WO1999045669A1

WO1999045669A1 - Apparatus for incorporating multiple data rates in an orthogonal direct sequence code division multiple access (ods-cdma) communications system

Info

Publication number: WO1999045669A1
Application number: PCT/US1999/003722
Authority: WO
Inventors: Timothy F. Cox; Francis D. Natali; John E. Ohlson; Shilpa Talwar
Original assignee: Stanford Telecommunications, Inc.
Priority date: 1998-03-04
Filing date: 1999-03-01
Publication date: 1999-09-10
Also published as: JP4361682B2; AU2778199A; CN1299542A; CA2322543A1; EP1060588A1; EP1060588A4; CN1193528C; JP2002506320A; US6563808B1; AU748010B2

Abstract

An ODS-CDMA communications system is disclosed with at least one hub station and a plurality of user terminals. Each user is assigned a code which is orthogonal to all of the other user codes. The orthogonal code period is chosen such that the code repeats an integer number of times in a data symbol time and the code is synchronized with the symbol transitions so that no data transitions occur within the code. Thus, the selection of an orthogonal code book which enables a high rate data to be spread using shorter code words, and conversely, low data rate to be spread using longer code words, all or which remain mutually orthogonal.

Description

APPARATUS FOR INCORPORATING MULTIPLE DATA RATES IN AN ORTHOGONAL DIRECT SEQUENCE CODE DIVISION MULTIPLE ACCESS (ODS-CDMA) COMMUNICATIONS SYSTEM

Background and Brief Description of Prior Art

Spread spectrum communications is being used for a number of commercial applications and is proliferating at a rapid rate. Synchronous orthogonal direct sequence coda division multiple access (ODS-CDMA) has been proposed (see U.S. Patent No. 5,375,140, 'Wireie** Direct Sequence Spread Spectrum Digital Cellular Telephone System", incorporated herein by reference) as an affective technique for improving the capacity, i.e., bandwidth efficiency, of the more conventional quasi-orthogonal CDMA.

in conventional direct sequence (DS) spread spectrum CDMA systems, the individual users transmit on the same frequency using different pseudo-noise (PN) codes. The PN codes are quasi-ortnogonal, i.e. they have relatively low but nonzero cross-correlation values with each other.

ODS-CDMA systems are designed such that all signals are received in tone and frequency synchronism. Thus all users remain orthogonal to each other and, in an ideal world, any user can be recovered with no multiple access noise from other users. This is most practical in a star configured network where a multiplicity of users transmit to and receive from a single Hub Station. This configuration is used in cellular as well as satellite networks.

in an ODS-CDMA system, each user is assigned a code which is ortnogonal to all of the other user codes (i.e. the ortnogonal codes have a cross-correlation value of zero with each other). Further, the orthogonal code period is chosen such that the code repeats an integer number of times in a data symbol time (usually once, since this results in the maximum number of available ortnogonal functions). The code epoch is synchronized with the symbol transitions so that no data transitions occur within the code. The number of users is limited by the number of orthogonal codes available, which is equal, at most, to the length of the code. Therefore, the chipping rate is equal to the maximum number of orthogonal users times the symbol rate.

Efficient use of the available bandwidth is accomplished by using bi-phaβe spreading and MPSK data modulation as taught in U.S. Patent Number 5,687,166, "Modulation System for Spread Spectrum CDMA Communication," incorporated herein by reference.

It is often desirable to accommodate a mix of different rate users where the rates are related by 2" where n is a positive integer. One coαe-efficient way to do this is to size the system for the lowest user rate and then demultiplex higher rate data onto multiple orthogonal codes, i.e. data of a user at 4 times the nominal rate would be demultiplexed and spread onto 4 codes which are then summed for transmission. This scheme, while efficient in the use of orthogonal codes, produces a signal with a wide dynamic range which is a disadvantage for the subscriber terminal power amplifier efficiency. It also requires multiple correlators and multiplexing to recover the original data stream. This technique is discussed by Ejza , et al in "BALI: A Solution for High-Speed CDMA Data," in Bell Labs Technical Journal, vol.2, no.3, Summer 1997.

