WO2008086044A1

WO2008086044A1 - Local maximum likelihood detection in a communication system

Info

Publication number: WO2008086044A1
Application number: PCT/US2008/000485
Authority: WO
Inventors: Yi Sun
Original assignee: Yi Sun
Priority date: 2007-01-13
Filing date: 2008-01-14
Publication date: 2008-07-17

Abstract

A method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as single-user performance in a high SNR regime in random densely and sparsely spread CDMA. The method is based on local maximum likelihood (''LML') detectors and bit extending and multiplexing, and can approach optimum performance of a GML detector as well as the single-user performance in the high SNR regime, while average per-bit complexity is liner in the number of detected bits and thus is suitable for implementation in practical CDMA systems.

Description

LOCAL MAXIMUM LIKELIHOOD DETECTION IN A COMMUNICATION SYSTEM

Background of the Invention

Field of the Invention:

The embodiments of the present invention relate to a CDMA multiuser detector, and more particularly, the embodiments of the present invention relate to a method of local maximum likelihood detection with bit extending and multiplexing to approach the optimum performance as well as the single-user performance in the high SNR regime in random densely and sparsely spread CDMA.

Description of the Prior Art:

Due to the advantages of efficient spectrum usage, robustness to dynamic traffic, and security, the code division multiple access ("CDMA") technique is widely used in wireless communication networks and is expected to be dominant in 4^th generation wireless networks.

As the number of wireless subscribers is ever growing, the radio frequency spectrum suitable for wireless communications becomes more and more stringent and expensive. To accommodate more wireless users with a fixed radio frequency band or to achieve high efficiency of spectrum and power usage in CDMA wireless networks with/without centralized infrastructure, it is critical to discover multiuser detectors and related techniques that can perform comparably with the optimum global maximum likelihood ("GML") detector as well as single-user bound in the high SNR regime but have liner complexity that can be implemented in practical communication systems. It is well-known that the GML detector minimizes the bit error rate ("BER"), which can be lower than the BER of the conventional MF by a factor of 1000 or more, but it is NP-hard in complexity and thus is prohibited in practical communication systems. The liner multiuser detectors, such as MF, decorrelator, and MMSE, have per-bit complexity liner to the number of users but their BER is far worse than that of the GML detector. The nonlinear suboptimal detectors, such as the PIC, PDA, SDR, coordinate ascent, and SDP, etc. — though lower than NP-hard — still have a complexity higher than liner and thus is not feasible for practical communication systems. Moreover, they still perform much worse than the GML detector.

Thus, there exists a need to provide a CDMA multiuser detector that achieves high performance with minimal complexity. Numerous innovations for CDMA multiuser detectors have been provided in the prior art, which will be described below in chronological order to show advancement in the art, and which are incorporated herein by reference thereto. Even though these innovations may be suitable for the specific individual purposes to which they address, they each differ in structure and/or operation and/or purpose from the embodiments of the present invention in that they do not teach a method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as single-user performance in the high SNR regime in random densely and sparsely spread CDMA. United States Patent Number 5,544,156 issued to Teder et al. on August 6, 1996 in class 370 and subclass 342 teaches a system and method for coherently demodulating an uplink signal in a multirate, CDMA system. By first demodulating information in a control channel, which relates to the data rate of a data field in a frame of the data channel of the received signal, phase information can be derived so as to generate a reference for coherent demodulation.

United States Patent Number 5,917,829 issued to Hertz et al. on June 29, 1999 in class 370 and subclass 47 teaches a method and apparatus for optimally decoding messages from a CDMA signal sent by a plurality of users and received asynchronously at one receiver using a minimal number of computations and minimal memory and processing resources. It is based on signal correlation, as well as to subsequent decoding by decorrelation, requiring a correlation period of only one symbol length, by providing for each user a pair of partial signatures sequences, with which the signal is correlated, deccorelating the results with the inverse of the cross-correlation matrix of all partial sequences, and combining the resultant partial symbol estimates to obtain final estimated symbol values. The partial sequences are formed by separating each original sequence at a point corresponding to the estimated symbol boundary time, relative to an arbitrary correlation window, of one symbol length. The method can be modified to also apply to the case that any of the signals is received over multiple paths, any path possibly undergoing Doppler shift. United States Patent Number 6,466,566 issued to De Gaudenzi et al. on October

15, 2002 in class 370 and subclass 342 teaches an adaptive signal receiver including at least one blind detection unit arranged to be robust to asynchronous multiple access interference ("MAI"). The useful signal is detected using a user signature sequence including a fixed term and a complex adaptive part having a length extending over a number of samples within a defined observation window. Provision is made for updating automatically and periodically the complex adaptive part of the signature sequence. United States Patent Number 6,654,365 issued to Sylvester et al. on November 25, 2003 in class 370 and subclass 342 teaches a maximum likelihood ("ML") detector providing performance in the presence of multiple user interference ("MUI"), particularly performance of a multiuser receiver for asynchronous CDMA. The detector can be implemented using a Viterbi algorithm. This greatly reduces system sensitivity to MUI. An approximation to the ML detector provides a sparse-trellis search based on the structure of the ML detector. The resulting detector, which may be referred to as a reduced-complexity recursive detector ("RCRD"), has a dynamic structure allowing a trade-off between complexity and performance. Use is made of a metric to define the trellis-structure and the M-algorithm to reduce the number of surviving paths. The metric calculation is then repeated at decision points to provide soft-decision information for further signal processing, soft-decision decoding of an error-correction code, or iterative reception of the multiuser signal.

