GB2477918A - Design of spreading codes in wireless communications - Google Patents

Abstract

Multi user interference (MUI), which can be caused by carrier frequency offset (CFO) or in the form of timing delays, gives rise to decoding problems which can ultimately limit the capacity of a channel. Disclosed herein is a series of techniques for designing spreading and/or despreading codes to take account of the causes of multi user interference, and to mitigate for its impact in BS-CDMA systems. A first method allows the design of codes without knowledge of the CFO at the transmitter and receiver. If CFO is known at the receiver, a second method uses fixed codes at the transmitter while designing dispreading codes at the receiver by solving an optimization problem. In a third method, channel state information in addition to CFO are assumed to be known at the receiver and a closed form solution for the dispreading codes is obtained.

Description

Wireless Communications Apparatus and Method This invention relates to a method of generating a signal for transmission. More particularly it relates to a method of generating a signal for multiple access transmission. It also relates to a method of receiving such a signal.

Code division multiple access (CDMA) is a popular multiple access technique that is used to support multiple users simultaneously in a network. Many variants of CDMA exist, including direct sequence (DS) CDMA, multi-carrier (MC) CDMA, cyclic prefixed (CP) COMA, and chip interleaved block spread (CIBS) CDMA. In addition to these variations, many receiver architectures are often available for implementation in CDMA systems, such as the well-known RAKE receiver, interference cancellation receivers, and receivers that rely on channel equalisation.

Some CDMA schemes are interference limited; that is to say, as the number of users in the network increases, residual interference caused by each user eventually overwhelms the network, thus rendering simultaneous multiple access practically impossible. This residual interference generally results from the loss of orthogonality amongst users, which primarily occurs when the channel is temporally dispersive.

Several recent developments have been made in block COMA systems, such as: * so-called generalised MG-COMA' (GMC-CDMA) Zhengdao Wang and G.B.

Giannakis, Wireless Multicarrier Communications, IEEE Signal Processing Magazine, Vol. 17, May 2000, pp 29-48); * CIBS-GDMA (Shengli Zhou and G.B. Giannakis, Chip-interleaved block-spread code division multiple access, IEEE Transaction on Communications, Vol. 50, Feb. 2002, pp. 235-248); * single-carrier frequency division multiple access (SC-FDMA); * OFT-spread OFDM ("Performance comparison of distributed FDMA and localised FOMA with frequency hopping for EUTRA uplink,' NEC Group and NIT DoCoMo, ISO RAN WG1 Meeting 42 R1-050791, Aug. 2005, and D. Galda and H. Rohling, "A low complexity transmitter structure for OFDM-FDMA uplink systems," in Proc. of the IEEE Vehicular Technology Conference (VTC), vol. 4, May 2002, pp. 1737-1741); the throughput-efficient block CDMA system proposed in S. Tomasin and F. Tosato, "Throughput Efficient Block-Spreading CDMA: Sequence Design and Performance Comparison," in Proc. of the IEEE Global Telecommunications Conference (Globecom), Nov.-Dec. 2005; and * the bandwidth-efficient scheme disclosed in UK Patent Application GB2433397 and J.P. Coon, "Precoded Block-Spread CDMA with Maximum User Support and Frequency-Domain Equalization," in Proc. of the IEEE International Conference on Communications (ICC), Glasgow, 2007.

These developments have led to multi-user interference (MUI) free transmission techniques. In these systems, in theory, any number of users (up to a given maximum) can transmit simultaneously without causing any degradation in system performance.

Beyond this maximum number of allowable users, the system becomes interference limited in a similar manner to other CDMA systems.

For the benefit of the reader, the term BS-CDMA refers to a general CDMA system with block spreading and despreading operations at the transmitter and receiver, respectively. Examples of such BS-CDMA systems include the low-complexity OFDMA, single carrier-CDMA systems, and the bandwidth-efficient BS-CDMA systems disclosed in UK Patent Application GB2433397.

In a communication system, signals are usually transmitted by carrier modulation, where the modulation at the transmitter generates a band-pass signal whose spectrum is concentrated in a band of frequencies centred at the carrier frequency. The receiver demodulates the band-pass signal with this carrier frequency. However, perfect frequency synchronization between the transmitter and receiver local oscillators is difficult to obtain. The difference in carrier frequencies between the oscillators of the base station and subscriber devices is referred to as carrier frequency offset (CFO). In ideal transmissions, in which there is no CFO between the transmitter and the receiver, MUI and IBI free reception is achieved in the prior art by using orthogonal (e.g., Hadamard codes in Zhou and Giannakis) or mutually shift orthogonal spreading codes (e.g., DFT codes in GB2433397 and Coon).

The invention relates particularly to block spreading (BS) CDMA systems. n practical scenarios, where CEO is present, the orthogonality between users is destroyed. This results in severe performance degradation in a block spreading CDMA system (see figure 2). In order to combat the impact of CFO, CEO estimation and compensation can be performed at the receiver, at the expense of a reduced throughput (for example with pilot/preamble-aided methods (EP1793548A1)) and/or an increased complexity (for example iterative estimation methods (US7139339B2).

In realistic BS-CDMA systems, the timing control at the base station is good enough such that signals from different users are approximately synchronized to within the memory order of the dispersive channel, resulting in a quasi-synchronous BS-CDMA system.

Although many examples in the prior art can provide MUI and inter-block interference (lBl) free reception using BS-CDMA techniques, freedom from interference can only be achieved when perfect frequency and timing synchronization is obtained between the base station and the subscriber station. In practice, however, due to the instability and inaccuracy of local oscillators per station, it is usually hard to achieve perfect frequency synchronization between the subscriber station and the base station. The resulting CFO destroys orthogonality among users, which causes severe performance degradation in a BS-CDMA system due to MUI and IBI. Similarly, orthogonality between users can be destroyed when the signal reception between users cannot be perfectly synchronized due to delays in transmission or delays from the channel, resulting in severe performance degradation due to MUI and IBI.

