the above is explicitly brought out in Fig. 5, where we have plotted the average SNR required to achieve a target uncoded BER of 10~3, as a function of N=Nr for ZFLAS and ZFSIC. It can be seen that the SNR required to achieve 10 3 with ZFLAS significantly reduces for increasingly large N=Nr. For example, this required SNR reduces from about 25 dB for a SISO system to about 7 dB for a 400 x 400 VBLAST system using ZFLAS. Turbo Coded BER Performance While the practical realization of MIMO systems with large number of antennas could be far away into the future because of various other system level issues, including the issue of placing several antennas in smallsized communication terminals, we looked at the practicality and benefit of ZFLAS in MIMO systems which could be of practical interest in the nearterm. Towards that end, we considered 8x8 and 15x15 VBLAST systems, by noting that practical 8 antenna systems are being talked about [27]. We point out that for number of antennas up to about 30, ZFSIC has been found to perform better than ZF LAS (see Fig. 2). So, for the 8 x 8 and 15x15 systems, there is no performance gain in favor of ZFLAS compared to ZFSIC. However, there is a substantial complexity gain that is achieved with ZFLAS over ZFSIC. We highlight this point by pointing to our observation that the complexity (in terms of simulation run time) of an uncoded 8x8 ZF SIC is about the same as a rate1/2 turbo coded 8x8 ZFLAS with 3 turbo decoding iterations. In Fig. 6, we present the uncoded as well as the rate1/2 turbo coded BER performance as a function of Eb/No for the 8 x 8 system using 4QAM modulation (i.e., 8 bps/Hz spectral efficiency). Figure 7 presents similar plots for the 15 x 15 system with rate1/3 turbo code and 4QAM (10 bps/Hz spectral efficiency). Interestingly, in the rate 1/2 turbo coded 8x8 VBLAST system, ZFLAS achieves a BER of 10"4 at an Eh/N0 of 6 dB with 3 turbo decoding iterations. Likewise, in the rate1/3 turbo coded 15x15 VBLAST system, ZFLAS achieves a BER of 10~5 at an Eh/N0 of just 3 dB with 3 turbo decoding iterations. The complexity involved with achieving similar performances using the well known ZFSIC detector along with turbo decoding is comparatively very large. • The present invention for VBLAST multiantenna systems have the following characteristics: o the present invention achieves both complexity gain as well as performance gain compared to a well known MIMO detector in prior art (i.e., ZFSIC) when the number of antennas is more than 20. This can be seen from the performance crossover at the 20 antennas pointing Fig. 1. o when number of antennas is less than 20, the present invention achieves only complexity gain compared to priorart MIMO detector. The performance of prior art MIMO detector is better when the number of antennas is small, i.e., less than 20 (see Fig. 1). o The present invention achieves nearML performance only for large number of antennas. Typically nearML performance is achieved for more than 60 antennas (see Fig. 1). • Placement of tens or hundreds of antennas in communication terminals is a challenge when the communication terminals are small in size. This would require a high carrier frequency operation, i.e., small carrier wavelengths for XH separation to ensure independence between antennas. Communication terminals of reasonable size (e.g., laptops, etc.) can have tens of antennas (e.g., 32 or 64 antennas) using which the present invention can achieve ML performance. Fixed communication terminals in indoor environments can have even higher number of antennas. Also, a much larger number of antennas can be embedded in the body of vehicles in moving platform applications (e.g., cars, trucks, tanks, jeeps, autonomous under water vehicles in under water acoustic communications, etc.). • Since the highrate STBC mutliantenna approach would require less number of antennas compared to VBLAST mutliantenna approach, the antenna placement issue can be alleviated by the use of highrate STBC approach. • In V_BLAST, the number of receive antennas must be greater than or equal to number of transmit antennas. • Accurate channel estimation at the receiver is a requirement in the proposed invention. ZFLAS for highrate STBCs Since the placement of several antennas can be an issue in smallsized communication terminals, highrate space time codes can be used instead of pure VBLAST; the advantages of the spacetime codes approach