United States Patent Number 7,076,015 issued to Bhatoolaul et al. on July 1 1, 2006 in class 375 and subclass 365 teaches a method of detecting one of a set of preamble sequences in a spread signal. The method includes the steps of correlating the received spread signal with sequences of a first orthogonal Gold code ("OGC") set in accordance with a first fast transform to provide a preamble signal, correlating the preamble signal with the set of preamble sequences in accordance with a second fast transform to generate a set of index values, forming a decision statistic based on the set of index values, and selecting, as the detected one of the set of preamble sequences, a preamble sequence corresponding to the decision statistic. The forming step includes the steps of forming an initial decision statistic based on the relative maximum index of the set of index values, selecting the signal generated by the preamble sequence combined with the preamble signal corresponding to the initial decision statistic, adjusting, in one or more of amplitude and phase, the signal selected in the selecting step, and forming the decision statistic based on the adjusted signal.

It is apparent that numerous innovations for CDMA multiuser detectors have been provided in the prior art that are adapted to be used. Furthermore, even though these innovations may be suitable for the specific individual purposes to which they address, they would not be suitable for the purposes of the embodiments of the present invention as heretofore described, namely, a method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as single-user performance in high SNR regime in random densely and sparsely spread CDMA. Summary of the Invention

Thus, it is an object of the embodiments of the present invention to provide a method of local maximum likelihood detection with bit extending and multiplexing to approach the optimum performance as well as the single-user performance in the high SNR regime in random densely and sparsely spread CDMA that avoids the disadvantages of the prior art by achieving optimum performance with linear complexity and being suitable for implementation in practical CDMA communication systems even though computational complexity is slightly increased by a constant of bit block size with bit multiplexing but the complexity is still in the same order and is suitable for implementation in practical communications.

Briefly stated, another object of the embodiments of the present invention is to provide a method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as the single-user performance in the high SNR regime in random densely and sparsely spread CDMA. The method is based on local maximum likelihood ("LML") detectors and bit extending and multiplexing, and can approach optimum performance of a GML detector as well as the single-user performance in the high SNR regime, while average per-bit complexity is liner in the number of detected bits and thus is suitable for implementation in practical CDMA systems. Given a CDMA system, the method does not change total RF bandwidth, data transmission rate, and transmission power for each user, while achieving GML and single-user performance. The method includes the steps of: extending, at a transmitter, each bit by a factor of integer B to have BT _h seconds where T_h is the bit period; selecting randomly equiprobably, by each user, B extended spreading sequences, each of which having BN chips and a unit length; spreading an extended bit by an extended spreading sequence; transmitting, by each user, B extended bits, with the integer B being sufficiently large so as to allow a total number of transmitted bits BK to be greater than about five hundred; and, applying, at a receiver, a LAS detector or an LML detector to detect the transmitted BK bits. The spreading sequence can be densely or sparsely spread. In a densely spread sequence, all chips are i.i.d. with mean zero and variance XI(BN), say equiprobably take on ± Ms/ BN. In a sparsely spread sequence, there are only a small number of nonzero chips and most chips are zero. The nonzero chips are randomly located and are i.i.d. with mean zero and a variance such that the Euclidean distance of the sequence is equal to one. For example, each spares sequence has L « BN nonzero chips that are randomly located and equiprobably take on ± 1/VZ! While the bit extending factor is the same for all users, each user can also have a different number of multiplexed bits to achieve a different and adjustable transmission rate. The GML detector in CDMA communication systems is well-known to achieve a bit error rate ("BER") that is the lowest for all possible detectors and can be significantly lower than the BER of a matched filter, which is used in practical CDMA systems, say by a factor of over a thousand. But the GML detector is NP-hard, whose per-bit complexity exponentially increases as the number of users increases and thus is prohibited to be implemented in practical CDMA systems. For a long time, the developed family of likelihood ascent search ("LAS") detectors, as well as the developed family of LML detectors, achieved a BER monotonically decreasing and reaching the BER of the GML detector as the number of users increases to over five hundred in a random spreading CDMA system. This phenomenon has been verified recently by theoretical analysis. It is important that the LAS and the LML detectors can be implemented with only an average per — bit complexity linear in the number of transmitted bits and therefore can be implemented in practical CDMA systems. Practical CDMA systems, however, usually have about fifty users or fewer, much less than five hundred. In order for the LAS and the LML detectors to achieve the BER of the GML detector, the embodiments of the present invention construct a quasi-large random sequence CDMA (QLRS-CDMA) system as well as quasi — large sparse sequence CDMA (QLSS-CDMA). The method extends transmitted bits and spreading sequences by a same integer factor of B. Each user multiplexes and transmits B extended bits in a B bit period. The bit extending and multiplexing do not change data transmission rate, bandwidth, and transmission power of the original CDMA system. The constructed CDMA system, however, transmits a total of BK bits in each time, which corresponds to a CDMA system with BK users, with BK being arbitrarily large if B is sufficiently large. Thus, if BK is over five hundred, the LAS and the LML detectors can achieve the BER of the GML detector as well as single-user BER in the high SNR regime for practical CDMA systems.