In an aspect of the present invention, particular spreading/despreading codes are used to reduce the interference due to CEO or quasi-synchronous reception caused by timing errors for BS-CDMA systems.

In particular, aspects of the invention comprise at least one of three methods intended to reduce MUI due to CFO.

The first method allows the design of interference-eliminating spreading/despreading codes without any knowledge of the CFO at the transmitter and the receiver. The expense, however, is a reduced user load, where the maximum user support is half of the length of the spreading codes.

Under the assumption that CFO is perfectly known at the receiver, the second method uses fixed spreading codes at the transmitter, while designing the despreading codes at the receiver by solving a particular optimization problem. As an alternative to optimisation, a closed form solution for dispreading codes is also disclosed later.

In the third method, channel state information in addition to CFO are assumed to be perfectly known at the receiver, and a closed form solution for the despreading codes is obtained.

All of these methods are explained in depth below, from which the reader will be able to establish that multiuser interference due to CFO can be suppressed substantially effectively. In particular, specific implementations of the invention employing despreading codes such as obtained from the second and third methods described briefly above, can result in performance of a BS-CDMA system exhibiting CFO close to that of the ideal case not exhibiting CFO.

Spreading and despreading codes that can, in certain specific embodiments of the invention, provide a reduced MUI due to quasi-synchronous reception caused by timing errors, are also disclosed below.

An aspect of the invention provides a method of using spreading and despreading codes to suppress multiuser interference (MU I) due to asynchronous reception for a block spreading CDMA (BS-CDMA) system.

An aspect of the invention provides a method of suppressing interference arising from timing errors, through the use of spreading and despreading codes. Another aspect of the invention concerns the design of such codes such that, in use, interference arising from such timing errors can be so suppressed.

An aspect of the invention provides a method of suppressing interference arising from CFO, through the use of spreading and despreading codes. Another aspect of the invention concerns the design of such codes such that, in use, such interference can be so suppressed.

The above method may be configured to suppress MUI due to asynchronous reception caused by frequency errors (e.g., carrier frequency offset or Doppler shifts) or timing synchronization errors.

The spreading and despreading codes may be designed such that the interference due to asynchronous reception is reduced. It will be understood that asynchronous reception can refer to asynchronization in the time domain (i.e. timing errors) or the frequency domain (i.e. CFO).

The particular spreading and/or despreading codes to suppress multiuser interference due to CFO may be designed such that the following criteria are satisfied HE _çP =m 134 n1a1n -and rq =m I't mJMm pm. where

and P -1, .... Ms) are the lengthM spreading code and the despreading code for the P th user, respectively; j27Tkm I is a M x M diagonal matrix with its k th diagonal entry being e M, where is the normalized frequency offset of the m th user; h: is a M x M circulant matrix obtained by shifting the M x M identity matrix down by 1; Pt and q are arbitrary real or complex numbers; and M3 is the total number of users that can be supported in the BS-CDMA system.

In the equations above, (.f denotes Hermitian transpose.

Both the spreading codes and the despreading codes may be designed, at the transmitter and receiver, respectively, to satisfy the criteria given above.

On the other hand, the spreading codes at the transmitter may be fixed (e.g., the DFT spreading codes), in which case only the despreading codes at the receiver may be designed to satisfy the criteria given above.

The spreading code for the " th user may be chosen as a length2M2 column vector with its (2?fl)th and the ((2111 -1) mod M)th entries being 1. and the others being zero, where M3 is the total number of users that can be supported in the BS-CDMA system.

The despreading code for the 3fl th user may be chosen as a length2Ms column vector with its (2m)th entry being 1 and the others being zero.

A system implementing the above method and using the particular spreading/despreading codes as noted in the preceding two paragraphs may be operable to switch to TDMA transmission when (M -M)P is greater than or equal to MLp, where M is the length of the spreading/despreading codes; M is the total number of users that can be supported by the BS-CDMA system; p is the sub-block length; and is the length of cyclic prefix.

The spreading/despreading codes may be designed such that the interference power is minimized. The spreading codes may or may not be fixed at the transmitter.

When the spreading codes are fixed at the transmitter, for the given length-M spreading codes a (e.g., the DFT spreading codes), the method may be configured such that the interference reducing despreading codes can be obtained by performing an optimization procedure which comprises the formula: minimize llA!1B -PIF + lIA!I -Ql12 where B is the M x M matrix to be designed, with its Ifl th column being the despreading code for the m th user; A is a M3 x MM block diagonal matrix with occupying the in th row and the ((m -1)M + 1)th to the (inM)th columns (in. 1,.,., Mg); is a Ifi'.1 x M matrix with the AW x M matrix E1 occupying its ((ni -1)M + 1)th to the (mM)th rows (in = 1, .... M3, and the aforementioned M x M matrix is a diagonal 12?zkEm matrix with its C th diagonal entry being e N, where Em is the carrier frequency offset of the m th user normalized over the carrier frequency.

Moreover, in the above, is a MM x M matrix with the M X M matrix occupying its (Cm-i)M + 1)th to the (mOth rows (m= Mg), where hc is a M x M circulant matrix obtained by shifting the M x Al identity matrix down by 1; p and Q are M x M diagonal matrices with its rn th diagonal entry being Pm and qm, respectively, where Pm and q,, may be determined by the design criterion given above when 1m is an identity matrix. In the equations above, (.)hi denotes Hermitian transpose.