Another technique is disclosed in U.S . ^patent Application Serial No. 08/352 , 313 , now U.S . Patent Mo. 5 , 574 , 721 , entitled "Orthogonal Code Division Multiple Access Communication System Having Multicarrier Modulation" incorporated herein by reference, ∑n this disclosure, it is suggested that multiple ODS-CDMA signals be transmitted on orthogonally spaced carriers (i.e. spaced at the chipping rate ) and the data from a single high rate user is demultiplexed onto the multiple carriers. Once again, this results in a signal with vide amplitude variation. In U.S. Patent Numoer 5,416,797 "System and Method for Generating Signal Waveforms in a CDMA Cellular Telephone System," incorporated herein by reference, lower data rates than the nominal are supported on the cβll-to-mobile link (which is orthogonal), by repeating data symbols of a low rate user a number of times to obtain the nominal symbol rate. This sequence of symbols is then spread by an orthogonal code and transmitted at a lower power proportional to the lower rate. This technique has the disadvantage of not being orthogonal code space efficient, i.e. each low rate user uses the same amount of code space as a high rate user.

In "Design Study for a CDMA-Based Third Generation Mobile Radio System," IEEE Journal on Selected Areas in Communication, vol. 12, no. 4, May 1994, Baier, et ai, propose to use variable length spreading codes to support variable data rates in a CDMA system. However, they propose to use PN codes that are not necessarily orthogonal.

Objects of the invention

An object of this invention is to provide a means by which an ODS-CDMA communications system can function efficiently with data rates that are not all equal. This non-homogeneity in data rates allows different users to communicate with different data bandwidths while the ODS-CDMA communications system signaling rate and orthogonal nature remain the same as in a homogeneous data rate system. λ further object of this invention is to provide an ODS-CDMA system which supports a mix of users , with data rates related by 2', which makes efficient use of the available orthogonal code space, i.e. a user with symbol rate R/k uses 1/k of the code space of a user with symbol rate R.

it is a further object of this invention to ensure that users of all rates transmit a relatively constant amplitude signal. This is of particular importance to the subscriber terminal where high transmitter power efficiency (at or near saturation) is desirable due to the impact on cost and power consumption.

It is a further object of this invention to keep signal proceaaing complexity to a minimum.

Summary of the invention

In an ODS-CDMA system, each user is assigned a code which is orthogonal to all of the other user codes (i.e. the orthogonal codes have a cross-correlation value of zero with each other). Further, the orthogonal code period is chosen such that the code repeats an integer number of times in a data symbol time (usually once, since this results in the maximum numoer of available orthogonal functions) and the code epoch is synchronized with the symbol transitions so that no data transitions occur within the code. Thus, in a perfectly synchronized system, the individual users can be demodulated with no interference from other users.

The number of users is limited by the number of orthogonal codes available, which is equal, at most, to the length of the code. Note that the chipping rate is equal to the maximum number of orthogonal users times the symbol rate. This implies that, for a fixed chipping rate, a system transmitting data at a rate of R/4 should be able to accommodate 4 timeβ as many users as a system with rate R

Efficient use of code apace in a system with a mix of user rates ensures that a user with rate R4 will only occupy 1/4 of the orthogonal function space of a user with rate A The invention disclosed herein teaches an efficient way to construct such orthogonal cooes by selection of an orthogonal codebook wherein siihsequences of the codewords are also orthogonal. With such a codebook, short codes for high rate users are determined directly by the subsequences, and long codes for tow rate users are determined by the Kronecker product of the subsequences with an orthogonal codeword allocated to these users. As a preferred embodiment, the Sylvester construction of a Haoamard matrix is used to generate the orthogonal codebook. Thus, this invention discloses how to efficiently support variable data rates in a synchronous ODS-CDMA communication system with constant chip rate.

The novelty of this invention lies in the selection of an orthogonal codebook which enables high rate data to be spread using shorter codewords, and conversely, low rate data to be spread using longer codewords, ail of which remain mutually orthogonal.

Further, using this invention, each user transmits a single code that is constant in amplitude and requires no data multiplexing or demultiplexing. The disclosed technique results in low receiver and transmitter complexity since no additional code generators or correlators are required to accommodate rates that are higher or lower than the nominal data rate. Further, the constant amplitude nature of the signal allows efficient power amplification.