The novel features considered characteristic of the embodiments of the present invention are set forth in the appended claims. The embodiments of the present invention themselves, however, both as to their construction and to their method of operation together with additional objects and advantages thereof will be best understood from the following description of the specific embodiments when read and understood in connection with the accompanying drawings. Brief description of the Drawings

The figures of the drawings are briefly described as follows:

FIGURE l(a) is a graph of BER versus BK, where a = KIN = 0.8 and SNR = 1 IdB; FIGURE l(b) is a graph of BFR versus BK, where a = 0.8 and SNR = 1 IdB; FIGURE 2(a) is a graph of BER versus a, where 1 136 < BK ≤ 3328 and SNR = 1 IdB; FIGURE 2(b) is a graph of BFR versus a, where 1 136 < 5AT < 3328 and SNR = 1 IdB; FIGURE 3(a) is a graph of BER versus SNR for a system where a = 0.8 and BK = 3000; FIGURE 3(b) is a graph of BFR versus SNR for a system where a = 0.8 and BK = 3000; FIGURE 4(a) is a graph of BER versus bit number BK with a = 0.8 bits/s/Hz and SNR = H dB;

FIGURE 4(b) is a graph of complexity versus bit number BK with a = 0.8 bits/s/Hz and

SNR = 11 dB; FIGURE 5 (a) is a graph of BER versus nonzero-chip number L with a = 0.8 bits/s/Hz and SNR = 11 dB; FIGURE 5(b) is a graph of complexity versus nonzero-chip number L with a = 0.8 bits/s/Hz and SNR = 1 1 dB; and FIGURE 6 is a graph of BER versus SNR with a = 0.8 bits/s/Hz and BK = 1024 bits.

Detailed Description of the Preferred Embodiments

Given a CDMA system

Consider a Abuser Gaussian CDMA channel where the bit period is T_h and the chip period is T₀, and then the spreading gain is N = T/T_c. Hence, the bandwidth of the system is approximately equal to W = 1/T_C Hertz, the data rate per user equals 1/7 \ bits per second, and a = KJN indicates the system load in the transmitted bits per second per Hz. The systems with different K and N but the same a have the same load. Given the transmission power, the signal amplitude of a &"¹ user at the receiver is A_k. Each bit b_k of each user is independently spread by a sequence s_k. For a densely spread sequence, the chips of s_k are i.i.d. with mean zero and variance 1/N, say randomly, independently, equiprobably take on ± 1Λ/ΛT For a sparsely spread sequence, there are a small number of nonzero chips and most of the chips are zero. The nonzero chips are randomly located and are i.i.d. with mean zero and the variance that makes the Euclidean of the sequence equal to one. For example, each sparse sequence has L « N nonzero chips that are randomly located and equiprobably take on ± 1 /vTT The sequence can be initially assigned to each user corresponding to a practically short sequence or randomly chosen bit-by-bit corresponding to a practically long sequence. Suppose bits are synchronized by some synchronization techniques, the approach can be applied to bit-asynchronous CDMA systems. During one bit period, the chip-matched filter at the receiver outputs the following TV-dimensional vector:

K τ = Σs_lrA_kb_κ + m = SAb + m ,..

where S = (S₁, ..., s^) is the matrix of spreading sequences, each of which is normalized to Il s_A Il = I₅ A = diag(Λ,, ..., A_x) is the diagonal matrix of user's received signal amplitudes, b E {-1, l }^λ' is the vector of transmitted bits of K users, and m ~ N(O, O²I^) is an N- dimensional white Gaussian noise random vector. Then a sufficient statistic is obtained by:

y = S⁷r = RAb + n (2)

where R = S⁷S is the cross-correlation matrix of spreading sequences and n = S⁷m ~ N(O, O²R).

The same statistic y can be also obtained by a standard matched filter ("MF") bank matching the signature waveforms in the received CDMA signal. IfK is sufficiently large, say K >500, the CDMA system is called a large random spreading CDMA ("LRS-CDMA") system.