When the spreading codes are fixed at the transmitter, for the given length-M spreading codes (e.g., the DFT spreading codes), the despreading code for the JA th user, denoted as may be obtained by solving an optimization problem as set out in the following formula:

H VM

Qm) 1 fljL minimize -1 subjectto where = + JJMff = Tn'f H( H.Y} = Tr Hu(Hpu)H} HL is the P x P lower triangular channel matrix for the Y th user, with its first column being the channel impulse response for the 1A th user (denoted as h = [h(0),,...h(L1)]T expanded to length P is the P x P upper triangular channel matrix for the IL th user, with its first row being [0' . hCL 1),.'* ,h(1)1 TrC) denotes the trace of a matrix, (Y denotes Hermitian transpose, and (.)T denotes matrix transpose.

The despreading code for the P th user, denoted as Pw may be the eigenvector corresponding to the smallest eigenvalue of the Hermitian matrix When the spreading codes are the OFT spreading codes at the transmitter, the matrix in the objective function may be rendered as Q1. (i + 2)E,.a1.1a111, and the despreading code for the IL th user, denoted as may be the eigenvector >Qm corresponding to the smallest eigenvalue of the Hermitian matrix Ii The spreading and despreading codes may be designed for quasi-synchronous systems with timing errors.

In this case, the spreading codes and despreading codes may satisfy one or multiple particular criteria such that MUI due to quasi-synchronous reception is reduced.

One of the said criteria may be 11a. IL-rn " .O, and - pim 13JM -p m. and

0 forany andP where am and l3 are the spreading and despreading codes for the m th and i th user, respectively, IM is a square matrix obtained by shifting the identity matrix down by 1, and ( denotes Hermitian transpose.

One of the said criteria may be Ha _çl p-nt to prn and

H -

I3J2 TM -to, p and 13Za 0 for any m and i' where Zi is a square matrix with the entry on its left-down corner being 1, and the others being zero.

In the event that more than one criterion is employed, another one of the said criteria may be aH.11 f4-m -to. m and H -çA,. P-PjMarn -to, p in and = 0 for any " and where Z is a square matrix with the entry on its right-down corner being 1, and the others being zero.

A spreading code that satisfies the above criteria may be designed as a length(M + 2) column vector using a base vector Cm, where the said base vector is a lengthM mutually shift orthogonal code, and the spreading code may be designed such that am [Q,c,0], where (Y' denotes Hermitian transpose; and the corresponding -r Htr H despreading code may be designed such that t.1,n -LC,n%. j. CnvCm.L.lJ, where IS the total number of users in the BS-CDMA system.

The spreading code and despreading code designed for a specific user may be interchangeable, i.e., the spreading codes may be used as the despreading codes and the despreading codes may be used as the spreading codes.

In the following description of specific embodiments of the invention, it will be understood that particular implementations of the invention can involve computer implemented technology. In such cases, aspects of the invention can be implemented with the use of computer executable instructions. Such instructions may be introduced to an appropriate computer in a number of manners. For instance, a computer program product, comprising computer executable instructions, could be stored on a computer readable storage medium. This could be in the form of an optical or magnetic disk, or alternatively in the form of an electronic device, such as read only memory. On the other hand, the computer program product could be carried on a computer receivable signal.

Moreover, the computer program product could include all of the instructions required by the computer to perform a method in accordance with an aspect of the invention, or it could include a portion of such instructions. In that latter case, the constructor of such a computer product would be working on the basis that a computer would have an assumed library of available instructions, to which the computer program product could include reference. Ii

Aspects of the invention will now be illustrated by reference to the following description of specific embodiments thereof. The reader will appreciate that the following is but an example of implementation of the invention, and is not intended to limit the scope of application of the invention. The description makes reference to the accompanying drawings, in which: Figure 1 illustrates a wireless communication device in accordance with a first specific embodiment of the invention, configured for suppression of interference arising from CFO; Figure 2 illustrates a graph of performance of the first embodiment of the invention, in the suppression of CFO, in comparison with an uncorrected system suffering from the effect of CFO; Figure 3 comprises a timing diagram illustrative of the impact of quasi-synchronous reception on communication in a wireless communication network; Figure 4 illustrates a wireless communication device in accordance with a second specific embodiment of the invention configured for suppression of interference arising from quasi-synchronous reception; and Figure 5 comprises a graph of performance of an implementation of the described second specific embodiment of the invention, in comparison with an uncorrected system suffering from the effect of quasi-synchronous reception.

Embodiment I -Suppressing effect of CFO Figure 1 illustrates a base station of a bandwidth-efficient BS.-CDMA system in accordance with a first embodiment of the invention, including a transmitter and a corresponding receiver.

In that arrangement, a transmitter train comprises an encoder, interleaver and symbol mapper (Ti), a serial to parallel converter (T2), a precoder (T3) a block spreading unit (T4) and a stage for addition of a cyclic prefix (T5), leading to an antenna.

The corresponding receiver train comprises, from an antenna, a stage for removal of the cyclic prefix (Ri), a block despreader (R2), a block decoder (R3), a Fast Fourier Transform (FFT) stage (R4), an equalizer (R5), an inverse FFT stage (R6), a parallel to serial converter (R7) and a demapper, deinterleaver and decoder stage (R8).

As shown in figure 1, only one user device is supported, whereas in a practical system, the base station will need to have capacity to process information from and prepare for transmission of information to numerous devices. This might entail duplication of various of the components illustrated for the receiver, or at least parallel processing capability. Likewise, a user device might have a similar requirement, and consequent increase in capability.

Moreover, the reader will appreciate that only the uplink model is considered here.

That is, only transmission of information from the user device to the base station is illustrated. The base station detects the signal of each user from a composite received signal from all users, where each subscriber station experiences a different CFO.

In this first embodiment of the invention, in a first method, the implementation of the system is concerned with the design of spreading codes (T4) at the transmitter, and the design of despreading codes (R2) at the receiver to reduce multi-user interference due to CFO.

