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A Novel Signalling Scheme For Cdma System

Abstract: A construction for a family, AM2, of sequences over A/2-QAM, M = 2m, of length N = 2r - 1, family size (N+ 1)/2m-1 and maximum nontrivial normalized correlation parameter bounded by dmax S V5v~N is presented. Apart from low correlation values, the family possesses several interesting and useful features. In Family AM2, users have an ability to transmit 2m bits of data per period of the spreading sequence. The Euclidean distance between the signals assigned to a particular user, corresponding to different data symbols, is larger than the corresponding value for the case when M2-PSK, M= 2m, modulation and spreading is used. Family AM2 permits users on the reverse link of a CDMA system to communicate asynchronously at varying data rates by switching between different QAM constellations. Family AM2 is compatible with QPSK sequence families S(p) in the sense that the maximum correlation magnitude is increased only slightly if one adds sequences from S(p) / S(0) to Family AM2. Also included are constructions for large families of sequences over the A/2-QAM alphabet and families of orthogonal sequences over the M2-QAM alphabet.

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Notices, Deadlines & Correspondence

Patent Information

Application #
Filing Date
26 September 2006
Publication Number
48/2008
Publication Type
INA
Invention Field
COMMUNICATION
Status
Email
Parent Application

Applicants

INDIAN INSTITUTE OF SCIENCE
BANGALORE -560012 KARNATAKA, INDIA

Inventors

1. PROF. P. VIJAYA KUMAR
DEPT. OF ELECTRICAL COMMUNICATION ENGINEERING INDIAN INSTITUTE OF SCIENCE, BANGALORE -560012 KARNATAKA
2. MR. M.ANAND
DEPT. OF ELECTRICAL COMMUNICATION ENGINEERING INDIAN INSTITUTE OF SCIENCE, BANGALORE -560012 KARNATAKA