being i) less number of antennas, and ii) transmit diversity. Since multiple time slots are involved in the spacetime approach, additional decoding delay would be involved compared to VBLAST. Lowcomplexity decoding of highrate, nonorthogonal spacetime block codes (STBC) is a challenge. Here, we show that highrate, nonorthogonal STBCs can be easily decoded using ZF LAS while achieving good performance. Explicit construction of highrate, full diversity, nonorthogonal STBCs have been discussed in detail in [26], An n x n STBC is said to be of fullrate, if there are n2 variables in it, or, equivalently, the rate of the code is n complex symbols per channel use. An example of a fullrate, fulldiversity STBC for 4 antennas is shown below [26]: su 2 s 11 s = *21 *22 *23 's'24 . (10) ■">'31 S3J s 33 s34 . *41 SJ'J *43 SI J . where the j^}, Uj e {1,2,34} are given in the Appendix. A detailed discussion on such codes for arbitrary number of antennas can be seen in [26]. The best known decoding algorithms which extract the fulldiversity property of these codes are the sphere decoding and MCMC algorithms [12],[13], which are not practical when the number of antennas exceed 10 for the use of QAM constellation. With ZFLAS, however, we show that such highrate, nonorthogonal STBCs can be easily decoded while achieving good performance as well. Figure 8 shows the uncoded as well as rate1/3 turbo coded BER performance of ZFLAS in decoding the rate4, nonorthogonal STBC4 from division algebra given by (19). This STBC in 919) sends 16 symbols in 4 time slots using 4 transmit antennas. From Fig. 8, we can observe that a coded BER of 10~4 is achieved at about 5 dB Eh/N0 using ZFLAS and 2 iterations of turbo decoding. ZFLAS Detector for Multicarrier CDMA In this section, we present the ZFLAS detector for multicarrier CDMA, its performance and complexity. Consider a Kuser synchronous multicarrier DSCDMA system with M subcarriers. Let bk e{ + l,l} denote the binary data symbol of the kth user, which is sent in parallel on M subcarriers [23],[24], Let N denote the number of chipsperbit in the signature waveforms. It is assumed that the channel is frequency nonselective on each subcarrier and the fading is slow (assumed constant over one bit interval) and independent from one subcarrier to the other. r „„(it U) ('' Let. v •' — V\ '!■> • ■ • V/v ' "J denote the Klength received signal vector on the U) i subcarrier; i.e Vk is the output of the k user's matched filter on the ith subcarrier. Assuming that the intercarrier interference is negligible, the Klength received signal vector on the ith subcarrier y(i) can be written in the form y(i)  R('H;'AI> 4 ii(/\ ('20) where R(i) is the K x K crosscorrelation matrix on the ith subcarrier, given by . I !l i?i 1 PV1 ■ ■ ■ l'\K h"' = 1 & . m> (?) (0 ., . (>K 1 PK 2 1 . it) where lj is the normalized cross correlation coefficient between the signature waveforms of the 1th and jth users on the ith subcarrier. H(l) represents the K*K channel matrix, given by We note that once the likelihood function for the MC CDMA system in the above is obtained, then it is straightforward to adopt the ZFLAS algorithm for MC CDMA. Accordingly, in the multicarrier system considered, the most likely b is taken as that b which maximizes The likelihood function in (26) can be written in a form similar to Eqn. (4.11) in [14] as A Where >W.r = ¿((H M Hce.ff = jAH^R^itf'YA. (21)) 1=1 Now observing the similarity of (27) with that of (4) in Section "ZFLAS for VBLAST: method" the LAS algorithm for MC CDMA can be arrived at, along the same lines as that of VBLAST in the previous section, with yveif Hwff and Hvreal replaced by ycc/f, HceJf, and Hcreal, respectively, with all other notations, definitions, and procedures in the algorithm remaining the same. ZFLAS for MC CDMA: Complexity In terms of complexity, given an initial vector, the LAS operation part alone has an average perbit complexity of O(MK). This can be explained as follows. The complexity involved in the LAS operation is due o two components: i) initial computation of g(0) in (8), which requires O(MK) complexity per bit, and ii) update of g(n) as per (18), which requires O(K) complexity whenever there is a flip in a given step. So the total average perbit complexity in ii) in the above is determined by the average number of flips per bit, referred to as the bit flip rate. From simulations (which will be shown in the next