Although to be described in more depth later in this disclosure, a second method of implementing the first embodiment of the invention comprises a technique focused on design of despreading codes (R2) rather than the design of spreading codes.

The following describes the bandwidth efficient BS-CDMA transmitter and receiver.

Transmitter It is assumed in this disclosure that the system can support a maximum number of users M3 The information bits of the m th (771 O.... -1) user are encoded, interleaved, and mapped to constellation symbols (Ti). The constellation symbols are then arranged into sub-blocks (T2), each of which consists of P symbols. The th sub-block of the 171 th user, is therefore represented by a length-s column vector S. Each block is then precoded with a Px P user-specific precoding matrix r(T3), and subsequently block spread by a lengthM (M M5) spreading code c (T4). The precoded and spreaded block is therefore given by = (c1®r1)s, where X contains chips and = [x(i\'1P)1....x1(@. + 1)MP -and ® denotes the Kronecker product. A skilled person will note that these operations in T3 and T4 can be interchanged.

Cyclic prefix of length Lcp is then inserted at the beginning of each precoded and spreaded block (T5). The length of the cyclic prefix is assumed to be greater than or equal to the memory order of the channel impulse response. The th block transmitted signal of the fl2 th user is therefore given by a length-(MP + Lcp) column vector.... ym((i + 1)N -where N MP ÷ L9.

Receiver In the receiver, the cyclic prefix is first removed (Ri). It is known that the insertion and removal of the cyclic prefix at the transmitter and receiver forms a MP x MP circulant channel matrix Hm, with its first column being the channel impulse response of the m th user L zero padded to length MP. A skilled person will note that (T5) and (Ri) can be replaced by zero-padding and overlapping operations at the transmitter and receiver respectively, and still yields the circulant channel matrix M,.

At the receiver, after cyclic prefix removal, a block despreading and decoding operation (R2 and R3) is applied. The block despreading codes and the decoding matrix for the U th user are defined as and iz, and the received signal for the IL th user is given z = (flH®Q by I, where r is the composite discrete received signal after passage through the channel and experiencing CFO.

The carrier frequency of the base station is set at f. The difference between the carrier frequencies of the flt th user and the base station is denoted fm, known as the CFO. It can thus be established that = = , ( (a11®F77)s1 (1) j2r( UV+L).

where 1rn, and E,,1, representing the effect of CFO, is a MP g MP j2rkE diagonal matrix with the k th diagonal entry being MP E, is the CFO of the m th user normalized over the carrier frequency. Ideally, when the effects of CEO can be removed, i.e., when E.m is an identity matrix, the mutually shift orthogonality nature of the spreading and the despreading codes allows MUI and IBI free reception, and the noiseless received signal for the J.4 th user is given by *tL UU where H is a P X P kernel circulant matrix with its first column being the channel impulse response of the m th user zero padded to length P. Having obtained the received signal for a single user, the rest of the signal processing is the same as in single user detection, where a fast Fourier transform (FF1) operation, a frequency domain equalizer, and an inverse FFT (IFFT) operation are applied to recover the transmitted blocks for each user, which are then demapped, deinterleaved, and decoded to obtain the transmitted bits. It should be noted that the described specific embodiment is focused on eliminating multiuser interference, and it does not require the formation of the circulant matrix L for each user. Therefore, the FFT operation, frequency domain equalizer, and the IFFT operation are demonstrably not essential to the invention. In fact, once the signals from different users are separated by using the spreading/despreading codes, any single user signal detection techniques (e.g., MMSE detection) can be applied to recover the transmitted signal of each user.

Use of above described arrangement to achieve MUI free reception in the presence of CFO will now be discussed.

In practice, when CFO is present, a BS-CDMA system can no longer achieve MUI free reception since the orthogonality among users is destroyed, which will be elaborated in the following.

It is known that the MP x MP circulant matrix H,, can be decomposed as discussed in Coon, referred to above, as: II®Hn,L + JM®Hlfl,U where M is a M X M identity matrix, Lr is a M x M circulant matrix with its first column being [�,1,0,*,,O]T HmL is a P X P lower Toeplitz matrix with its first column being lhrn zero padded to length P; and 11,,i.U is a P X P upper triangular Toeplitz matrix with its first row being a length-s row vector containing 1z1(L -1) to hmtl1) in its last (L -1. ) elements and zeros elsewhere.

Moreover, it can be confirmed that the CFO matrix E can be decomposed as Em where j27km 2m is a M x M diagonal matrix with its k th diagonal entry being e, and j27rkEm m is a P X P diagonal matrix with its IC th diagonal entry being e MP Following (1), the noiseless received signal for the U th user can be rewritten as lint ( ®;)m®Ym(!r®Mnt + JM®Hrnu)(am®1)n pit = 1 = i lint E( a®11YH r,,) s + ((3 JM ®Yrn S]. (2) In the bandwidth-efficient BS-CDMA systems disclosed in Coon and in GB2433397, the spreading and despreading codes are the same, i.e., a = = C,,,, and they are designed to be mutually shift orthogonal, i.e., H _cl P-Cti p (3) and H _cA i-m C JM C -to, p: fl (4) In the case where there is no CEO, both rn and Yrn are identity matrices. Using the design as represented by equations (3) and (4) (as in the bandwidth efficient BS-CDMA system of Coon and GB 2433397) effectively removes the interference from the other users due to the fact that the two addition terms in equation (2) are only non-zero when p!=7fl For example, when the spreading and despreading codes are chosen as the DFT spreading codes, and the precoding and decoding matrices are those given in Coon, and GB2433397, MUI free and IBI free reception can be achieved. In the case where CEO is present, however, it can easily be verified that the mutual shift orthogonal property of the DFT spreading codes is destroyed, resulting in MUI and 161.