Proposed OLRS-CDMA with bit extending and multiplexing

In practical CDMA communication systems, the number of users is much less than 500, and therefore they are not LRS-CDMA systems. Given a practical CDMA system, however, a quasi-large random sequence CDMA ("QLRS-CDMA") system by bit extending and multiplexing is constructed.

Consider the given CDMA system in the above section. B bits of each user are collected, and let each bit be extended to occupy B bit periods or BT_b seconds. Each extended bit is spread by an extended random spreading sequence that has BN chips.

During BT _h seconds, each user transmits a number of extended bits that are multiplexed. Specifically, user k transmits B bits b_kj, j = 1, ..., B, that are spread by 5iV-chip spreading sequences s_kj The spreading sequences can be densely or sparsely spread. In a densely spread sequence, all chips are i.i.d. with mean zero and variance \/(BN), say equiprobably take on ± \N BN. In a sparsely spread sequence, there are only a small number of nonzero chips and most chips are zero. The nonzero chips are randomly located and are i.i.d. with mean zero and a variance such that the Euclidean distance of the sequence is equal to one. For example, each sparse sequence has L « BN nonzero chips that are randomly located and equiprobably take on ± 1/vTT The sequences for each user can be assigned in two ways. One is that user k initially, randomly, and equiprobably selects B_k sequences, and then in every transmission uses the same B_k spreading sequences to spread B_k multiplexed bits. The other is that a user newly, randomly, and equiprobably selects B_k spreading sequences for every B_k transmitted bits in an extended period. The former are practically called short sequences and the latter are practically long sequences. The bit sequence of each user can be coded or uncoded. Then, during B bit periods, the chip MF at the receiver outputs the following Z?vV-dimensional real vector:

K B r = ∑ Λ_k ∑s_kjb_kj + m ₍₃₎

A=I /=1

where m ~ N(O, O²I_8N) is a A/V-dimensional white Gaussian noise vector. Then the channel load is equal to:

bits per second per Hertz where β_k = B/B is fixed as B increases.

It is easy to verify that compared with the CDMA system of equation (1) above, the CDMA system in equation (3) above, where bit duration is extended by a factor of B and B_k bits of user k are multiplexed, has the same number of users K, bandwidth W, data transmission rate \IT_h, received signal amplitude A_k for each user, and the system load a if B_k — B for all k. The total number of transmitted bits BK, however, can be arbitrarily large as B increases. When B is sufficiently large so that BK >^00, it is a QLRS-CDMA system. In statistic sense, a QLRS-CDMA system is identical to an LRS-CDMA system. When the sparsely spread sequences are applied, the QLRS-CDMA becomes the QLSS- CDMA.

The family of LAS detectors and the family of LML detectors

Two families of multiuser detectors for CDMA multiuser detection have been developed by applicant. One is the family of likelihood ascent search ("LAS") detectors¹ and the other is the local maximum likelihood ("LML") detectors². The family of LAS detectors contains many special instances, each operating in a sequence of updating modes.

A particularly interested class of LAS detectors in the family is called the wide- sense sequential LAS ("WSLAS") detectors that are also LML detectors with neighborhood size one and have an average per-bit complexity linear in the number of transmitted bits. The WSLAS detectors include the eliminating-highest-error and fastest-

¹ Y. Sun, "A family of linear complexity likelihood ascent search detectors for CDMA multiuser detection," in Proc. IEEE 6"' Int. Symp. on Spread-Spectrum Tech. & Appli., ISSSTA '2000, Parsippany, NJ, Sept. 6-8, 2000; Y. Sun, "A generalized updating rule for modified Hopfield neural network for quadratic optimization," Neurocomputing, pp.133-143, 19 (1998).

² Y. Sun, "A family of likelihood ascent search detectors achieving local maximum likelihood with an arbitrary neighborhood size for CDMA multiuser detection," in Proc. 38'^h Annual Allerton Conf. on Commun., control, and computing, pp. 826-833, University of Illinois at Urbana- Champaign, Oct. 4-6, 2000; Y. Sun, "Local maximum likelihood multiuser detection," in Proc. 34th Annual Conference on Information Science and Systems, CISS '2001 , pp. 7-12, The Johns Hopkins University, Baltimore, Maryland, March 21 -23, 2001. metric-descent detectors developed by applicant,³ the SAGE algorithm,⁴ the local search algorithm,⁵ and the EM based algorithm⁶ with symbols ±1 's. The LML detectors with any neighborhood size equal to one up to the number of users are defined in footnote ², which include the gradient guided search algorithms found in footnote ⁷.