Description of the Drawings

Figure 1. Diagram of multi-rate ODS-CDMA Return Link Structure with M users Figure 2. Diagram of an Exemplary ODS-CDMA Receiver at the Hub Station

Detailed Description of the Invention

A generalized structure for an ODS-CDMA communications system is illustrated in Figure 1. A Return Link structure is shown to facilitate the invention description, however, the concept can be applied to the Forward Link as well, in the Return Link structure, many users communicate with the Hub Station by means of a modulator and transmitter process that uses some medium for tran^βmission. The most common medium for transmission is radio frequency electromagnetic radiation. In this example, all users in the Return Link transmit on the same carrier frequency using the same type of modulator, it is necessary that the users transmit at time instances such that all signals received at the Hub 6

Station are time synchronous. The waveform transmitted by each user comprises of MPSK modulated data spread with an orthogonal ODS-CDMA code.

In order to accommodate multiple data rates whiiβ maintaining a constant chip rate for all users, the length of spreading code for each user is varied. An orthogonal codebook is constructed which enables high rate data to be spread using shorter codewords, and conversely, low rate data to be spread using longer codewords, all of which remain mutually orthogonal. In a preferred embodiment, the Sylvester construction of a Hadamard matrix is used to generate the codebook.

It is well known in the art that a Syivβster-Hadamard matrix of dimension N Is defined recursively as

H(N >- \^{H(N/2 ) (N/2> '} ^[ ' [H(N 2) -H(N/2)_m where H(1) ■ [f] and N « 2", where n is a positive integer. The N rows of the Hadamard matrix H(N) define an orthogonal codebook. For convenience, the rows are indexed from 0 to N-1 , starting from the top row. It can be seen from the recursive construction of H(N) that it is composed of Sytvester-Hadamard submatrices of the form ±H(NΣ*), where k is a positive integer ranging from 1 to n-7. Since the rows of H(N/2?) are orthogonal, it follows that the codewords of H(N) consist of subsequences of length N/2* that are orthogonal as well.

Consider a multi-rate ODS-CDMA communications system with fixed chip rate L some fundamental data symbol rate /_«, and a codebook of N orthogonal sequences such that t_c*Nf÷ If there exist M Return Link users with data streams at the fundamental symbol rate, each user may be assigned one of the N orthogonal codewords as long as M ≤ N. However, if there exist users that request higher or tower data rates compared to the fundamental rate, they may be assigned shorter or longer codewords, respectively. These shorter (longer) codes are constructed from the codeword in a fashion such that the orthogonal nature of the ODS-CDMA system is maintained and the code space is used efficiently. An illustrative example is considered first to motivate the general approach for constructing these variable length codewords.

Suppose one of the users request a higher symbol rate, say at twice the fundamental rate 2f_$. Since the chip rate, which is the product of the spreading sequence length and the symbol rate, is fixed, it follows from i_e =(N2)(2f_), that the spreading sequence length per symbol must be reduced to N/2. This can be implemented by spreading alternate symbols of the high rate user by the first N/2 chips of a codeword and the last N/2 chips of the same codeword. Since this codeword is sub-divided into two N/2 subsequences, the remaining codewords must be orthogonal over each of these two subsequences such that the users at fundamental rate /, and the high rate user at 2f, do not mutually interfere, thereby maintaining orthogonality in the ODS-CDMA system. Consider allocating the ft* . codeword to this user (k = 0, 1,...,N-1). If a Syivester-Hadamard matrix is used as the orthogonal codebook, the (k+(N2))moa(N) codeword does not possess the required N/2 subsequence orthogonality since it contains the same two subsequences (up to a ± sign) and therefore cannot be allocated to other users. For example, if the high rate user is assigned the A* code word c* = fSrø Snal, the codeword a « [S*_? SNOH for /^' « (k+(N/2))mo<m cannot be assigned to another user, and vice versa. Note that if a user at rate 21, is assigned a single short subsequence in N2 space (say subsequence Srø), this is equivalent to using two codewords in the N space codebook. Hence, in an alternative implementation, a rate 2f, user may be supported by assigning the user a shorter subsequence of length N/2, and removing the codewords which contain this subsequence from the list of aliocabie codewords.

in general, a multi-rate ODS-CDMA system with a codebook of N Syivester- Hadamard sequences (N ε _? for some integer p), fundamental data symbol rate f$, and a fixed chip rate « Λ//„ can support users with higher data rates than the fundamental rate. The users may request to transmit data at rates Zf„ where r ranges from 0 to p. This is achieved by reducing tne iengtn of the spreading code to N2 such that the chipping rate, «'- s(N/Z)(_ft_)_t remains constant Subsequences of length N/2f can be generated by sub-dividing an allocated codeword of iβngth N into 2? sub-codes. These sub-codes are used to spread 2 consecutive symbols of a data stream at rate 1, . Note that in the case of the Syivester-Hadamard sequences, any coαeword of length N is a repeated subsequence of length N/2 (up to a ± sign), which is orthogonal to the other non- identical subsequences of the same length.