In this embodiment, to eliminate MUI in the presence of CFO, the spreading and despreading codes are required that satisfy -fP.z I=m " tO, (5) and -ç q I mJ.'4m - m (6) It can be verified that, when the new criteria above ((5) and (6)) are satisfied, only the signal of the i th user is received, and the interference from the other users is removed. Once the multiuser interference is removed, any signal detection techniques for a single user can be used. Examples of such single user detection techniques include the minimum-mean squared error (MMSE) detector, well known in the field of the invention. In particular, when P! = q, a circulant channel matrix can be formed using the identity matrix as the precoding and decoding matrices. In such cases, it follows from (2) that z. Having obtained the signal for each individual user, the remainder of the signal processing method is the same as in conventional BS-CDMA systems where an FFT operation, a frequency domain equalizer, and an IFFT operation are applied.

It can easily be verified that the criteria described in (5) and (6) can also be used to design the spreading/despreading codes for other type of BS-CDMA systems to achieve MUI free reception in the presence of CFO.

Method I (TDMA-type code) There are simple spreading and despreading codes that satisfy (5) and (6). An example of the spreading and despreading codes to support two users is given below, where

Example 1:

a1 [1,Q,0,1]T = [0,14,0]T and ft = [1,0,0,011, 132 = [010,iJ]T The reader will verify that given the spreading/despreading codes above, Ph and Pz = = In general, in BS-CDMA systems that support M users, to satisfy the criteria described in (5) and (6), the spreading code for the rn th user may be chosen as a length2Ms column vector with its (2m)th and the (2in -1) mod Ms)th entries being L and the others being zero; and the despreading codes may be chosen as a length2Mg column vector with its (27m)th entry being 1. and the others being zero. It will be appreciated by the reader that length 2M spreading/despreading codes are used to support M number of users, the system therefore achieves MUI free with a half user load.

An advantage of method 1 is that the receiver does not require any channel or CFO knowledge in order to eliminate the interference due to CFO. Moreover, a kernel circulant channel matrix can be formed which then facilitates the use of a one-tap frequency domain equalizer at the receiver. However, using the spreading/despreading codes provided in method 1, only half user load can be achieved. Moreover, as will be shown later, an enhanced noise power can be observed, resulting in a performance degradation compared to the ideal case where there is no CFO.

Method 2 (Cross-correlation minimization (CC)-minimization code)) Spreading/despreading codes that support full user load and satisfy the given criteria ((5) and (6)) exist. These codes can be obtained by solving an optimization problem which consists of: minimize I1A!B -PIF + IIA!2B -QIF where B is the M X M matrix to be designed, with its m th column being the despreading code for the rn th user; A is a M, x MMg block diagonal matrix with a occupying the in th row and the ((in -1)M ÷ 1)th to the C'nM)th columns (m = E1 is a MM. x M matrix with the M x M matrix E occupying its (Cm -1)M + 1)th to the (mM)th rows (in 1,.... Mg), and, the aforementioned M x M matrix 1n is a diagonal matrix with its k th diagonal entry j2rkErn being eM, where Em is the carrier frequency offset of the m th user normalized over the carrier frequency; and 2 is a MM x M matrix with the M X M matrix occupying its ((rn -1)M ÷ 1)th to the (mM)th rows (in = 1,.... M5) where h,c is a M X M circulant matrix obtained by shifting the M X M identity matrix down by 1.

The matrices 1' and Q are flexible. For example, each may be chosen as a diagonal M X Mg matrix with its m th diagonal entry being Pm and qm, respectively, where Pm and Q may be determined by the design criterion given in (5) and (6) when there is no CFO, i.e., Em is an identity matrix.

Matrix B containing the despreading codes can be obtained by solving the optimization problems above, and the optimal matrix B is given by B (PA1 + QAR!2)(!AE1 ÷ where.Y' denotes matrix inverse.

Unlike the spreading/despreading codes design in example 1, the receiver needs to know the carrier frequency offset in order to obtain the despreading codes, and different carrier frequency offset results in different despreading codes. Therefore the receiver needs to update the despreading codes every time the CFO changes. Also, in this example, Pm qm, is not a required condition. Therefore, in the absence of this condition being met, a circulant channel matrix cannot be formed and the frequency domain equalizers cannot be used. To account for this, a circulant channel matrix could be constructed by using the precoding and decoding matrices at the transmitter and receiver, respectively.

However, once the signals from different users are separated, other signal detection techniques, such as the MMSE detector, can be used to detect the signals for each single user.

The advantage of using the optimization procedure as in example 2 is that the subscriber stations do not need to adapt the spreading codes in the presence of CFO.

When the base station find the system is suffering from CEO, it can perform the optimization procedure, use the obtained interference-eliminating despreading codes, and detect the signals for each single user. Moreover, the system can support the maximum number of users which is determined by the length of the spreading/despreading codes.

Method 3 (Interference Minimization (IP-minimization code)) When the spreading codes are fixed at the transmitter, the despreading codes can be designed by solving a different optimization problem than that in example 2. The optimization problem is formulated as oHc'c'M P t.4m =1 Qrn) P1 minimize subject to 1 where = + 2JMJMEiL, j Tr[H(HO} z =Tr{H(Hi')i is the X P lower triangular channel matrix for the 1' th user, with its first column being the channel impulse response for the IL th user (denoted as h, = * , -expanded to length P. H is the P X P upper triangular channel matrix for the P th user, with its first row being [0'" isa -1)...h(1)] where L is the length of, Tr[} denotes the trace of a matrix, ( denotes Hermitian transpose, and (Y denotes matrix transpose.