The embodiments of the present invention

The embodiments of the present invention apply the family of LAS detectors and the family of LML detectors to the proposed QLRS-CDMA and QLSS-CDMA systems. The GML detector in CDMA communication systems is well-known to achieve a bit error rate ("BER") that is the lowest for all possible detectors and can be lower than the BER of a matched filter, which is used in practical CDMA systems, by a factor of over a thousand. But the GML detector is NP-hard, whose per — bit complexity exponentially increases as the number of users increases, and thus is prohibited to be implemented in practical CDMA systems. For a long time, the developed family of likelihood ascent search ("LAS") detectors, as well as the developed family of LML detectors, achieved a BER monotonically decreasing and reaching the BER of the GML detector as well as the single-user BER in the high SNR regime as the number of users increases to over five hundred in a random spreading CDMA system. This phenomenon has been verified recently by theoretical analysis. It is important that the LAS and the LML detectors can be implemented with only an average per-bit complexity linear in the number of transmitted bits and therefore can be implemented in practical CDMA systems. Practical CDMA systems, however, usually have about fifty users or fewer, much less than five hundred. In order for the LAS and the LML detectors to achieve the BER of the GML detector, it is proposed to construct a quasi-large random sequence CDMA (QLRS- CDMA) system and a quasi-large sparse sequence CDMA (QLSS-CDMA) system.

³ Y. Sun, "Eliminating-highest-error and fastest-metric-descent criteria and iterative algorithms for bit-synchronous CDMA multiuser detection," in Proc. IEEE International Conference on Communications, ICC 98, pp. 1576-1580, Atlanta, Georgia, June 7-1 1 , 1998.

⁴ L. B. Nelson and H. V. Poor, "Iterative multiuser receivers for CDMA channels: an EM-based approach," IEEE Trans, on Commun., vol. 44, no. 12, pp. 1700-1710, Dec. 1996.

⁵ B. Wu and Q. Wang, "New suboptimal multiuser detectors for Synchronous CDMA systems," IEEE Trans. Commun., vol. 44, no. 1, pp. 782-785, July 1996.

⁶ D. Raphaeli, "Suboptimal maximum-likelihood multiuser detection of synchronous CDMA on frequency-selective multipath channels,^"' IEEE Trans. Commun., vol. 48, no. 5, pp. 875-885, May 2000.

⁷ J. Hu and R. S. Blum, "A gradient guided search algorithm for multiuser detection," IEEE Commun. lett., vol. 4, no. 1 1 , pp. 340-342, Nov. 2000. The method extends transmitted bits and spreads sequences by a same integer factor of B. Each user multiplexes and transmits B extended bits in a B bit period (in practice, each user can also multiplex a different number of bits to achieve different data transmission rate). The bit extending and multiplexing do not change data transmission rate, bandwidth, and transmission power of the original CDMA system. The constructed CDMA system, however, transmits a total of BK bits in each time, which corresponds to a CDMA system with BK users, with BK being arbitrarily large if B is sufficiently large. Thus, if BK is over five hundred, the LAS and the LML detectors can achieve the BER of the GML detector as well as the single-user BER in the high SNR regime for practical CDMA systems.

The method

Suppose a K-user CDMA communication system has a chip period T₀ or a bandwidth 1/7 \, a bit period T_b, and thus a spreading gain N = T_b/T_c. The system can be a centralized cellular network or an ad hoc network. For a cellular network, communication can be either an up-link or a down-link.

The method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as the single-user performance in the high SNR regime in CDMA, comprises the steps of:

Step 1 : Extending, at a. transmitter, each bit by a factor of integer B to have BT _h seconds;

Step 2: Selecting randomly equiprobably, by user k {k = 1 , ..., K), B_k extended spreading sequences, each of which has BN chips and a unit length and can be densely or sparsely as stated above;

Step 3: Spreading an extended bit by an extended spreading sequence; Step 4: Transmitting, by user k (k = 1, ..., K), B_k extended bits, with the integer B being sufficiently large (but with KJN fixed) so as to allow a total number B_x + B₂ + ... + B_κ of transmitted bits for K users to be greater than five hundred; and

Step 5: Applying, at a receiver, an LAS detector or an LML detector to detect the transmitted B_x + B₂ + ... + B_κ bits, with many LAS and LML detectors being seen in the discussion herein.

The advantage of the embodiments of the present invention

The family of LAS detectors and the family of LML detectors have the characteristic that the BER in QLRS-CDMA (or QLSS-CDMA) systems, as well as LRS- CDMA systems, monotonically decreases as the total number of multiplexed bits increases — with a kept unchanged K/N. Moreover, when the total number of transmitted bits is greater than 500, the LML detectors — including the WSLAS detectors in the family of LAS detectors — approach the BER of the GML detector as well as the single- user BER in the high SNR regime. The latter means that these detectors achieve the single user bound as if there is no interference bit in the high SNR regime. More detailed theoretical analysis and simulation results can be found in footnote ⁸.