subsection), we find that these flip operations have constant average perbit complexity c, where the constant c depends on SNR, a, and the initial vector b(0). So, putting the complexities of i) and ii) in the above together, we see that the average perbit complexity of LAS operation alone is O(MK). Also, the initial vector generation using ZF has a complexity of O(K2) for K > M, and so the overall average perbit complexity of ZF LAS detector for MCCDMA is 0(A^2). If the MF output is used as the initial vector instead, then the overall average perbit complexity of the MFLAS is the same as that of the LAS alone, which is O(MK). For the MC CDMA system considered, we will see that the MFLAS, with lesser complexity than ZFLAS, performs very close to ZFLAS. Therefore, MFLAS is quite attractive in terms of complexity as well as performance in the MCCDMA systems considered. ZFLAS for MC CDMA: Performance Results & Discussions We evaluated the BER performance and complexity of the ZFLAS algorithm for MC CDMA through extensive simulations. We also evaluated the complexity of the LAS part in the algorithm in terms of average number of flips performed per bit, which, as we mentioned above, refer to as the bit flip rate (BFR). We evaluate the BER and BFR performance measures for LAS as a function of average SNR, number of users (K), number of subcarriers (M), number of chips per bit (N). We also evaluate the BER performance of ZFLAS as a function of loading factor, a , where, as done in the CDMA literature [14], we define a .We call the system as underloaded when a MN loaded when a = 1, and overloaded when a >1. Random binary sequences of length N are used as the spreading sequences on each subcarrier. In order to make a fair comparison between the performance of MC CDMA systems with different number of subcarriers, we keep the system and width the same by keeping MN constant. Also, in that case we keep the total transmit power to be the same irrespective of the number of subcarriers used. In the simulation plots we show here, we have assumed that all users transmit with equal amplitude (We note that we have simulated the ZF/MFLAS performance in nearfar conditions as well. Even with nearfar effect, the ZF/MFLAS has been observed to achieve near SU performance).The LAS algorithm used is the SLAS with circular checking of bits starting from the first user's bit. First, in Fig. 9, we present the BER performance of ZFLAS as a function of average SNR in a single carrier (i.e., M = 1) underloaded system, where we consider a = 2/3 by taking K = 200 users and N = 300 chips per bit. For comparison purposes, we also plot the performance of i) MF detector, ii) ZF detector, and iii) MFLAS detector. Single user (SU) performance which corresponds to the case of no multiuser interference (i.e., K = 1) is also shown as a lower bound on the achievable multiuser performance. From Fig. 9, we can observe that the performance of MF and ZF detectors are far away from the SU performance. Whereas, the ZFLAS as well as MFLAS detectors almost achieve the SU performance. We point out that, like ZF detector, other suboptimum detectors including MMSE, SIC, and PIC detectors [14] also do not achieve near SU performance for the considered loading factor of 2/3, whereas the MFLAS detector achieves near SU performance, that too with a lesser complexity than these other suboptimum detectors. Next, in Fig. 10, we show the BER performance of the ZF/MFLAS detectors for M = 1 as a function of number of users, K, for a fixed value of a = 2/3 at an average SNR of 15 dB. We varied K from 10 to 1000 users. SU performance is also shown (as the bottom most horizontal line) for comparison. It can be seen that, for the fixed value of a = 2/3, both the MFLAS as well as the ZFLAS achieve near SU performance, whereas the ZF and MF detectors do not achieve the SU performance. In Fig. 11, we show the BER performance of the ZF/MFLAS detectors as a function of average SNR for different number of subcarriers, namely, M = 1,2,4, keeping a constant MN = 100, for a fully loaded system (i.e., a = 1) with K = 100. Keeping a = 1 and K = 100 for all cases means that i) N = 100 for M = 1, ii) N = 50 for M = 2, and iii) N = 25 for M = 4. The SU performance for M = 1 (1st order diversity), M = 2 (2nd order diversity), and M = 4 (4th order diversity) are also plotted for comparison. These diversities are essentially due to the frequency diversity