Since 1 is a Hermitian matrix, closed-form solutions for the optimization problem above exist, where despreading code for the th user, denoted as is the

M Q?n

eigenvector corresponding to the smallest eigenvalue of the Hermitian matrix i particularly when the spreading codes are chosen as the DFT spreading codes, ( -(7 7 5,i 1 2-' Method 3 has all of the advantages of method 2, except that a circulant matrix cannot be formed using method 3, but can be formed using method 2. Alongside this, a closed-form solution of the despreading codes is obtained, as in the second implementation of method 2 set out above, especially when the CFO changes and the receiver needs to update the despreading codes accordingly. Compared to method 2, one drawback of method 3 is that, in addition to the CFO, the receiver needs to know the channel state information in order to obtain the despreading codes.

An example is given below, of the despreading codes for a particular channel when M 2, where the spreading codes are the DFT spreading codes, and the carrier frequency offsets are 0.1 and 0.01 for the first and the second user, respectively.

Switching between using the interference-reducing spreading/despreading codes and a TDMA system In example 1, the BS-CDMA system using the designed spreading/despreading codes above essentially uses a TDMA-like transmission where the first user transmits data in the first and the last time slots, and the second user transmits data in the second and the third time slots. However, this differs from the conventional TDMA systems with block transmission, in that the present example adds a cyclic prefix after the spreading operation while the conventional TDMA systems adds a cyclic prefix before the spreading/despreading operations.

To support M users, with each user having P symbols per sub-block, a conventional TDMA transmission inserts!-.cp symbols for each block, and therefore has a redundancy of MLc while, for the bandwidth efficient BS-CDMA system, the redundancy is (M -MS)P. One advantage of the bandwidth efficient BS-CDMA is that it allows small P compared to Lap, as cyclic prefix is appended after spreading. The present example therefore has a higher bandwidth efficiency than the conventional TDMA systems with block transmission when (M -MS)P is smaller than or equal to M3L. When (M -M3P is larger than 1gLp the system can switch to conventional TDMA transmission to achieve a higher bandwidth efficiency.

Conventional BS-CDMA systems achieve MUI free reception under the assumption that perfect frequency synchronization can be obtained. Perfect frequency synchronization, however, is usually hard to obtain due to the instability and inaccuracy of oscillators. Orthgonality among users is distorted in the presence of CFO, and MUI occurs.

The above described example achieves MUI free transmission for BS-CDMA systems in the presence of CFO. Figure 2 illustrates the impact of CFO on a bandwidth-efficient BS-CDMA system and the effectiveness of the prescribed spreadirtgldespreadirig codes in removing the MUI. The figures are plotted by assuming two active users, with the first and the second user having a normalized carrier frequency offset of 0.01 and - 0.01, respectively.

The spreading/depreading codes for the present embodiment of the invention are the codes given in the examples when i1 = 2. The length of each sub-block is P =16, the length of channel is L 5, and the length of cyclic prefix is = 4. It would be possible to choose smaller P or larger L without affecting the performance. It is assumed in the simulation that the base station has knowledge of the instantaneous CFO.

It can be observed from Figure 2 that BS-CDMA systems using the DFT spreading and despreading codes suffer from performance degradation in the presence of CFO, even when the carrier frequency offset is as small as ±0.01. The BS-CDMA systems employing the proposed spreading codes, however, can effectively suppress the interference due to CFO.

The effectiveness of using the interference-reducing spreading/despreading codes provided in this invention becomes more obvious when the CFO becomes larger.

The gap between the performance of the BS-CDMA system using the proposed spreading codes in example 1 and that of the ideal system performance without CFO is due to the different equivalent noise power generated by different spreading/despreading codes.

Embodiment 2 -Suppressing Impact of Time Domain Asynchronism Figure 3 illustrates a quasi-synchronous reception where signals from different users are delayed by a different amount of time. In a preferred embodiment, the receiver synchronizes to the received signal of the th user, which can be referred to as the reference user. The users whose received signals are not synchronized to that of the reference user are referred to as the interference users. The signals from the interference users can arrive earlier or later than those of the reference user. The delay between the signals of the k th user and the reference user are denoted as rk.

For simplicity and without causing any confusion, are restricted to integer values, and the user signals that arrives earlier or later than that of the reference user are differentiated by specifically mentioning that fact in the text. Chip-level synchronization is considered in this example, wherein the delays are a multiple of the chip duration, i.e., Tk 1,2,...

The present example can be applied to the bandwidth efficient BS-CDMA system or its variants, (e.g., the low complexity OFDMA system). A bandwidth efficient BS-CDMA transmitter and receiver are described in the following as an example.

The transmitter and receiver structure of the bandwidth-efficient BS-CDMA system is illustrated in Figure 4 where only one user is shown. The example concerns the design of the spreading codes (T4) at the transmitter, and correspondingly, the despreading codes (R2) at the receiver to reduce the interference due to quasi-synchronous reception.

Transmitter In this example, it is supposed that the system can support a maximum M number of users. The information bits of the fl th (fl = I M) user are encoded, interleaved, and mapped to constellation symbols (TI). The constellation symbols are then arranged into blocks (T2), each of which consists of P symbols. The i th block signal of the ?n th user, is therefore represented by a length-n column vector S* Each block is then precoded with a K x P (IC »= P) user-specific precoding matrix Fm (T3), and subsequently block spread by a lengthM (M' M) spreading code am (T4).

The precoded and spreaded block is therefore given by Xn (Cni®rn3Sn, where x contains M'K chips and Xn = [Xm(MK),....Xm((t + 1)M'K-1)], and ®denotes the Kronecker product A skilled person will note that these operations in T3 and T4 can be interchanged.