Further, if the A* codeword is composed of a repeated subsequence of length N/2 (up to a ± sign), tnen the codewords (k+i⁽N2y,_ma< H)' ^or ^ ^{i m} 1 £.-•>. / -1 and r > 0, are also composed of the same suoseαuence (up to a ± sign), and are no longer available tor allocation, if system orthogonality is to be preserved. Indeed, supporting 1 user at data rate 2f, is effectively equivalent to supporting Queers at rate f, since 2-1 codes are rendered unusable.

In a network setting where multiple users are transmitting at different data rates, appropriate provisions must be made for accommodating the data rate request of a new user in terms of checking for aiiocabie subsequences. In fact, the network controller must, before assigning a subsequence, make certain that it is not contained in the iongersubsequence of a lower rate user (since the lower rate user would not be orthogonal over the subsequence length). Further, t must not contain a subsequence of shorter length that is already in use.

it ia advantageous for the network controller to have the capability to change orthogonal sequence assignments periodically in order to most efficiently use the code space as the mix of user rates changes, in addition, since the symbol interval of data at rate 2f, is reduced to 12 times the symbol interval of data at rate /» it may be desired, depending on the application, to increase the transmit power tif2 to maintain the same level of performance. Conversely, a multi-rate ODS-CDMA communication system with a codebook of N orthogonal sequences, fundamental data rate /, , and a fixed chip rate " Nf_{9 t} can support usere with tower data rates than the fundamental rate. The users may request to transmit data at rates fj2, where r is a positive integer ranging from Oto σ. A tower rate user, at rate f/2, is assigned a longer spreading code of length 2N such that the chipping rate, _*(2N)(fβ Z), remains constant The long code is constructed from the codeword allocated to this user, c_. k m C,...,Λ , as follows.

First, an orthogonal function set G(2) of size 2 is constructed. This could be, but la not necessarily, a Syivester-Hadamard matrix. The Kronecker product of the f row of G(2) with the codeword c* produces a member L*_ j* C,...,2-1 of a set of 2 mutually orthogonal codes of length 2N. Each of these long sequences is orthogonal to codewords a, where i≠k, &a well aa longer code words Lf formed by the Kronecker product of each row of G(2) with the codewords Q. Thus, up to .2* users of rate fj can be assigned to a single code word c_ by assigning each user a different row of G(2). This code construction technique can be generalized to accommodate a mix of users with different rates of the form f 2, with the maximum aggregate symbol rate bounded by .

The proposed scheme suggests that the symbol interval of data at rate /2 is increased to ^ times the symbol interval of data at rate /_«. It may be desired that a user at the tower data rate reduce transmit power by 2 in order to maintain the eamβ symbol-to-noiso energy ratio (Es No).

The Hub Station receives a superposition of signal waveforms transmitted by the Return Link users. The received signal is demodulated and deapread by the multi-rate ODS-CDMA receiver. The despreading operation involves correlating the received waveform with the spreading sequence of the desired user over a symbol interval. Hence, in a multi-rate system that supports users at higher data rates than /* the waveform of a user at rate 2f, is deapread by correlating it 10

against the user's allocated N2 chip subsequence. Conversely, in a multi-rate system that supports users at lower data rates than /„ the waveform of a user at rate 1J2 is despread by correlating rt with the user's allocated 2N chip Kronecker-product code. In both cases, the dβspreading operation requires that the codewords of all users be time aligned at the code boundaries in order to preserve orthogonality, and that the data symbol rates of all users be known at the receiver. Furthermore, in a system supporting lower rates, the row index of G(2), used in forming the Kronecker-product code, must be known at the receiver. Appropriate provisions are to be made in a multi-rate ODS-CDMA system to satisfy these requirements.