Specification

FIELD OF THE INVENTION This invention relates to a novel signaling scheme for CDMA systems. DISCUSSION OF PRIOR ART In order to allow multiple users to access the channel simultaneously, CDMA systems assign signatures to different users. CDMA sequence families or spreading codes require careful design and remain an important consideration, impacting a variety of communication applications. Technology trends that push towards wideband digital mobile cellular and personal communication systems based on CDMA, lead to the consideration of generalizations of CDMA. Direct-Sequence Code Division Multiple Access (DS-CDMA) systems are widely in use in modern communication systems. For example, 3G cellular standards use DS- CDMA. In 3GPP WCDMA standard [30], the system supports variable data rates (from 1 bit to 64 bits per sequence period with sequences of period 256) at a chip rate of 3.84 Mcps in a 5 MHz bandwidth. The variable data rate feature is achieved through variable processing gains using orthogonal Walsh codes. Therefore, Walsh codes are used for multiplexing of different channels in WCDMA. Either sequences from the Gold family or the sequences from Family S(2) are used as scrambling sequences in WCDMA. With the widespread usage of binary digits to represent data, low-correlation sequence families are emphasized whose symbol-alphabet is a subset of the complex numbers having size that is a power of 2. Sequences over real-valued alphabet such as the BPSK {±1} alphabet or the PAM alphabet are not considered since apart from their inherent ability to provide increased spectral efficiency, the corresponding complex counterparts of these alphabets, namely QPSK and QAM, offer better correlation performance in general. For instance, for family sizes that are approximately equal to the sequence period N, for the best known BPSK and QPSK sequence families is approximately given by -JlN and ViV respectively [6,5]. Table 1 provides a quick overview of some prior constructions over the 2* -PSK constellation for various k, and over the 16-QAM constellation. The quaternary sequence family, Family A [22,3,5], has the same size as the family of Gold sequences [6], but smaller value of 0^. Quaternary families {S(p)}, p > 1, [12] are larger families with correspondingly larger values of 0^. Sequence family 5(2) appears in the W-CDMA standard [27] as the short scrambling code. In [11], a general technique for constructing low-correlation 2m-PSK sequences is presented that is based on a Galois-ring analogue of the Weil-Carlitz-Uchiyama (WCU) bound on exponential sums over finite fields. In the table, the label WCU is used to refer to sequence families constructed using this technique. Bozta§[4] describes a construction of 16-QAM sequences, which is referred to as Family QB. The sequences in Family QB do not have good correlation properties. Also, Bozta§ does not discuss techniques to modulate or demodulate the sequences. The sequences in Family QB are not necessarily balanced and Bozta§ does not discuss the possibility of variable-rate signaling with the sequence family. Family Constellation Period Family Size Data Rate Upper Bound per Sequence on 0max Period A 4-PSK N = 2r - 1 N+2 2 i+>/w+i [22,3,5] 5(1) [12] 4-PSK N = 2r - 1 >(N+1)2 2 1 + 2-v/jV+l 5(2) [12] 4-PSK N = 2r - 1 >(N+lf 2 l+4>jN+l S(p) [12] 4-PSK N = 2r - ■1 > (iV+l)p+1 2 1 + 2p JN+1 4-PSK N = 2r - 1 1, r even 2 l + 2y/N + l WCU 8-PSK N = r-\ odd Sequences 8 -PSK N = 2r-1 8-PSK AT = 2r-l 3 3 3 Not Discussed >(W+1)4 >(iV+l)5 >(JV+1)6 (iV+l)/2 1+4VJV+1 1+5JN+1 l + 6y/N + l 1.8 y[N 8-PSK N = 2r-l QB[4] 16-QAM 7V = 2r -1 Table I In the present invention, sequences over the M2 -QAM constellation are constructed by adding scaled sequences over Z4. The theory of Galois Rings plays a key role in understanding the properties of sequences over Z4. Details concerning the connection between Galois Rings and sequences over Z4 be found in [16,7,19,11]. The maximum non-trivial correlation magnitude of a sequence family is defined to be either s(j, t),s(k,t) (1) M 0„„ := max is an important parameter for assessing and comparing sequence families to be used in CDMA communication^,9]. In the present invention, the constituent Z4 sequences comprising a M2 -QAM sequence have been chosen from Family A [22,3,5]. Various desirable properties of Family A like near-optimality with respect to correlation, mathematical tractability and ease of generation make it a prime candidate for use in constructing M2 -QAM sequences. BRIEF DESCRIPTION OF DRAWINGS have been assigned to distinct users or r*0 Fig. 1 shows a 16-QAM constellation, which is an example of the M2-QAM constellation for the case M= 4. Fig. 2 shows variable-Rate signaling with Families A i6 and A, where the users in the CDMA system have the option to transmit at a data rate of either 1 bit per sequence period or 2 bits per sequence period Fig. 3 shows variable-rate signaling with Family A' i6. Fig. 4 shows variable-rate signaling when N= 15 with five users in a CDMA system communicating at various data rates by choosing among different sequence families and hence among different QAM constellations. Fig. 5 shows an encoder for a single user in Family A\(,. Sequences corresponding to different users are obtained by changing the initialization of the quaternary shift register generating the Family sequence. Fig. 6 shows an Encoder for a single user in Family Am- Sequences corresponding to different users are obtained by changing the initialization of the quaternary shift register generating the Family A sequence. Fig. 7 shows a decoder for a single user in Family A\s, where data transmitted by different users can be decoded by changing the initialization of the quaternary shift register generating the Family A sequence. Fig. 8 shows a decoder for a single user in Family Ami where data transmitted by different users can be decoded by changing the initialization of the quaternary shift register generating the Family sequence. DETAILED DESCRIPTION OF THE INVENTION It is an object of this invention to provide a system, apparatus and method which enables communication on the reverse link of a CDMA system. By constructing a new family of sequences over the M2 -QAM constellation, with a lower correlation when compared to other sequence families in the same constellation, a high- performance communication system, apparatus and method is provided. The M2 - QAM constellation is the set {a+^b\-M +\gi,—>gm-i) • Here, G denotes the set which contains all the indexes. Each user is thus assigned the set Let m>2 be a positive integer. Let r>3 be an integer and set q = 2r. Let fa, r2,..., rm_J be a set of non-zero, distinct time-shifts with {1, ar>, aH,..., aTm'x} being a linearly independent set. Let /c=(fc0,/c1,...,fcm_1)eZ4m. Let the finite field Fy be divided to groups of m elements each with each set indexed by a single letter. A mathematical expression for Family Qm2 is provided below. of sequences with the Af-th sequence given by m-1 U=o where uk{t) = T{[ l + 2ft]«m 2. Modulation and Family size The g-th user is assigned a set of 2Zm sequences as described in (1). Therefore, the data to be transmitted by each user can be mapped onto the tuple Each user can transmit 2m bits of data per sequence period with the subset of sequences allotted to him. Actually, each Ki rotates the corresponding QPSK sequence comprising the QAM sequence. Data is transmitted by allowing rotations of the constituent QPSK sequences by multiples of 90°. From the way the elements of the finite field Fr are divided, it is clear that Family Q 2 can support a total of 2r !m distinct users. 3. Correlation and Energy of sequences 0„„ := max The maximum non-trivial correlation magnitude of a sequence family is defined to be either s(j,t),s(k,t) have been assigned to distinct users or T* 0 The family of sequences constructed here has values of . This property is helpful in reducing the mutual interference among transmissions from different users and also helps in self synchronizing the receiver to a certain user's transmission. Consider two sequences from Family Qm1 given by {-Kg,*",')} and {^(g ,K ,t)} where BI-1 U=o and m-1 y 2k JUkQ^k k=0 with uk(t) = T([l + 2gk]z Jt=0 m-l AT-1 N-i t=0 Bl-l 1=0 *,/=0 /=0 *,/=o The above expression for correlation of two sequences from Q T will be repeatedly used in the rest of the document. It indicates the convenience with which a problem regarding correlation of two M2 -QAM sequences, M = 2™, can be reduced to a problem concerning the correlation of several pairs of Z4 sequences. Using (6), can be bounded for Family g 2 as m-l 0 =2Y 2k+l 0 .