effect resulting from multicarrier combining of signals from M subcarriers. It is interesting to see that even in a fully loaded system, the ZF/MFLAS detectors achieve all the frequency diversity possible in the system (i.e., ZF/MFLAS detectors achieve SU performance with 1 st, 2nd and 4th order diversities for M = 1, 2 and 4, respectively). On the other hand, ZF detector is unable to achieve the frequency diversity in the fully loaded system, and its performance is very poor compared to ZF/MFLAS detectors. Next, in Fig. 12, we present the BER performance of ZF/MFLAS detectors in a MC CDMA system with M = 4 as a function of loading factor, a, where we vary a from 0.025 to 1.5. We realize this variation in _ by fixing K = 30, M = 4, and varying N from 300 to 5. The average SNR considered is 8 dB. From Fig. 12, it can be observed that as _ increases all detectors loose performance, but the ZF/MFLAS detectors can offer relatively good performance even at overloaded conditions of a > 1. Another observation is that at a >1, MFLAS performs slightly better than ZFLAS. This is because a > 1 corresponds to a high interference condition, and it is known in MUD literature [14] that ZF can perform worse than MF at low SNRs and high interference. In such cases, starting with a better performing MF output as the initial vector, MFLAS performs better. Finally, in Fig. 13, we present the complexity of the flip operations in the LAS algorithm, in terms of BFR (bit flip rate) obtained from simulations. BFR as a function of number of users K is plotted for different values of average SNR and loading factor, a , for M = 1. It can be seen that the BFR remains constant as a function of K, implying that the LAS operation has a constant average perbit complexity in K. As can be seen, this constant depends on the values of SNR and a , and the initial vector used. For example, the BFR decreases with increasing SNR. This is because, for a given initial detector, at high SNRs, the initial vector is less erroneous and so the fixed point is reached in less number of search steps. For a similar reason, BFR is less for small values of a . As pointed out in Section "ZFLAS for MC CDMA: complexity", since the BFR operations have only a constant average perbit complexity, it is the initial detector's complexity which dominates the overall complexity. Based on the above, we note that MFLAS is quite attractive in terms of complexity as well as performance in the MC CDMA systems considered. Further to our present work on the application of ZF/MFLAS for MC CDMA, several extensions are possible on the practical application of ZF/MFLAS in CDMA. Two such useful extensions include i) ZF/MFLAS for frequency selective CDMA channels with RAKE combining; we point out that a similar approach and system model adopted here for MC CDMA is applicable, by taking a view of equivalence between frequency diversity through MC combining and multipath diversity through RAKE combining, and ii) ZF/MFLAS for asynchronous CDMA systems, which can be carried out once the system model is appropriately written [14] in a form similar to (20). These two extensions can allow ZF/MFLAS detectors to be practical in CDMA systems (e.g., 2G and 3G CDMA systems), with potential for significant gains in system capacity. Current approaches to MUD in practical CDMA systems are mainly PIC and SIC. However, the illustrated fact that MFLAS can easily outperform PIC/SIC detectors in performance and complexity for large number of users suggests that MFLAS can be a powerful MUD approach in practical CDMA applications. MIMO systems with multiple antennas at both transmitter and receiver sides have become very popular owing to the several advantages they promise to offer, including high data rates and transmit diversity. Figure 14 shows an example of a MIMO system that has Nt number of transmit antennas at the transmitter and Nr number of receiv antennas at the receiver. The transmit signal passes through the MIMO fading channel. The channel gain form one transmitter antenna to one receiving antenna is characterized by a random channel gain. It is known that the MIMO channels have a capacity that grows linearly with the minimum of the number of antennas on the transmitter and receiver sides. A key component of a MIMO system is the MIMO detector at the receiver, whose job is to recover the symbols that are transmitted simultaneously from multiple transmitting