The average per-bit complexity for the family of LAS detector is lower than 0.79BK, which is linear in the number of multiplexed and transmitted bits BK, and for the LML detector with neighborhood size J is at the order of the number of combinations selecting J out of BK.⁹

Clearly, the LML detectors with neighborhood size one — including the WSLAS detectors — are particularly useful because while achieving the BER of the GML detector, they have a complexity linear in the number of transmitted bits and thus is suitable for implementation in practical CDMA systems. The embodiments of the present invention are a significant innovation for wireless-communications. They will be adoptable in the standards of next generation wireless communications that will be popularly used worldwide.

The 3^rd generation standard of wireless communications is being commercialized, but no multi-user detection technique is properly used. As the number of wireless customers is ever increasing, however, multi-user detection technique must be ultimately used in the next generations standard, i.e., 4^th and 5^th. The embodiments of the present invention are a strong candidate for the multi-user detection in the next generation wireless systems.

The embodiments of the present invention are the core technique. They target the next generation of wireless communications with high data rate transmissions.

Though for the purpose of the presentation convenience here presented is bit- synchronous uncoded data transmission over Gaussian CDMA channels, the invented QLRS-CDMA as well as QLSS-CDMA with bit extending and multiplexing and employing the LAS and LML detectors is obviously applicable to other system

⁸ Y. Sun, "Approach to optimum performance in random spreading CDMA by linear-complex LAS detectors," in Proc. 4 P' Annual Conference on Information Science and Systems, CISS '2007, The Johns Hopkins University, Baltimore, Maryland, March 14-16, 2007; Y. Sun, :A family of likelihood ascent search multiuser detectors: an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency," submitted to IEEE Trans. Commun. (ArXiv:071 1.3869).

⁹ Y. Sun, "A family of likelihood ascent search detectors achieving local maximum likelihood with an arbitrary neighborhood size for CDMA multiuser detection," in Proc. 38^th Annual Allerton Conf. on Commun., control, and computing, pp. 826-833, University of Illinois at Urbana- Champaign, Oct. 4-6, 2000; Y. Sun, "Local maximum likelihood multiuser detection," in Proc. 34th Annual Conference on Information Science and Systems, CISS '2001 , pp. 7-12, The Johns Hopkins University, Baltimore, Maryland, March 21 -23, 2001. configurations including, but obviously not limited to, bit-asynchronous, coded data transmission, fading, multipath, MIMP, or/and multicarrier CDMA channels. The spreading in both frequency and time can combat dispersion both in time and frequency when the QLRS-CDMA is applied in fading channels.

Computer simulation results

To demonstrate the significant improvement of performance by the embodiments of the present invention of LML detection in QLRS-CDMA and QLSS-CDMA with bit extending and multiplexing, computer simulations are carried out.

In all simulations, four GPLAS detectors¹⁰ with group sizes of J= 8, 4, 2, and 1 are cascaded in the order of group size. That is, the output of the GPLAS detector with a size 8 is the initial of the GPLAS detector with a size 4. Because of this, the GPLAS detector from group size 8 through 1 is a WSLAS detector. In all these GPLAS detectors, bits are partitioned into groups and are updated group-by-group in the order of group indices. In all simulations, we consider all users-multiplex and transmit simultaneously the same number B_k = B bits so that the total number of transmitted bits is BK. All users have equal power and then the BER is averaged over all users in order to reduce simulation time.

In the simulations, spreading sequences are initially, independently, and equiprobably selected and then fixed. The bit flip rate ("BFR") is defined as the number of bit flips divided by the total number of detected bits. Then the per-bit complexity is equal to the BFR times BK.^U Correspondingly, if BFR is a constant regardless of BK, then the complexity is linear in BK. In all simulations, only BK is given, and thus the results are applicable to any pair of integers B and K with the given BK. The BER's and the BFR's for five samples of spreading sequences are estimated and are shown with their averages in the drawing, which will be discussed in more detail below. As reference, the BER's of the MMSE-DF and the SIC detectors are estimated in simulations. The BER's of the MF, decorrelator, MMSE, and GML detectors in the LRS-

¹⁰ Y. Sun, "A family of linear complexity likelihood ascent search detectors for CDMA multiuser detection," in Proc. IEEE 6^th Int. Symp. on Spread-Spectrum Tech. & ApplL, ISSSTA '2000, Parsippany, NJ, Sept. 6-8, 2000; Y. Sun, "A family of likelihood ascent search multiuser detectors: an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency," submitted to IEEE Trans. Commiin (arXiv:071 1.3869).

" Y. Sun, "A family of likelihood ascent search multiuser detectors; an upper bound of bit error rate and a lower bound of asymptotic mulituser efficiency" submitted to IEEE Trans. Commun. (ArXiv:071 1.3867); Y. Sun, "A family of likelihood ascent search multiuser detectors: approach to single-user performance by random sequences in CDMA," submitted to IEEE Trans. Commun. (ArXiv:071 1.3867). CDMA limit are also shown based on the result found in footnote ^l2. In all figures showing BER, the initial vector of the GPLAS detectors is MF, while the BFR is shown with both the random vector and the MF, respectively, being the initial vector. Given a fixed set of spreading sequences, all these suboptimal detectors including the LAS detectors are linearly complex.