A functional block diagram of the Return Link structure in the proposed multi-rate ODS-CDMA system is shown in Figure . In this figure, M users transmit data to the Hub Station at data symbol rates 2 i» 2*L..., 2"f_t , where η j « 1,...,M, ranges from 0 to p for a system supporting higher rates than from -q to 0 for a system supporting lower rates than /«, and -<7 to p for a system supporting both high rate and tow rates. If the fix user requests a higher rate {ή ≥ 0), the user's code generator generates a codeword of length N at rate /«, which is equivalent to generating 2 sub-codes of length 2^rήN in time-division multiplex at rate f₊ On the other hand, if the yth user requests a lower rate (ij ≤ 0), the user's code generator generates a Kronecker-product code of length 2*H at rate 2^ff_. Hence, at each symbol interval, 7} - 1/(2* fj, the data symbol of the h user is multiplied by the codeword from the code generator, and the resulting chip sequence is modulated and transmitted to the Hub station.

The Hub Station receives the composite signal waveform of the M Return Link users. The functional block diagram of an exemplary multi-rate ODS-CDMA receiver at the Hub Station is shown in Figure 2. The receiver demodulates the received waveform and despreads it For the /h user with ή ≥ 0, dβspreading involves formatting each block of N chips of demodulated data into subsequences of length Z N, and correlating each of these subsequences with 11

the sub-code from the code generator. If ή ≤ 0, each block of Z N chips is correlated with the long code from the code generator. In the absence of channel distortions, the correlator output yields the user data.

A simple illustrative example which embodies the present invention is as follows.

Consider a multi-rate ODS-CDMA system with a codebook derived from Syivester-Hadamard matrix of dimension N» 4,

+ 1 + 1 +1 + 1 C,

+1 - 1 + 1 - 1 Cι

#(4)>

+ 1 + 1 - 1 -1 c_

+ 1 - 1 - 1 +1 fundamental data symbol rate /«, and fixed chip rate f_c »4f₉.

Suppose User 1 is assigned codeword 0, Co ** [+1 +1 +1 +1]. and is transmitting at rate /,. Now, a new user, User 2, requests to transmit at rate 2f₊ From the codes available for allocation, c, c₂ and c& only c, or c₃ may be allocated to User 2 since the length 2 subsequences of c* namely [+1 +1] and [-1 -1], are not orthogonal to the corresponding subsequences of Co. Let code ci be assigned to User 2. The chip sequence transmitted by User 1 within the time interval T_»« 1/f, is x ■ s^+1 +1 +1 +1], where sf¹* is the current data symbol. Similarly, the chip sequence transmitted by User 2 within the same time interval is x® s [s_β*t+1 -1] 5^+1 -ID, where s_^& and SiP are the current data symbols. Note that with the current allocation scenario, only code c₉ is available for allocation to a new user with symbol rate /, or lower. A user that requests a higher symbol rate cannot be supported unless the codes are reassigned.

The signal received at the Hub Station (after demodulation) is of the form

, **> + >

«s" ι +1 +ι +i] + tøΛ+ι -1] «Λ+ι -1J. 12

The signal is de-spread by correlating it with the appropriate spreading code. For User 1, this is achieved by computing the following inner product

+1

4 +1 +1 which yields the transmitted data symbol. The data symbols of User 2 are retrieved by first partitioning the received chip sequence into 2 subsequences, /"■[/* /i], where ϋ-^β^t+l +1] + s«^Λt+1 -1] end *^«s^+1 +1} + sΛ+1 -1] and then computing the following inner products

and

Now, suppose a third user, User 3, requests to transmit at rate f$/2. Let this user be assigned codeword c and row 0 of G(2), the Sytvester-Hadamard of order 2. The tong spreading code for User 3 is given by the Kronecker product of row 0 of G(2) with the codeword cp

Lα>«[+1 +1]®C» -I C], which la β chips long.

An additional user at rate f/2 may be accomodated with the orthogonal code constructed by taking the Kronecker product of row1 of Grø) with Cι to give L»* [+1 -1) ® cy [ cy -Cj], or 2 additional users can be supported at the rate f 4 by taking the Kronecker product of the rows of G(2) with Lijto construct La*- [4*1 ^•+1)® w^« [C -c* cj -cjjj andLw* [+1 -1 Jβiw -l<* -Cj -Cj cj. Note that the codes L'* and i j are 16 chips long. 13

At the Hub Station, the data symbols of User 3 are retrieved by correlating the signal received over time period T, = 2/f$ with the long code rø. It follows from the constniction of the codes that the interference from Users 1 and 2 is zero at the correlator output

In summary, the example system described above can support higher rates than of 21,, 4f„ and lower symbol rates of 1J2, f^4, ... fj2.