(r)H*-*< k,l=0 m-l <2^ 2*+'(1+VjV+I) *,/=0 2(2M-1 fyfN The energy of any sequence, say {s(g, K,t)}, in Family Qm2 is given by =2 A*^)^'^) k*l = 2[yAkN-T2k+' U=o k*l (8) m r\m+1 J 4m -1 2 |(M2-1)W. After normalizing the sequences in the Family to have energy N, the normalized maximum magnitude of correlation of Family ^^ is given by 4. Euclidean distance The normalized minimum squared Euclidean distance between all sequences assigned to a user is given by This is achieved by looking at the squared Euclidean distance between two modulations of a sequence given by and {s(g,(l,0,...,0),f)} • (9) Family Qm1 , being a family of sequences over the M2 -QAM constellation, must be compared against families of sequences over the M2 -PSK constellation. The M2 - PSK constellation is given by All the points in the M2 -PSK constellation are on a circle of unit radius around the origin and have unit energy. If there were to exist an optimal family of sequences over the M -PSK constellation containing 0(N) sequences of the same period N as that of sequences in Family QM2, then each user would be able to transmit 2M bits of information by modulating the PSK sequence assigned to him. Now, the PSK family would be comparable to Family Qul in terms of family size and number of bits of data that can be transmitted by each user per period of the signature sequence. The minimum squared Euclidean distance between two distinct modulations of a sequence over M2 -PSK can be shown the subset of sequences assigned to a user in Family Qm2 have better distance properties when compared against modulations of a single sequence over the M2 - PSK constellation. Favorable Euclidean distance properties of Family Qul render it suitable for use in a communication system. 5. Downward Compatibility with families over Z4 In this subsection, it is proven that it is possible to use sequences from S(p) along with sequences from Qm1 in a CDMA environment. For this purpose, a new family of sequences is defined2: QM>(p) = QMiV{S(p), 5(0)}. Here, sequences in S(p) have been considered as sequences over the 4-QAM alphabet. A maximum of | S(p) | —(AT+1)^1— ^br) users can be supported in Family Qm1 (p). • The normalized maximum correlation parameter for Family Qm2 (p) can be bounded as 6. Decoding sequences in Family Q M Simple means of decoding sequences in Family QM% are presented, using the sub- optimal correlation detector. ^V3 2'^,forlargejV. Let the received signal be {r(f)} • Let the transmitted code sequence be {s(g,/c,t)}. Decoding can be accomplished by computing [JV-l m-l [ N-l (1) r(t) t=0 k=0 .1=0 at the receiver. The above quantity needs to be computed for all values of K. A decision is made in favor of the appropriate k by observing the phase of the output of the chosen detector. The structure of the receiver can be simplified by rewriting (1) as {m-l f N-l N *=o V/=o > {N-l E'te.*". /=0 (2) t)r(t) Now, just m correlators at the receiver are sufficient; each of them computing N-l t=0 In order to get the expression in (2), the outputs of the correlators described above are weighed with the appropriate power of 2 and the necessary choice of rck to get the desired value for any choice of K . Hence, just m correlators and some simple circuitry is enough to implement the receiver required to decode sequences from Family Qul. A natural question that comes up is the complexity of this receiver when compared against other possible schemes. Suppose users in a CDMA environment deploying Family A want to transmit 2m bits of data per sequence period, then each user would have to be allotted 22m sequences from Family A. Then, the CDMA environment would be able to support a maximum of (N+1) / 22m users with data rate requirement of 2m bits when compared against (N+\)/ m potential users in a system deploying Family Qm1 . Also, a total of 2lm correlators would be required at the receiver to demodulate the data transmitted by a certain user. In this case, the number of correlators grows exponentially in the size of the QAM alphabet, and in turn in the amount of data bits that a user can transmit. Whereas, in the case of Family Q^, the number of correlators increases linearly in the size of the QAM alphabet. 2. Variable-Rate Signalling in the Reverse Link One of the issues in the reverse link, in a class of CDMA systems, is the lack of synchronization among various users. Moreover, users may have different data rate requirements, i.e., may wish to communicate different bits of data per sequence period. A technique is outlined in this section by which different users can communicate at different rates, asynchronously, in the reverse link of a CDMA system. It must be emphasized that this technique can be employed at no extra complexity as far as sequence allocation is concerned, i.e., no other spreading or channelization codes will be used in conjunction with the QAM spreading sequences. Fig. 2 shows variable-Rate signaling with Families Am and A, where the users in the CDMA system have the option to transmit at a data rate of either 1 bit per sequence period or 2 bits per sequence period. Fig. 3 shows variable-rate signaling with Family A'i6. Fig. 4 shows variable-rate signaling when N= 15 with five users in a CDMA system communicating at various data rates by choosing among different sequence families and hence among different QAM constellations. Here, it is shown that the magnitude of correlation between sequences assigned to two users can be bounded over two distinct QAM alphabet. Let the two users, A and B, be transmitting sequences over M\ -QAM and M\ -QAM where Mx = 2m, and M2 = 2m2 with m, > m2. Let user A be indexed by gj = (gAgjl,...,^,^ and let user B be indexed by g2 =(g2^S2^-->S2,m2-f Let the indexes be chosen such that gu * g2J,Vi,j • Then, the normalized magnitude of the worst-case correlation between a sequence assigned to A and another sequence assigned to B, which is denoted by ~$mui, can be bounded as This result suggests that users can communicate at different data rates in the reverse link of a CDMA environment by choosing sequences over different QAM alphabet. 1. Balance The sequences in Family Qm2 are also balanced, i.e., all points from the M2 -QAM constellation occur approximately equally often in sequences of long period. Consider a sequence, from Family Qul. Let N(a), a = (a0,a1,...,an_1)€Z", be the number of occurrences of the element (1+in one period of {s(g, K,t)}. Then, the following bound on N(a): -y/N + l. M2-1 XT/ X ^ + 1 N(a) 77T M Since the above bound holds for all values of a, it is concluded that the QAM sequences are balanced. This balance property makes the sequences look random-like and is useful feature to be included in a sequence family being considered for CDMA systems. An apparatus is proposed in the present invention comprising an encoder and decoder to enable users to communicate on the reverse link of a CDMA system wherein the encoder is used for encoding by means of / quaternary shift registers, the constituent quaternary sequences uk(t),k = 0,1,-m-l which when weighted according to the expression m-l (1+H) M k=0 will generate the signal to be transmitted to generate one or more sequences over the M2 -QAM constellation, M = 2m wherein the M2 -QAM constellation is the set {a +ib | —M +1 < a, b < M -1, a, b odd} such that the new family of sequences will be called Family Qm2 Fig. 5 shows an encoder for a single user in Family A^. Sequences corresponding to different users are obtained by changing die initialization of the quaternary shift register generating the Family A sequence. Fig. 6 shows an Encoder for a single user in Family Ami- Sequences corresponding to different users are obtained by changing the initialization of the quaternary shift register generating the Family A sequence. In the present invention, a decoder is used for decoding by correlations involving signals generated by quaternary shift register. Fig. 7 shows a decoder for a single user in Family A^, where data transmitted by different users can be decoded by changing the initialization of the quaternary shift register generating the Family A sequence. Fig. 8 shows a decoder for a single user in Family Ami where data transmitted by different users can be decoded by changing the initialization of the quaternary shift register generating the Family sequence. This invention further proposes a method to enable users to communicate on the reverse link of a CMDA system including the steps of: Constructing a new family of sequences over the Af2 -QAM constellation, M = 2m where the M2 -QAM constellation is the set {a+ib \ -M +1 < a, b < M -1, a, b odd} alternatively referred to as the Family Qm1 . References [1] M. Anand and P. Vijay Kumar, "16-QAM Sequences with Low Periodic Correlation," Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, Technical Report No. TR-PME-2006-05, May 2006. [2] M. Anand, "Low Correlation Sequences over AM-PSK and QAM Constellations," M.Sc.(Engg.) Thesis, Dept of ECE, Indian Institute of Science, Bangalore, April 2007. [3] S. Bozta§, "Near-Optimal A