Simulation results for OLRS-CDMA

FIGURES l(a) and l(b), which are, respectively, a graph of BER versus BK, where a = K/N= 0.8 and SNR = 1 IdB, and a graph of BFR versus BK, where a = 0.8 and SNR = 1 IdB, demonstrate, respectively, the BER and BFR versus BK. As the total number of multiplexed bits increases, the BER' s of the GPLAS detectors monotonically decrease. In particular, when the group size is relatively small — say the WSLAS detector — the BER' s achieve the BER of the GML detector when BK is greater than one thousand. The average per-bit complexity of all the GPLAS detectors shown in FIGURE l(b) is less than 0.65BK with the random initial vector and only less than 0.23BK with the MF initial detector. In contrast, the complexity is the higher 1.5BK for the MMSE-DF and the NP-hard O(2^BKl{BKj) for the GML detector.

FIGURES 2 (a) and 2 (b), which are, respectively, a graph of BER versus a, where 1 136 < BK < 3328 and SNR = 1 IdB, and a graph of BFR versus a, where 1136 < BK < 3328 and SNR = 1 IdB, illustrate, respectively, the BER and BFR versus a with MF being the initial detector. In the regime of a < 1.0, the GPLAS detectors perform much better than the other suboptimal detectors. As a increases, the GPLAS detectors are slightly affected, while other suboptimal detectors apparently suffer from the increasing interference. It is significant that the GPLAS detectors with J= 1 and 2 perform equally well as the GML detector does. Beyond this regime, the BER' s of the GPLAS detectors sharply increase around the transition a = 1.1, while the GML detector on average behaves similarly at a = 1.324, which takes on three different BER values for a > 1.324. As shown in FIGURE 2(b), the complexity of the GPLAS detector is less than 0.79BK with a random initial vector and less than QAlBK with the initial MF detector.

Meanwhile, it is observed that in the regime of a < 1, the initial detector has no affect on the BER of the GPLAS detectors when BK < -¹OO. Compared with the random initial, however, the MF initial increases the transition a by about 0.05 (i.e. from 1.1 to 1.15).

¹² D. N. C. Tse and S. V. Hanly, "Linear multiuser receivers: effective interference, effective bandwidth and user capacity," IEEE Trans Injorm Theory, vol. 45, pp. 641 -657, Mar. 1999; T. Tanaka, "A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors,' IEEE Trans, on Inform. Theory, vol. 48, pp. 2888-2910, Nov. 2002. FIGURES 3 (a) and 3(b), which are, respectively, a graph of BER versus SNR for a system where a = 0.8 and BK = 3000, and a graph of BFR versus SNR for a system where a = 0.8 and BK = 3000, illustrate the BER and BFR versus SNR. Since a is less than 1.0, the GPLAS detectors with the small group sizes J= 1 and 2 achieve the BER of the NP-hard GML detector in all SNR. In particular, their BER' s converge to the single user bound as SNR increases. This suggests that they achieve the optimum asymptotic multiuser efficiency, which is proved equal to one.¹³ In contrast, all other suboptimal detectors have an asymptotic multiuser efficiency less than one. The complexity of the GPLAS detectors is slightly affected by SNR and is less than Q.69K with a random initial vector and less than 0.29K with the initial MF detector. In all the simulations, the SLAS detector¹⁴ achieves almost the same performance as the WSLAS detector since both are LML detectors with neighborhood size one. The former, however, has a little higher complexity.

Simulation results for QLSS-CDMA In the simulation, the SLAS detector with updating bits cyclically bit by bit is employed. The initial detector is the MF. The BER of the fixed point for each of the SLAS detectors is reported. For BK ≤ 128, completely random spreading sequences are used such that a set of sparse sequences is randomly selected in each transmission. For BK > 128, five sparse sequences with L nonzero chips are randomly selected and fixed for all transmissions, and the BER' s for five samples are estimated and shown together with their averages in figures. As a complexity measure, the number of additions per bit counted from the core operation is also estimated.

FIGURES 4 (a) and (b) demonstrate respectively the BER and complexity versus the total number of transmitted bits BK with a = 0.8 bits/s/Hz, and SNR = 11 dB. As BK increases, the BER's for all L monotonically decrease. This justifies our proposal to construct a QLSS-CDMA channel. When L increases, the BER approaches the limit of the dense spreading with L = N, which approaches the GML BER and the single-use performance in high SNR when BK > 500. When L = 16, the BER with sparse sequences with the SLAS detector is already very close to GML performance with dense spreading. The complexity in additions per bit monotonically increases with increasing BK and L but is saturated with respect to BK for small L (< 16). Hence, using sparse sequences with L

¹³ D. N. C. Tse and S. Verdϋ, "Optimum asymptotic multiuser efficiency of randomly spread CDMA," IEEE Trans. Inform. Theory, vol. 46, pp. 27 18-2722, Nov. 2000.