A cyclic prefix of length Lcp is then inserted at the beginning of each precoded and spreaded block (T5). The length of the cyclic prefix is assumed to be greater than or equal to the memory order of the channel impulse response. The th block transmitted signal of the rn th user is therefore given by a length(%1K + Li.s) column r vector y,1 = [ym(tN), .... y1((. + 1)N -1)] , where N = MK + Lap, and Yn TcpX, where is the cyclic prefix insertion matrix.

Receiver There now follows a description of the receiver of a BS-CDMA system where signals of all users are synchronized.

At the receiver, the cyclic prefix is first removed at the receiver (Ri). It is known that the insertion and removal of the cyclic prefix at the transmitter and receiver forms a M'K circulant channel matrix Hrn, with its first column being the channel impulse response of the ?fl th user zero padded to length MK A skilled person will note that (T5) and (Ri) can be replaced by zero-padding and overlap-add operations at the transmitter and receiver respectively, which still yields the circulant channel matrix TIm.

A block despreading and decoding operation (R2 and R3) is applied after CP removal.

The block despreading codes and the decoding matrix for the 1 th user are defined as and z, the received signal for the 14 th user is given by: = (f3®c)Rr' where Rp is the CP removal matrix, 1L (Ctm®Fni) + is the composite discrete received signal after going through the channel, and fl is the noise term.

In ideal transmissions, when there is no timing error, the spreading/despreading codes and the precoding/decoding matrices are disclosed in Coon, and GB2433397, (where P = K, and M' M) which yield where U,, is a P x P kernel circulant matrix with its first column being the channel impulse response of the fl th user zero padded to length P. In the case when there are no timing errors, the spreading codes and precoding/decoding matrices that satisfy the equation above are given in Coon and GB2433397, where n and f-are lengthM mutually shift orthogonal code such that 1? _1 i=' I3pam o, != m (7) and H -çA, y=rn ftu JM - 0, ft!= rn (8) where Li is a square matrix obtained by shifting the identity matrix down by 1, and A is determined by the spreading/despreading codes used. When Cm is chosen as the DEl spreading codes, the corresponding precoding/decoding matrices are given by (-j2n(?n--i)\ (-j2m(m-i)(P-1)\ = ci lag [1, exp I\ MP) exp t\ Having obtained the received signal for a single user, the rest of the signal processing is the same as in single user detection, where a fast Fourier transform (FFT) operation, a frequency domain equalizer, and an inverse FFT (IFFT) operation are applied to recover the transmitted blocks for each user, which are then demapped, deinterleaved, and decoded to obtain the transmitted bits. Note that the FFT operation, frequency domain equalizer, and the IFFT operation are not essential to the current invention.

When the signals from different users are separated at the receiver, any single user detection technique can be applied (e.g., the MMMSE detector) to recover the transmitted signal of each user.

Spreading/despreading code design for quasi-synchronous reception It has been shown that, in a bandwidth-efficient BS-CDMA system, signals of a user that arrive earlier than those of the reference user contribute the majority of the interference to the reference transmission, The disclosed embodiments of the invention eliminate the interference from a user that arrives earlier through spreading/despreading codes.

To eliminate interference from the synchronized users other than the reference user, the spreading/despreading codes need to have the mutually shift orthogonal property given in equations (7) and (8). The additional properties that are required in this example for the spreading/despreading codes to eliminate the interference from the signals of a user that arrive earlier than those of the reference user, will now be discussed.

The interference term from a user (e.g., the bth user) whose signal arrives earlier than the reference user is given by: = (®f)(vvhflbx + LbX, -AbCLrpXb) = ( ®1)[D.Üb(ab®Fb)s, + b (ab®rb)s bCLCP(ab®Fb)sb] where C is a f K X.M1 circular shifting matrix obtained by circularly shifting a x MK identity matrix down by X, is a M'K x MK circular shifting matrix obtained by circularly shifting a M'Kx MK identity matrix up by X; Ab is a M'K x M'K lower triangular Toeplitz matrix with its first column being [0, "Ofr -hb(O), -hb(l), ...-h b(rb where hbQ) is the th tap of the channel impulse response of the b th user. The objective here is to design the spreading/despreading codes such that b 0 The following decompositions are provided: D Z1® where 2 is a M x M' matrix with its left-down corner entry being 1 and the rest being zero, is a P x P lower triangular Toeplitz matrix with its first column being {O,...O,-hb(O),-hb(1),...,--hb(Tb _1)]D and IIJCLCP = Z2® where Z3 is a M' x M' matrix with its right-down corner entry being I and the rest being zero, is a P x P matrix with its (P -Lcp + l)th to the (P + T,)th columns and the last rb rows being a Th X T lower triangular Toeplitz matrix with its first column being [hb(U),hb(1),"hb(Tb -Moreover, VTblII I.ff®Hb1 + JM'®Hb2 + JM1®XJ where 1r is a M' x M' identity matrix, J1 is a M' x M' circulant matrix with its first column being [0,i,0,-,0]T The definition of Hb,l and Hb3 is omitted here as it is irrelevant to the invention. Having the decompositions above, and using the property of the Kronecker product that (A®B)(C®D) AC®BD, (9) can be rewritten as 1b = (i®flL)[IM'®Hb,i + Jkfi®Hb2 + -(Z2®)(ab®Fb)s71] = (ab®;Hb1 b + + DJM' ab®;blbcb)sb +(Zlab®fl, fb)s -(f3z1 ab®f)s7' The property of the mutually shift orthogonal codes guarantees that the first two summation terms are zero due to (7) and (8). To eliminate the interference from signals that arrive earlier than the reference signal (e.g., the signal for the th user), the spreading/despreading codes may satisfy the following additional criteria: Criterion 1: The spreadingldespreadinc.i codes may be designed such that

-

13JUm 0 for any i and m Criterion 2: The spreadingidespreading codes may be designed such that for any 1 and m Criterion 3: The spreadingidespreading codes may be designed such that I3Z2a.m 0 for any! and m Example I (spreading/despreadinci codes design): To satisfy the mutually shift orthogonal property and criteria 1, 2 and 3, the spreading and despreading codes may be chosen as -7.

am = [O,c,O] and 13m [cm(M). C. C,(1)] where cm (c(i)....c(M)]T is a IengthM mutually shift code satisfying (7) and (8). The DFT spreading codes are an example of such mutually shift codes.