If the multi-rate system allows high rates only, at full capacity with total system throughput 4f„ the following allocation scenarios can be supported: a) 4 users transmit at f, b) 2 users transmit at f„ and 1 user transmits at 21, c) 2 users transmit at 2f, d) 1 user transmits at 4f»

Conversely, if the multi-rate system allows low rates only, for each codeword c_ k m θ, 1,2,3, some of the scenarios that can be supported are: a) 1 user transmits at f$ b) 2 users transmit at fJ2 c) 2 users transmit at 4, and 1 user transmits at 1J2 d) 4 users transmit at f/4 e) 2* users transmit at f 2¹

Note that a maximum data rate of /, can be supported per codeword, yielding, as before, a total system throughput of 41,. Finally, if the multi-rate system allows both high and tow data rates, a variety of allocation scenarios are possible, and again the total system throughput is bounded by 4f_t.

Claims

14Claims

1. in an ODS-CDMA communications system with at least one Hub Station and a plurality of user terminals, a means for generating a codebook of N orthogonal sequences where N a 2 for some integer p, a fundamental data symbol rate fΓÇ₧ and a fixed chip rate 1_C where = N1ΓÇ₧ the improvement comprising: means for supporting users with multiple data rates by assigning them mutually orthogonal codes of different lengths, while maintaining, the same chip rate, and the same peak-to-average ratio at the transmitter as in a homogeneous data rate system.

2. In the system of Claim 1 , where users desiring to transmit data at a rate of 2fΓÇ₧ where r ranges from 0 to p, are assigned orthogonal subsequences of length N/2 generated by sub-dividing the allocated codeword of length N, from the codebook of N orthogonal sequences, into ^subsequences.

3. In the system of Claim 1 , the Sylvester construction of a Hadamard matrix is used to generate the orthogonal codebook such that select subsequences of the codewords in the codebook are also orthogonal.

4. The system of Claim 1 , wherein users may request lower rates than the fundamental data symbol rate /,. The data symbols of a low rate user at rate 1J2, where rmay range from Oto q, are spread using a longer code of length 2N, which is constructed by the Kronecker product of a length 2 orthogonal code and the N chip codeword allocated to this user.

5. The system of Claim 1 , wherein users may request lower rates than the fundamental data symbol rate 1,. The data symbols of a low rate user at rate 1J2, where rmay range from Oto q, are spread using a longer code of length 2N, which is constructed by the Kronecker product of a row of the Syivester- Hadamard matrix H{2) and the ╬¢/chip codeword allocated to this user.

6. In an ODS-CDMA communications system with at least one Hub station and a plurality of user terminals, one or more satellites or other means for relaying the signals to and from the Hub Station, a means for generating a codebook of N orthogonal sequences where N = 2 for some integer p, a fundamental 15

data symbol rate /ΓÇ₧ and a fixed chip rate 1_e where f_e * NfΓÇ₧ the improvement comprising: means for supporting users with multiple data rates by assigning them mutually orthogonal codes of different lengths, while maintaining, the same chip rate, and the same poak-to-average ratio at the transmitter as in a homogeneous data rate system.

7. In the system of Claim 6, where users desiring to transmit data at a rate of 2fΓÇ₧ where r ranges from 0 to p, are assigned orthogonal subsequences of length N2 generated by sub-dividing the allocated codeword of length N, from the codebook of N orthogonal sequences, into ^subsequences.

8. In the system of Claim 6, the Sylvester construction of a Hadamard matrix is used to generate the orthogonal codebook such that select subsequences of the codewords in the codebook are also orthogonal.

9. The system of Claim 6, wherein users may request lower rates than the fundamental data symbol rate f,. The data symbols of a low rate user at rate fJ2, where rmay range from to q, are spread using a longer code of length 2N, which is constructed by the Kronecker product of a length 2 orthogonal code and the ╬¢/chip codeword allocated to this user.

10. The system of Claim 6, wherein users may request lower rates than the fundamental data symbol rate f,. The data symbols of a low rate user at rate 1J2 , where rmay range from Oto q, are spread using a longer code of length 2N, which is constructed by the Kronecker product of a row of the Syivester- Hadamard matrix H2) and the N chip codeword allocated to this user.