¹⁴ Y. Sun, "A family of linear complexity likelihood ascent search detectors for CDMA multiuser detection," in Proc. IEEE 6"' Int. Symp. on Spread-Spectrum Tech. & Appli., ISSSTA '2000, Parsippany, NJ, Sept. 6-8, 2000. =16 can approach the GML performance while the complexity is significantly reduced in comparison with the dense spreading. The same result is demonstrated in FIGURES 5 (a) and (b) that respectively show the BER and complexity versus the nonzero-chip number L with a= 0.8 and SNR = 1 IdB. FIGURE 6 shows the BER versus SNR with BK = 1024 and a = 0.8. As L increases, the BER monotonically decreases. In particular, the SLAS BER with L = 16 is already indistinguishable from the GML BER with the dense spreading and approaches the single-user bound in the high SNR regime. The complexity of the SLAS detector is insensitive to SNR and the value can be seen from FIGURES 4 (b) and 5 (b). In all the simulations, the WSLAS detectors approach almost the same performance of the SLAS detector since both are LML detectors. However, the former has a little lower complexity. All the simulations show that the variation of BER' s over different spreading sequence samples is large when L is small (say L = 4, 6) but decreases as L increases. It is significantly demonstrated in simulation results that the BER of the QLSS

CDMA monotonically decreases and the complexity increases as L increases. When L = 16, the BER of the QLSS CDMA is already very close to the BER of the QLRS CDMA, approaching the single-user performance in the high SNR regime; and the complexity is significantly reduced by several orders compared with QLRS CDMA. Since the core operation of LAS detector is the update of likelihood gradient,¹⁰ the sparse sequences can significantly reduces the complexity of the LAS detector.

Conclusions

It will be understood that each of the elements described above or two or more together may also find a useful application in other types of constructions differing from the types described above.

While the embodiments of the present invention have been illustrated and described as embodied in a method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as single-user performance in the high SNR regime in random densely and sparsely spread CDMA, however, they are not limited to the details shown, since it will be understood that various omissions, modifications, substitutions, and changes in the forms and details of the embodiments of the present invention illustrated and their operation can be made by those skilled in the art without departing in any way from the spirit of the embodiments of the present invention. Without further analysis, the foregoing will so fully reveal the gist of the embodiments of the present invention that others can by applying current knowledge readily adapt them for various applications without omitting features from the standpoint of prior art fairly constitute characteristics of the generic or specific aspects of the embodiments of the present invention.

Claims

ClaimsThe invention claimed is:

1. A method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as single-user performance in a high SNR regime in random densely and sparsely spread

CDMA, comprising the steps of: a) extending, at a transmitter, each bit by a factor of integer B; b) selecting randomly equiprobably, by each user, a number of extended dense or sparse spreading sequences, each of which having BN chips and a unit length; c) spreading an extended bit by an extended spreading sequence; d) multiplexing and transmitting, by each user, a number of extended bits, with the extending factor B and the multiplexing factors being sufficiently large so as to allow a total number of transmitted bits to be greater than five hundred; and e) applying, at a receiver, a LAS detector or an LML detector to detect the transmitted bits of all users.

2. The method of claim 1, wherein said extending step includes extending, at a transmitter, each bit by a factor of integer B to have BT_h seconds.

3. The method of claim 1., wherein said selecting step includes selecting randomly equiprobably, by a user k (k = 1, ... K), B_k extended spreading sequences, each of which having BN chips and a unit length and being one of densely and sparsely spreadable.

4. The method of claim 1, wherein said multiplexing and transmitting step includes transmitting, by the user k (k = 1 , ... K), the B_k extended bits, with the integer B being sufficiently large, but with KJN fixed, so as to allow a total number B₁ + B₂ + ... + B_κ of transmitted bits to be greater than five hundred.

5. The method of claim 1, wherein said applying step includes applying, at a receiver, one of a LAS detector and an LML detector to detect the transmitted B₁ + B₂ + ... + 5^ bits.

6. A method of local maximum likelihood detection with bit extending and multiplexing to approach optimum performance as well as a single-user performance in a high SNR regime in CDMA, comprising the steps of: a) extending, at a transmitter, each bit by a factor of integer B to have BT _h seconds; b) selecting randomly equiprobably, by a user k (k = 1, ... K), B_k extended spreading sequences, each of which having BN chips and a unit length and being one of densely and sparsely spreadable; c) spreading an extended bit by an extended spreading sequence; d) transmitting, by the user k (k = 1 , ... K), the B_k extended bits, with the integer B being sufficiently large, but with K/N fixed, so as to allow a total number B₁ + B₂ + ... + B_κ of transmitted bits to be greater than five hundred; and e) applying, at a receiver, one of a LAS detector and an LML detector to detect the transmitted B₁ + B₂ + ... + B_κ bits.