antennas. In practical applications, the MIMO detector is often the bottleneck for both performance and complexity. Conclusions In this invention, we presented a lowcomplexity detector, termed as ZFLAS (zero forcing likelihood ascent search) detector, for large MIMO systems with antennas of the order of tens to thousands, including VBLAST as well as nonorthogonal STBC. The complexity advantage of this detector compared to other known detectors like ZFSIC detector is remarkable for large MIMO systems; 0(jV, JVf) for ZFLAS versus 0(N?Nr) for ZFSIC. We conclude this paper by pointing to the following remark made by the author of [2] in its preface in 2005: "It was just a few years ago, when I started working at AT&T Labs  Research, that many would ask 'who would use more than one antenna in a real system?' Today, such skepticism is gone." Extending this sentiment, we believe large MIMO systems would be practical in the future, and the feasibility of low complexity detectors like the ZFLAS detector presented in this invention, could be a potential trigger to create wide interest in the theory and practice of large MIMO systems. Instant invention does not posses limitation of number of antennas as such. Appendix Let x jc167 denote the data symbol vector. Then, the symbols {st/], i,j,e {1,2,3,4} in the spacetime block code S in Eqn. (19) are given by We claim: 1. A method to detect data transmitted from multiple antennas, said method comprising steps of: i. selecting a starting data block and calling it as previous data block; ii. defining a set of indices of bits to be checked for possible flip in the previous data block as a check candidate set; iii. applying update rule to obtain updated data block using the previous data block and the check candidate set, wherein the update is made in such a manner that change in likelihood is positive; iv. checking if the updated data block and several consecutive previous data blocks are the same; if yes, declare the updated data block as the detected data block; if no, make updated data block as previous data block and go to step ii. 2. The method as claimed in claim 1, wherein the starting data block is either a random data block or an output data block from known detectors. 3. The method as claimed in claim 1, wherein the sequence of check candidate set is chosen such that the bits are checked for possible flip in an order. 4. The method as claimed in claim 3, wherein the order is circular or random. 5. The method as claimed in claim 1, wherein the method provides for checking of multiple bits for possible flip. 6. The method as claimed in claim 1, wherein the method of defining update rule comprises steps of; i. making kth bit +1 in (n+l)th step data block if kth bit of the nth step data block is 1 and gradient of likelihood function corresponding to the kth bit in the nth step data block is greater than a threshold corresponding to the kth bit in the nth step data block; ii. making kth bit 1 in (n+l)th step data block if kth bit of the nth step data block is +1 and gradient of likelihood function corresponding to the kth bit in the nth step data block is less than a threshold corresponding to the kth bit in the nth step; and iii. if conditions in (i) and (ii) are not satisfied the kth bit in (n+l)th step data block is kept same as kth bit value in the nth step data block. 7. The method as claimed in claim 1, wherein the antennas in range of tens to thousands are used to transmit and to receive the data. 8. The method as claimed in claim 1, wherein signals transmitted from the antennas occupy same transmission bandwidth using same modulation format of either BPSK or QPSK. 9. The method as claimed in claim 1, wherein the method provides for low complexity detection with linear or quadratic complexity in multiple number of antennas. 10. The method as claimed in claim 1, wherein the method provides for near maximumlikelihood (ML) performance for multiple antennas in the range of tens to thousands. 11. The method as claimed in claim 1, wherein the method provides for spectral efficiencies of the order of tens to thousands of bps/Hz. 12. The method as claimed in claim 1, wherein the method provides for spatial processing gain equal to the number of transmit antennas by exploiting the spatial dimensions without expanding the transmission bandwidth. 