Example 2 (spreading/despreadincl codes desiqji): To satisfy the mutually shift orthogonal property and criteria 2, the spreading and despreading codes may be chosen as -Fi Zl' and 13m [Cm(l):CIT Example 3 (spreading/despreadiflcl codes design): To satisfy the mutually shift orthogonal property and criteria 3, the spreading and despreading codes may be chosen as

F F and

13rn = [c,c,n(i)1.

Conventional BS-CDMA systems achieve MUI free reception under the assumption that perfect timing synchronization can be obtained. Perfect timing synchronization, however, is usually hard to obtain due to delays over the channel. Orthogonality among users is distorted in the presence of timing errors, and MUI occurs.

The disclosed embodiments of the invention effectively reduce the impact of interference due to quasi-synchronous reception without changing the original transceiver structure of the BS-CDMA system. The performance is close to that of Successive Interference Cancellation (SIC) or BS-CDMA with synchronous reception, as is shown in Figure 5.

As will be understood by the reader, the purpose of the above disclosure of specific embodiments of the invention is to illustrate and exemplify implementation of the invention. It is not intended to imply any limitation on the scope of protection, which is to be understood from the following claims. The claims may be read in the light of the description, but not limited thereby, and with reference to the accompanying drawings, again not limited thereby.

Claims (14)

1. CLAIMS: 1. A method of transmitting a signal across a wireless communications channel, comprising generating a signal, spreading the signal using a spreading code, emitting the signal for reception across the channel, and despreading the transmitted signal using a despreading code, and further including designing at least one of the spreading code and the despreading code to mitigate for multiuser interference.
2. 2. A method in accordance with claim 1 wherein said designing comprises determining a timing asynchronicity of reception of signals at a receiving device, and determining a spreading code and a despreading code on the basis of that asynchronicity.
3. 3. A method in accordance with claim 1 wherein said designing comprises feeding channel information back from a receiving device to a transmitting device, and determining a spreading code on the basis of said channel information.
4. 4. A method in accordance with claim I including determining a carrier frequency offset at a receiving device relative a transmitting device and wherein said designing comprises designing despreading codes on the basis of said carrier frequency offset.
5. 5. A method in accordance with claim 4 wherein said designing comprises optimising spreading and despreading codes with regard to carrier frequency offset to minimise the effect of cross correlation between spreading and despreading codes.
6. 6. A method in accordance with claim 4 wherein said designing comprises designing only despreading codes to mitigate for multi user interference.
7. 7. A method in accordance with claim 5 wherein said designing comprises minimizing: lIA!1B -P112 + IIA!B -Q112 where B is the M x M matrix to be designed, with its th column being the despreading code for the flt th user; A is a M x MM block diagonal matrix with X occupying the fli th row and the (@ 1)M + 1)th to the (nM)th columns (m = 1,...,Ma); is a MM x M matrix with the M X M matrix occupying its ((rn -1)M + 1)th to the (rnM)th rows (rn = .... M) and, the aforementioned M x M matrix is a diagonal matrix with its k th j2rkem diagonal entry being e 24, where Em is the carrier frequency offset of the m th user normalized over the carrier frequency; and !2 is a MM x M matrix with the M x M matrix J1 occupying its ((m -1)M + 1)th to the (tflM)th rows (nt 1, ...,Mg) where Lr is a M X M circulant matrix obtained by shifting the M x M identity matrix down by 1.
8. 8. A method in accordance with claim 3 wherein said designing comprises minimizing: t Qm) f3p rn subject to 1 where Q 1auE ÷ Tsr{H(H)M] Tr H(H[)i is the P x P lower triangular channel matrix for the th user, with its first column being the channel impulse response for the P th user (denoted as 1? (A\ 1 (i i\iT Up --J) expanded to length P. is the PxP upper triangular channel matrix for the P th user, with its first row being [0'". 1) .",h(1)j, where.L is the length of h, Trt1 denotes the trace of a matrix, (Y denotes Hermitian transpose, and (.)T denotes matrix transpose.
9. 9. Wireless communications apparatus comprising a transmitter chain including spreading code determining means for determining a spreading code for preparation of a signal for transmission, the spreading code being determined to mitigate for multiuser interference.
10. 10. Apparatus in accordance with claim 9 and wherein said spreading code determining means is operable, on the basis of timing asynchronicity information describing timing asynchronicity of signals received at a receiver with which said apparatus is in communication, in use, to determine a spreading code on the basis of that asynchronicity.
11. 11. Wireless communications apparatus comprising a receiver chain comprising a despreading code determining means operable to determine a despreading code for despreading a received CDMA signal, said despreading code determining means being operable to determine said despreading code to mitigate for multiuser interference.
12. 12. Apparatus in accordance with claim 11 and including carrier offset determining means for determining a carrier frequency offset and wherein said despreading code determining means is operable to determine a despreading code on the basis of said carrier frequency offset.
13. 13. Apparatus in accordance with claim 11 and including timing offset determining means for determining a timing offset of received signals and wherein said despreading code determining means is operable to determine a despreading code on the basis of said timing offset.
14. 14. A computer program product comprising computer executable instructions which, when executed on a general purpose computing device, cause said device to become configured to perform a method in accordance with any one ofclaimslto8.