&i'""'£/-i} °f size I ranging from 1 to X (b) Assigning to each user a distinct subset; if this subset is of size I then that user will have 4' -QAM as the signal constellation and be able to transmit at data rate of 21 bit per sequence period wherein varying the partitioning of the Teichmuller set impacts the rate of transmission with a corresponding alteration in 11. A system of claim 1 wherein the sequences generated can co-exist with quaternary families of sequences. 12. An apparatus to enable users to communicate on the reverse link of a CDMA system comprising: 0+-9 (c) An encoder for encoding by means of / quaternary shift registers, the constituent quaternary sequences uk(t),k = 0,1,-■•,m-l which when weighted according to the expression m-l I2' U=o will generate the signal to be transmitted to generate one or more sequences over the M2 -QAM constellation, M = 2M wherein the M2 -QAM constellation is the set {a +ib | -M +1 < a,b < M-\,a,b odd} such that the new family of sequences will be called Family Qul (b) A decoder for decoding by correlations involving signals generated by quaternary shift register. 13. An apparatus of claim 12 wherein the family of sequences generated, Family Qul has the features of: i. users can transmit 2m bits of data per sequence period in Family Qul; ii. distinct users can be assigned sequences from any of the families in the set {QM1,M = 2;4;..} in accordance with their rate requirements such that this obliterates the need for separate channelization and spreading codes; and iii.in both of the above cases, the maximum magnitude of correlation between sequences assigned to distinct users can be bounded. 14. A method to enable users to communicate on the reverse link of a CMDA system including the steps of: Constructing a new family of sequences over the M2 -QAM constellation, M = 2m where the M2 -QAM constellation is the set {a+ib | -M +1 < a, b < M -1, a, b odd } alternatively referred to as the Family Qm2 . Dated this 25th day of September

Documents

Application Documents

# Name Date
1 1758-CHE-2006 ABSTRACT.pdf 2011-11-30
1 1758-CHE-2006 FORM-13 19-03-2009.pdf 2009-03-19
2 1758-CHE-2006 CLAIMS.pdf 2011-11-30
2 1758-che-2006-form 3.pdf 2011-09-03
3 1758-che-2006-form 26.pdf 2011-09-03
3 1758-CHE-2006 CORRESPONDENCE OTHERS.pdf 2011-11-30
4 1758-che-2006-form 1.pdf 2011-09-03
4 1758-CHE-2006 DESCRIPTION (COMPLETE).pdf 2011-11-30
5 1758-che-2006-drawings.pdf 2011-09-03
5 1758-CHE-2006 DRAWINGS.pdf 2011-11-30
6 1758-che-2006-description(provisional).pdf 2011-09-03
6 1758-CHE-2006 FORM-1.pdf 2011-11-30
7 1758-che-2006-correspondnece-others.pdf 2011-09-03
7 1758-CHE-2006 FORM-13.pdf 2011-11-30
8 1758-CHE-2006 FORM-5.pdf 2011-11-30
8 1758-che-2006-abstract.pdf 2011-09-03
9 1758-CHE-2006 POWER OF ATTORNEY.pdf 2011-11-30
10 1758-che-2006-abstract.pdf 2011-09-03
10 1758-CHE-2006 FORM-5.pdf 2011-11-30
11 1758-che-2006-correspondnece-others.pdf 2011-09-03
11 1758-CHE-2006 FORM-13.pdf 2011-11-30
12 1758-che-2006-description(provisional).pdf 2011-09-03
12 1758-CHE-2006 FORM-1.pdf 2011-11-30
13 1758-che-2006-drawings.pdf 2011-09-03
13 1758-CHE-2006 DRAWINGS.pdf 2011-11-30
14 1758-che-2006-form 1.pdf 2011-09-03
14 1758-CHE-2006 DESCRIPTION (COMPLETE).pdf 2011-11-30
15 1758-che-2006-form 26.pdf 2011-09-03
15 1758-CHE-2006 CORRESPONDENCE OTHERS.pdf 2011-11-30
16 1758-che-2006-form 3.pdf 2011-09-03
16 1758-CHE-2006 CLAIMS.pdf 2011-11-30
17 1758-CHE-2006 FORM-13 19-03-2009.pdf 2009-03-19
17 1758-CHE-2006 ABSTRACT.pdf 2011-11-30