13. The method as claimed in claim 1, wherein the method provides for reduction in Eb/No (Bit energy to noise spectral density ratio) by a factor of the number of transmit antennas without expanding the transmission bandwidth. 14. The method as claimed in claim 1, wherein the method employs the data transmissions using higher order modulation format selected from a group comprising Mary Quadrature Amplitude Modulation (MQAM), Mary Pulse Amplitude Modulation (MPAM) and Mary Phase Shift Keying (MPSK). 15. The method as claimed in claim 1, wherein the method detects data symbols transmitted from multiple transmit antennas using MIMO technique selected from a group comprising SpaceTime Block Coding (STBC) and VBLAST. 16. The method as claimed in claim 1, wherein the method provides for detection in distributed/cooperative MIMO systems and networks with multiple number of co¬operating nodes. 17. The method as claimed in claim 1, wherein the method provides for detection in Ultrawide band (UWB) systems with multiple users, multiple channel taps and multiple subcarriers. 18. The method as claimed in claim 1, wherein the method provides for detection in underwater acoustic communications with multiple nodes deployed to sense and send information. 19. The method as claimed in claim 1, wherein the method provides for detection in multiuser OFDM and MIMOOFDM systems with multiple subcarriers. 20. The method as claimed in claim 1, wherein the method provides for detection in outercoded MIMO systems with outcode selected form group comprising turbo coding, LDPC coding, convolutional coding and block coding. 21. A MIMO system comprising: i. multiple transmit antennas for data transmission, ii. multiple receive antennas for data reception iii. a data detector using ZF/MF/MMSE/RVLAS (zeroforcing/matched filter/minimum mean square error/random vector likelihood ascent search) to detect transmitted data, and iv. a data detector which uses output data block from any known detector as the starting data block. 22. The system as claimed in claim 21, wherein the antennas are ranging from tens to thousands in number. 23. The system as claimed in claim 21, wherein signals transmitted from the antennas occupy same transmission bandwidth using same modulation format of either BPSK or QPSK. 24. The system as claimed in claim 21, wherein the system employs MIMO technique selected from a group comprising SpaceTime Block Coding (STBC) and V BLAST. 25. The system as claimed in claim 21, wherein the system provides for low complexity detection with linear or quadratic complexity in multiple number of antennas. 26. The system as claimed in claim 21, wherein the system provides for near maximumlikelihood (ML) performance for multiple antennas in the range of tens to thousands. 27. The system as claimed in claim 21, wherein the system provides for spectral efficiencies of the order of tens to thousands of bps/Hz. 28. The system as claimed in claim 21, wherein the system provides spatial processing gain equal to the number of transmit antennas by exploiting the spatial dimensions without expanding the transmission bandwidth. 29. The system as claimed in claim 21, wherein the system provides for reduction in Et/No (Energy per bit to noise spectral density ratio) by a factor of the number of transmit antennas without expanding the transmission bandwidth. 30. The system as claimed in claim 21, wherein the system employs the data transmissions using higher order modulation format selected from a group comprising Mary Quadrature Amplitude Modulation(MQAM), Mary Pulse Amplitude Modulation (MPAM) and Mary Phase Shift Keying (MPSK). 31. The system as claimed in claim 21, wherein the system provides for detection in outercoded MIMO systems with outercode selected from a group comprising turbo coding, LDPC coding, convolutional coding and block coding. 32. A method and system to detect data transmitted from multiple antennas herein substantiated with accompanying drawings. 

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Patent Number  253373  

Indian Patent Application Number  1725/CHE/2007  
PG Journal Number  29/2012  
Publication Date  20Jul2012  
Grant Date  16Jul2012  
Date of Filing  06Aug2007  
Name of Patentee  INDIAN INSTITUTE OF SCIENCE  
Applicant Address  IP CELL, SID, INNOVATION CENTER, IISC CAMPUS, BANGALORE560 012.  
Inventors:


PCT International Classification Number  H04L27/00  
PCT International Application Number  N/A  
PCT International Filing date  
PCT Conventions:
