GB2418327A - Common channel interference cancellation in a CDMA system - Google Patents

Abstract

A common channel interference cancellation processor is provided for cancelling common channel interference in a code division multiple access (CDMA) system. To this end the processor incorporates a receiver for receiving a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes, and a processing unit for extracting the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique. The matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix. Such a processor is capable of being computed using a reasonable level of computational complexity such that it can be applied for interference cancellation in a mobile terminal, for example.

Description

24 1 8327 id 1 Common Channel Interference Cancellation This invention

relates to common channel interference cancellation, and is concerned more particularly, but not exclusively, with the rejection of interference at a mobile terminal in a wideband code division multiple access (WCDMA) system.

Multiaccess communication is the ability of a number of transmitters (or a single transmitter with multiple data streams) to coexist in the same time-frequency domain whilst maintaining "adequate" levels of communication between transmitter and receiver. The major benefit of multiaccess communication is the efficient use of available bandwidth, which can be a significant factor where the communications infrastructure may be sparse (for example in systems utilising trans-oceanic cables, satellites or regulatory control) and/or the number of users is large (for example in systems utilising the Internet or wireless mobile services).

Two complimentary techniques for achieving multiaccess communication are frequency- division multiple access (FDMA) and time-division multiple access (TDMA). In FDMA a different carrier frequency is assigned to each transmitter (user), thereby ensuring the separation of each user in the frequency domain. Bandpass filtering at the receiver allows separation of each user's signal.

Conversely, in TDMA, the complete available spectrum is allocated to a single user for a fixed epoch after which it is allocated to a different user and so on in round-robin fashion. Demodulating (or more strictly demultiplexing) for a given user is done by switching to the appropriate epoch.

Hence a TDMA system requires all users to adhere to a strict timing schedule, whereas a FDMA system allows transmission in an ad hoc manner.

A measure of the separation between users that is offered by a particular multiaccess scheme is the cross-correlation between signals. Defining the cross-correlation between two signals, so and sk as PJk (SJ, Sk)= |Sj (r) Sk(r)dr (1-1) it can be that, in the case of two user signals occupying different non-overlapping time intervals, as in the case of TDMA, the cross-correlation will be zero. Similarly, for two users occupying different frequency bands, the cross-correlation will also be zero by virtue of the requirement for integration over frequency rather than integration over time. Signals for which the cross-correlation result is zero are known as orthogonal.

User signals that are modulated by a set of orthogonal codes may coexist simultaneously (identical in time and frequency) without causing interference to each other. Such a modulation scheme is known as direct sequence code division multiple access (DS-CDMA). Demodulation of such a signal is performed by applying equation (1-1) to the received signal Sj, with sk being the orthogonal code of the required user. Due to the orthogonality property, equation (1-1) will evaluate to zero for all the other user signals.

Figure 1 shows two orthogonal waveforms (sin(x) and cos(x)) that are used to modulate two data sets. The sine wave is used to modulate data set 1 and the cosine is used to modulate data set 2. The resulting modulated signals are summed and transmitted as signal R(X) which is subsequently received by two receivers. Both receivers receive the same input signal R(X), and, by applying their respective demodulating waveforms sin(x) and cos(x), the two sets of transmitted data, data 1 and data 2, can be recovered, as shown in Figure 2. Integrating the demodulated data over the duration of a bit period and zero thresholding results in the original data. This is the traditional matched filter approach.

In the above simple example two important assumptions are implicit. The first of these assumptions is that the orthogonality between the modulating signals sin(x) and cos(x) is maintained by the time that the signal R(X) reaches the receiver. The second of these assumptions is that the two data signals are bit synchronous and maintain synchronicity by the time that the signal reaches the receiver.

Equation (1-1) will not evaluate to zero if the two signals, so and Sk, fail to align perfectly, # 3 thereby introducing an interfering component into the demodulated signal. In a radio communication channel multiple copies of the transmission may exist due to reflections in the environment, termed multipath. Such multipath effects cause equation (l-l) to evaluate to a non- zero value, this being termed inter path interference (IPI). Where more than a single data stream is present in the transmission the resulting interference due to equation (l-l) not evaluating to zero (loss of orthogonality) is termed multiple access interference (MAI).

In the light of the above problems, interference rejection (JR) aims to improve digital demodulation in the presence of multiple access interference (MAI). In considering the feasibility of performing interference rejection in the mobile terminal, the fundamental problem is that of reducing MAI and, although the transmission from the base station should be of equal power for all users, there may be a reason to introduce unequal power distribution, in which case an artificial near- far effect is introduced at the mobile terminal. Two additional constraints for a mobile terminal are the availability of orthogonal codes of other users and computational power.

The basic synchronous CDMA model expressing the signal seen by the receiver in terms of the transmitted data and the channel noise is given by y(t)= AkbkSk (t)+ Nut) t e [O,T] (1-2 k=l where T is the inverse of the data rate, K is the number of users, sk(t) is the signature waveform for the kth user, normalised so as to have unit energy, Ak is the received amplitude of the kth user's signal, bk [-l,+l] is the bit transmitted by the kth user, and n(t) is white Gaussian noise with unit power spectral density (that is zero mean) and variance Is.

Extension from the synchronous channel model to an asynchronous channel model is straightforward by taking into account the M bits in the transmission. The asynchronous CDMA channel model may be described as 7 4 y(t) Akbk [i]Sk (t-iT-irk) + n(t) (1-3) k=l.=-M It is also possible, in a similar manner, to introduce the effects of multipath propagation.

The net effect of multipath propagation can be viewed as the addition of more users to the system.

Interference rejection techniques may be divided into optimal and suboptimal techniques.

However, such a division does not help in explaining the relationships between the different techniques; nor does it allow a logical progression from one technique to another. More usefully, interference rejection techniques may be classified on the basis of linear and non-linear decision statistics (observed values).

In a statistical inference problem where a parameter is to be inferred on the basis of observations y, a function of the observations, f(y), is a sufficient statistic (contains all the information in the original observations relevant to make an optimum decision) for if the conditional distribution for y no longer depends on,B. Once the sufficient statistic has been observed, the probability distribution function (PDF) of y will be changed to the conditional PDF, which no longer depends on p. Where f(y) is a linear function, that is where f(y) linearly combines the observed values (decision statistics), the resulting estimator is classed as being linear.

Conversely, where f(y) is non-linear, the estimator is classed as nonlinear.

The non-linear detectors described below use decisions on the data of the interfering users in demodulating the data of the wanted user. Some of the solutions use final (hard) decisions on the interfering user's data whilst others use tentative (soft) decisions. One class of non-linear detectors utilises the technique of subtractive interference cancellation whose basic principle is that, if a decision has been made on an interfering user's bit, then interference due to that user's bit may be recreated at the receiver and subtracted from the received signal. Two types of techniques, namely successive (serial) interference cancellation (SIC) and parallel interference cancellation (PIC), are discussed below.

An example of an SIC algorithm is described in S. Moshavi, "Multi-User Detection for DS- CDMA Communications", IEEE Communications Mag. Vol. 34, no. 10, pp. 124- 137, Oct. 1996.

Figure 3 shows a simplified implementation of an SIC receiver as described in the above reference.

The operation of such a receiver may be described in two stages. A signalranking unit orders the received signals in descending order based on received power. The second stage makes a decision, regenerates and cancels out one interfering signal (user). There can be multiple such second stages to cancel out interference to a required degree. The procedure carried out in the second stage is as follows: l) A conventional detector is used to despread the highest ranking signal, rk(t).

2) A hard decision is made on the signal rk(t).

3) An estimate of the signal, rk (t), is regenerated from the hard decision, the known spreading code and an estimate of the amplitude.

4) This estimate is subtracted from the received signal, resulting in a signal with less interference.

The above procedure may be repeated in a multi-stage structure to remove any number of interfering signals.

A weakness of SIC is the intrinsic delay of one symbol period per cancellation stage. For a number of such stages the cumulative delay incurred would be unacceptable particularly for user signals that are of lower relative power which would be amongst the last to be "cleaned-up".

Parallel Interference Cancellation (PIC), as also referred to in S. Moshavi, "Multi-User Detection for DS-CDMA Communications", EKE Communications Mag. Vol. 34, no. 10, pp. 124- 137, Oct. 1996, attempts to remove MAI for each user in a parallel simultaneous (by contrast to SIC) manner. Figure 4 shows a PIC architecture, as detailed in the above reference in which parallel unit sequences are provided for estimation of the received spread signal of each user and adders are provided to add together the estimated received spread signals of the different users in the required combinations prior to the interference subtraction process. Hard decisions made using a conventional detector for each user are passed onto an amplitude scaling unit. Estimates of individual user signal amplitude are used to scale the estimated bit for each user. These scaled, estimated signals are re- spread to produce a delayed estimate of each user's received signal. A summing unit systematically adds together all but one of the regenerated signals for every user signal in a parallel fashion. Thus, an estimate of the MAI for each user is produced. This estimated MAI is then subtracted from the received delayed signal resulting in a set of improved estimates.

Multiple such stages may be used to provide improved performance.

One of advantages of the PIC technique, compared to the SIC technique, is that the latency of the algorithm is independent of the number of users. However the hardware requirement is increased linearly with the number of users with such a technique. A drawback of the PIC algorithm is that the accuracy of a weaker user's estimated signal is low when compared to a strong user, resulting in a lower SIR at the weaker user's receiver branch. This inaccuracy may cause incorrect decisions for the weaker user's data, thus increasing the interference to the other users.

This problem is highlighted when the users' signals are of distinctly different strengths. Numerical results given in P. Patel and J. Holtzman, "Performance comparison of a DS/CDMA system using a successive interference cancellation (IC) scheme and a parallel IC scheme under fading", IEEE ICC., pp.510-514, 1994, have shown that the bit error probability (BEP) of a PIC system can be inferior to that of a SIC system. However, in a well power-controlled system (user powers more or less equal), the BEP of a PIC system is superior to that of a SIC system.

The PIC receiver can be extended to a multistage structure, as shown by R. Buehrer, A. Kaul, S. Striglis and B. Woerner, "Analysis of DS-CDMA parallel interference cancellation with phase and timing errors", IEEE Trans. Commun., pp.1522-1534, Oct., 1996. The multistage structure of such a receiver comprises N stages, associated delay units and a conventional receiver.

Each stage takes the estimated spread signals from the previous stage and produces a new set of estimates, so that the estimated received spread signal r(,J),n(t) is produced after elimination of users I and j at the output of the stage n. Simulation results for a particular system setting have shown that only the first few stages can provide a large improvement.

In general terms known systems for removing this interference from the received signal involve regenerating a replica of the interfering signal at the receiver and subtracting it from the received signal, but the approaches used are non-optimal in that they do not remove in totality the interfering signals due to computational cost.

It is an object of the invention to provide a method of common channel interference cancellation in a WCDMA system which can be carried out optimally with reduced computational complexity and which is therefore capable of being realised in a mobile terminal.

According to one aspect of the present there is provided a common channel interference cancellation processor for cancelling common channel interference in a code division multiple access (CDMA) system, the processor comprising: receiving means for receiving a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes; and data extraction means for extracting the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix.

According to another aspect of the present there is provided a method of common channel interference cancellation utilising interference cancellation in a code division multiple access (CDMA) system, the method comprising: receiving a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes; and extracting the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix.

This method is capable of being computed using a reasonable level of computational complexity such that it can be applied for interference cancellation in a mobile terminal, for

example.

In order that the invention may be more fully understood, reference will now be made, by way of example, to reference to the accompanying drawings, in which: Figure I is an explanatory diagram showing data modulation of two data sets with sine and cosine waveforms; Figure 2 is an explanatory diagram showing data demodulation of a received signal with sine and cosine waveforms to recover the two data sets; Figure 3 is a block diagram of a SIC receiver; Figure 4 is a block diagram of a PIC receiver; and Figures 5 to 15 are matrix layout diagrams The following description is concerned with a method of common channel interference cancellation for use in any system employing WCDMA technology incorporating a number of interfering common channels (with spreading codes) known to the receiving terminal.

In the method described linear equaliser based interference suppression techniques are applied to the downlink WCDMA receiver. Such techniques, in contrast to conventional interference cancellation, typically need the interfering signal to be cyclostationary (exhibit correlation with time/frequency shifted versions of itself). When such a condition is satisfied linear adaptive filtering may be used to obviate interference effects. However, the feasibility of implementing such a filter will, amongst other factors, be governed by the rate at which the filter coefficients need to be updated. To alleviate the difficulties in calculating filter coefficients, detailed below, an alternative direct form method is proposed specifically aimed at cancelling common channels whose channelisation codes are known at the receiver.

The 3GPP standard "UK Radio Transmission and Reception (FDD)", v3.3.1 June, 2000 defines a number of common physical channels for signalling and control purposes for use on the downlink from a base station to a handset. In a multipath channel loss of orthogonality may result in interference from other channels (such as other data and common channels), that is multiple access interference (MAI). Additionally, interference from one path of the desired data channel to another path of the desired data channel may also occur, that is inter path interference (IPI). A key difference, as far as the user equipment (UK) is concerned, between the other users' data channels and the common channels is the knowledge of the common channel channelisation codes possessed by the UK.

The technique described below utilises knowledge of the common channel channelisation codes and the multipath delay to effectively remove both MAI (due to the common channels) and IPI from the received signal.

A description of some of the common downlink channels is given below followed by a description of the downlink system model and the possibility of using direct matrix inversion for common channel cancellation.

1. Downlink Channels On the downlink user data is carried on the dedicated physical data channel (DPDCH) together with physical layer control information on the dedicated physical control channel (DPCCH), which are collectively known as the downlink dedicated physical channel (downlink DPCH). The common pilot channel (CPICH) maybe used to aid channel estimation at the UE for the DPCH. There are two types of CPICH, primary and secondary. The primary CPICH is unmodulated and has a fixed channelisation code and is scrambled with the primary scrambling code. The secondary CPICH may have any channelisation code of length 256 and may be under a secondary scrambling code. The Synchronisation Channel (SCM) is provided to enable cell searching and consists of a 256-chip channelisation code that is identical in every cell. The primary common control physical channel (P-CCPCH) is used to carry the broadcast channel (BCH) and needs to be demodulated by all the terminals. The P-CCPCH uses a fixed length 256-chip channelisation code. A paging indicator channel (PICH) along with a paging channel (PCH) provides efficient sleep mode operation. The PICH uses a channelisation code length of 256.

2. System Model A standard model, proposed by M Latva-Aho, "Advanced receivers for Wideband CDMA Systems", Ph.D Thesis, University of Oulu, Finland, 1998, for a synchronous direct sequence CDMA (DS-CDMA) system may be expressed as: N-1 K M r(t) = i Akbk Ck mSk (t nT rk,m)+ 77(t) ( ) n=0 k=1 m=1 where r(t) is the received signal K is the number of users M is the number of propagation paths Nb is the block of received symbols processed A k = where Ek is the energy per symbol T is the symbol interval b ins is the nth transmitted data symbolfor user k ckn,n is the complex gain of the mth propagation path for user k k (t) is the kth user 's spreading sequence (combination of scrambling, channelisation codes) irk m is the propagation delay of the mth propagation path for user k rot) is the complex zero mean Gaussian noise process with variance 2 The received signal is anti-aliased and time sampled, at a rate of T. '= T. where S is the number of samples per chip and G is the spreading factor (length of the Walsh code). The received time-sampled signal over a data block of Nb symbols may be represented in matrix form as r=SCAb+n (1) where r =[r( '"), , r( (N&-)] (2) is the sample input vector with: r(T'') =[r(Ts(nSG + 1)), ..., r(Ts(n + 1)SG)| S is the spreading matrix of the form set out below, C is the channel coefficient matrix of the form set out below, A is the received amplitude matrix of the form set out below, b is the transmitted data symbol of the form set out below, and n is the zero mean Gaussian noise process with variance a2 and where C(n) is the channel response for the Lth path of the Kth user's nth symbol. For a downlink synchronous channel the channel response for every user on a given multipath for a particular symbol will be the same, cant = cil K. 3. Direct Matrix Inversion for Common Channel Cancellation Interference rejection aims to remove the MAI due to other users (or channels) by reconstructing and subtracting the interfering signal based on an estimate of the data symbols and channel coefficients of each and every interfering user or channel. Also necessary is knowledge of the interfering user's channelisation code. Generally, two methods are used for subtractive interference cancellation: serial cancellation and parallel cancellation. Hybrid structures have also been proposed that are designed to exploit the benefits of both serial and parallel structures.

The pre-combining linear minimum mean squared error (pre-LMMSE) receiver has been shown to be effective in combating multi-user interference. The output of the pre-combining LMMSE receiver may be written as follows: Y = [ R + or] S r (4) where R is the cross-correlation matrix, Ash = diag LAl2Z A2 consists of user powers and the average channel tap powers with =diagtEt|ck,| :...,Et|ck| ]] where E||ck'| is the average power of the ash user's (h propagation path and a2 is the noise power spectral density, and H is the complex conjugate transpose.

In the following analysis without loss of generality, the general term of the cross-correlation matrix will be used to imply the cross-correlation matrix R whose diagonal elements may or may not have been modified depending on the particular receiver structure being used.

In a practical implementation, finding the inverse of the crosscorrelation matrix may be feasible where the cross-correlation properties of the spreading codes are not changing very quickly and the number of users (channels) is relatively small, i.e. recalculation of a large inverse matrix is infrequent. For a real system with multiple users and multipath propagation the matrix size traditionally precludes direct inversion. Adaptive formulations of the pre-LMMSE receiver have been developed by F. Swarts, P. van Rooyan, I. Opperman, M. Lotter, "CDMA Techniques for Third Generation Mobile Systems", Kluwer Academic Publishers, 1999 to work in scenarios with more than a few users and under changing channel conditions. Such adaptive equalisers rely on the interference being cyclostationary. However, the 3GPP standard specifies the use of a long scrambling code (38400 chip truncated gold sequence) on the downlink which effectively destroys the cyclostationarity of the interfering signal and causes the cross-correlation matrix to change from symbol to symbol.

The 3GPP standard 3GPP, "UK Radio Transmission and Reception (FDD)", v3.3. 1 June, 2000 specifies a channel model (case 2) with three multi-path components for which the maximum multi-path delay is given as 76.8 chips. For a spreading factor of eight this amounts to a window length of ten symbols. If the four common channels mentioned above are to be decorrelated from the desired signal then a 150x150 matrix ((4+1)x3x10) needs to be inverted every symbol, i.e. every 2,us.

Though this may represent an extreme and rare occurrence, it nevertheless highlights the potentially high computational requirement.

A general n x n matrix requires O(n3) operations to find the inverse. Thus, a 150 x 150 matrix requiring inversion every As would require approximately O(102) operations (multiplications, additions, subtractions, divisions) per second. This figure does not account for the particular structure common to a cross- correlation matrix of spreading codes in a multipath environment. By paying greater attention to the structure of the cross- correlation matrix and re- casting the LMMSE formulation it may be possible to greatly reduce the above processing requirement and remove the need to explicitly perform a matrix inversion.

Rewriting equation (5) as a linear algebraic equation, of the form Ax=b, where A is a non- singular n by n matrix, b is a vector and x is a vector of unknowns: [R+ Ash]Y S r (5) removes the requirement for directly calculating the inverse matrix. Such a linear algebraic equation may be solved either by direct methods or by iterative methods. Direct methods are based on Gauss elimination in which the unknowns of the system are modified until the solution is found. Iterative methods start with an initial guess of x that is subsequently improved until a required accuracy has been achieved. Since the purpose of this description is to elucidate the structure of the cross- correlation matrix, the analysis will be restricted to direct methods. A- ' may be expressed as a product of matrices such that the action on b is easy to compute. The usual way of solving the above form of linear algebraic equation is to compute the triangular factorization of A: A=LU (6) where U is an upper triangular matrix with a diagonal of ones and L is a lower triangular matrix (its upper triangle contains only zeros). Then A =U L andX=u W where w=L b. Thus the solutions for x maybe found by solving the linear systems: LW=b (7) for w end Ux=w (8) for x. Finding the solution of (8) is termed forward substitution and of (9) is termed backward substitution, further details of which may be found in G. Golub, C. F. Van Loan, "Matrix Computations", The Johns Hopkins University Press, third edition, published 1996.

S. Pizzanetzky, "Sparse Matrix Technology", Academic Press Inc. 1984 summarises the costs (computational and storage) associated with LU factorization and forwardlbackward substitution as a function of the structure of matrix A. A subset of the results from this reference is reproduced in Tables 1 and 2.

Multiplications and Additions and _ _ divisions subtractions Storage Full symmetric I n3+ I n2- 3- n - n, - 6 n 2 n2 + 2 n Band symmetric hth i)a is' /l lltr' I',, is, 2 (B+I)n- l2_ Sparse Sir, (r, +3/2 Sir, (r, +I)/2 n _. . Table 1 Storage and operation count for factorisation of a n x n matrix ___ Multiplications and Additions and divisions subtractions _. _ _ Full symmetric n2 n2_n Band symmetric (2f +I)n _2_≈2n _2_, Spars n +2 rU 2 ru Table 2 Operation count for forward and backward substitution where n is the order of matrix A B is half the bandwidth of matrix A ru is the number of off-diagonal non-zeros in row I of U The present analysis is constrained to the case of a single user of interest whose spreading length is less than 256 with four common channels each of spread length 256. Furthermore, the maximum excess delay spread is limited to less than 256 chips. D'<S where

Sit is the spread length of the common channels Do is the maximum multipath delay of the user of interest (which will be the same for the common channels) Appendix A gives a detailed analysis showing that the resulting cross-correlation matrix, R. will be sparse and Hermitian. Thus, the equivalent real linear system, of twice the order, will also be symmetric.

The operation count in factoring R is proportional to the number of off-diagonal non zeros in the upper triangular matrix, U. as given in Table l. In the proposed case the precise structure of U will be highly dependent on the cross-correlation properties of the spreading codes used and the multipath delay profile. As an example the structures of R and U are shown in Figures 12 to 17, where a dot denotes a non-zero entry, for the three different multipath delay profiles given in the 3GPP standard.

Table 3 shows the mean and peak number of off-diagonal non zeros per row in the upper triangular matrix and the associated cost (multiplications/divisions) as given in table 1, for the three cases above.

Case Matrix Mean Peak Multiplications/ Order Divisions 1 30 7 12 1254 2 150 24 44 56447 3 60 18 32 13834 Table 3 Non zeros per row in upper triangular matrix and associated factorization cost These figures may be reduced further by reordering (permuting) the cross-correlation matrix prior to factorization using standard techniques such as Reverse Cuthill-Mckee or Minimum Degree Ordering. Reordering the cross-correlation matrix has the effect of reducing the matrix bandwidth which in turn results in sparser factorisations. Results from application of the reverse Cuthill- Mckee algorithm are shown in Table 4. Clearly, large gains may be realised by preconditioning the cross-correlation matrix prior to factorization.

Case Matrix Mean Peak Multiplications/ Order _ _ Divisions 1 30 5 9 687 _. _ _ _ _ 2 150 11 32 13971 3 60 13 25 7165 _. . _ _ Table 4 Non zeros per row in upper triangular matrix and associated factorization cost reordered using reverse Cuthill-Mckee Using the figures given in Table 4, the number of multiply operations required per second (mops) for the factorization may be calculated based upon the requirement to solve the linear system every 2ps (i.e. every syinbol when using a spread length of eight for the data channel).

Case Matrix Multiplications/ mops Order Divisions 1 30 687 343.5 x 106 _ _. . _ _ 6.9855 x 109 3 60 7165 3.5825 x 109 Table 5 Multiply operations per second for factorization with a data channel of spread length eight The cross- correlation matrix of spreading codes has been shown to be Hermitian and sparse in the case of a single user with spreading code length shorter than the common channel spreading code lengths. By reformulating the interference cancellation problem as a linear algebra problem the need to perform an explicit matrix inversion is removed.

Although the precise conditions (e.g. number of multipaths, path delays, data rate etc.) encountered on the downlink are highly variable, the examples given above serve to illustrate the potential of using a direct form solution to the linear algebraic problem. In the examples above, the data channel spread length of eight results in the requirement to solve the linear system every 2,as which means that, even for a modest number of operations per symbol, the overall cost will be significant. Permuting the cross-correlation matrix prior to factorization has been shown to reduce the computational cost significantly.

A W-CDMA system operating in a multipath environment will suffer from the effects of MAI and IPI when a RAKE receiver is used at the receiver. Knowledge of the correlation properties of spreading codes between the different multipaths and users may be used to effectively reduce such deleterious effects. Though cross-correlation information is not available for all interfering users at a given user terminal, information pertaining to certain common channels is available.

Therefore, it should be possible to alleviate the effect of common channel interference by way of the cross-correlation matrix.

A long scrambling code (spanning multiple symbols) used on the downlink causes recalculation of the cross-correlation matrix every symbol when attempting to decorrelate interfering users. The order, n, of the crosscorrelation matrix is a product of the number of multipaths, symbols windowed and users to be decorrelated. The number of operations required to invert the matrix is of the O(n3) every symbol and consequently the computational cost can be substantial.

Detailed analysis of the structure of the cross-correlation matrix has shown it to be both sparse and Hermitian for the case of one user channel and a number of common channels. By reformulating the interference cancellation problem in terms of a linear system, it is possible to factor the cross-correlation whilst exploiting the sparsity to reduce computational costs. For the case 2 channel model, specified in 3GPP, the computational cost has been reduced from 0(102) to O(109) per second.

If the LU factorization can be performed using fixed-point arithmetic then the computational requirements shown are readily realisable with existing hardware. The determining factor is the numeric resolution necessary that is governed by the numeric stability.

Using the approach of a direct form solution to remove IPI and common channel MAI should provide optimum performance in contrast to serial, hybrid or parallel interference cancellation methods.

A pre-combining linear minimum mean squared error (LMMSE), effective at combating multi-user interference, may be written as follows: Y = [R + tr2X:t SHr where R is the cross-correlation matrix of the spreading codes, X is the inverse of the matrix containing user powers and average channel tap powers which is diagonal, H is the complex conjugate transpose, and al is the noise power spectral density.

The complexity of the LMMSE receiver will, as shown above, be determined largely by the computational cost of inverting the term in brackets. Since the X term is diagonal the structure of R will ultimately dictate the number of operations required for the inversion process.

Considering the case of common channel interference, R may be formed from knowledge of the common channel spreading codes. By this definition, the R matrix will not include contributions from other user data, since other user spreading codes are unknown to the terminal of interest, although, in the case of multi-code WCDMA, or terminals supporting multiple user channels, the R matrix may be augmented with information allowing removal of self-interference.

The above LMMSE equation may be rewritten as a linear algebraic equation, thereby removing the need to explicitly find the inverse term. Instead, methods such as Gauss elimination may be used to find the required term. This still requires factorization of the term in brackets and subsequent forward-backward substitution to find y. The computational costs of performing these operations for various matrix structures are given below.

Analysis of the structure of the R matrix has shown it to be both sparse and Hermitian when considering common channel interference. Thus the cost of forming y is greatly reduced from the general case whereby no account is taken of the form of R. Applying well-established methods for solving sparse Hermitian matrices it is therefore possible to remove common channel interference from the received signal.

The example given above pertains to the LMMSE receiver structure. However the analysis is applicable to any receiver based on the cross-correlation matrix of the spreading codes, such as a decorrelating detector.

By elucidating the structure of the cross-correlation matrix the total removal of common channel interference as observed at a receiver may be possible. This is in contrast to existing approaches that aim to remove common channel interference by removing an estimate of the interfering signal from the received signal.

The reduction in complexity allows the realization of common channel interference cancellation techniques on a mobile receiver.

The cross-correlation matrix of the spreading codes as seen on the downlink of a WCDMA system employing common channels (known to the user) is shown to be sparse and Hermitian.

Thus, it is possible to use well-established mathematical techniques to factor the cross-correlation matrix in an efficient manner leading to the possibility of realization in a mobile terminal.

Conventional methods for removing this form of interference from the received signal involve re-generating a replica of the interfering signal at the receiver and subtracting it from the received signal. As already discussed there are different ways in which this may be done, the common ones being parallel interference cancellation (PIC) and serial interference cancellation (SIC). However, the conventional approaches are non-optimal in that they do not remove in totality the interfering signals due to computational cost.

Appendix A R. the cross-correlation matrix (or any diagonally modified variant), is represented in the following form: R ') R (l,2) R 3) ... R , R (2,l) R (2,2) R (2,3) . . . R (2, N b) R = R(3,') R(3 2) R (3 3) .

R (3,Nb) (A-l) R(Nbyl) R(Nb,2) R(Nb,3) ... R(Nb,Nb) where rail lY] r,, X,Y2 r,X, 2Y! r,,X 2Y2 rIX} KL rX,Y rX'Y rX,Y r:,y By 12,11 12,12 12,21 12,22 rl2,KL X,y X,y X,y X,y X,y R(X,Y) = r2,,, r2,, 2 r2,,2, r2,,22 r2l,KL (A-2) rX,Y rX,Y rX,Y rX,y X,y 22,11 22,12 22,21 22,22 r22,KL : : : : . : rX,Y rX'Y rX,Y rX,y rxy KL,I I KL,12 KL,21 KL,22 KL,KL and Nb is the symbol window length, and rk'';'n is the cross-correlation between the spreading code used for symbol i of user k on path m with the spreading code used for symbol j of user I on path n. Since r, jhn,]n=(r', i,n,km), it is straightforward to show that R =R leading to R=R where H denotes the Hermitian. With R being Hermitian the equivalent real system (of twice the order) will also be symmetric...DTD: Since on the downlink all the users (channels) are synchronous, the delay associated with a given multipath will be identical for all users (channels). Hence, if D(p) is the delay associated with path p on symbol a, from the definition of the spreading matrix given in the system model description it is obvious that, when there is no overlap of spreading codes between any two columns in the matrix, the resulting cross- correlation will be zero. Mathematically, this property may be stated as follows: J (Dim + 5 j) 2 (D ' ') (i -1) for i > j rkmln Ov[ijklmn]if{(D+sti,)<(D',+ SJ'(J-l)f i.l (A-3) where St" is the spread length of user k on symbol i Additionally, the trivial cases of two different spreading codes aligning perfectly and a spreading code perfectly aligned with itself may be stated as follows: rbnJ'n = 0[k = Am = n,i = i] (A rims = l V[k = I'm = n, i = j] The analysis will begin with the case of all users with an equal spread length, and then move on to the case of one user with a smaller spread length than the other users.

Equal Spread Length For All Users For the case when all users are synchronous and have the same spreading length, S. each with L multipaths with the multipaths for user i being arranged such that: D(.)<D()<D)< <D() (A-5) then for i<j: rkm],ln = 0 \'[i, j, k, 1, m, n]if {(Dt'' + S i) < (Dj, + S( j-b)for i < j} (A-6) Dt''-D<', < S( j-1-i) (A-7) Since i < j, j - i > 0 the above inequality will be lower bounded when j - i = 1.

Hence, for the following condition, the cross-correlation between users k and I on paths m and n for symbols i andj will be zero: D(')2Dm) (A-8) Using equation A-5, for any pair of users with L paths there will L(L+1) be 2 instances where A-7 is true. With K users and Nb windowed symbols, for the case of i<j, there are: K2LNb (L + 1XNb - 1) (A-9) zeros. Similarly, for the case of i>j, there are an additional: K2LNb (L + 1XNb 1) (A- 10) zeros.

Additionally, from A-4, with K users, L paths and window length of Nb symbols, there are: KLNb(K-1) (A-11) zeros.

The lower bound of the total number of zeros in the cross-correlation matrix when all users have the same spread length therefore is: K2LNb (L + 1XNb -1) + KLNb (K -1) (A-12) It is instructive to find the circumstances under which the ratio of zero elements to the total number of elements in the cross-correlation matrix falls below fifty percent.

The total number of elements in the cross-correlation matrix is (&LNb)2, and the ratio of non-zero elements to total number of elements will fall below fifty percent when: K2 L Nb (L+l)(Nb-1) + 2 KLNb (K-1) <0.5 2 (KLNb) 2 K (I -L+Nb)<2 (A-13) as K oothis expression will be true for Nb <L-1 As long as the window length is greater than or equal to the number of multipaths less one, at least half the elements of the cross-correlation matrix will be zero.

F.L. Alvarado, "A note on sorting sparse matrices", Proc. IEEE, 1967, pp. 1362- 1363 gives the definition for sparseness of a matrix as follows: for a matrix of order n to be sparse, the number of non-zeros must be no), where < 1. It is straightforward to prove that < 1 in the case of equation A-12 showing the cross-correlation matrix to be sparse in the above case.

Additional User With Shorter Spread Length With the addition of another user of spread length So < S and L multipaths, the number of zeros due to the K-1 users of spread length S will be given by the expression above. Zeros resulting from the additional user may be calculated as follows. In the case of i<j, we have: reman =OV[i,j,k,l,m,nll>l,ii{(,Dt''+S,i)<(,Dt''+ S'(j-b)fori< j,l>l} (A14) where /D(m) is the delay associated with path m on symbol i for user 1. Constraining Sr to be an integer multiple of So makes the analysis more tractable.

Let S. = pS] = pS, p2 2 then ('D(')+Si) (,D(')+ pS(j-b)fori< j, p22,1>1 (A-15) The above inequality will always be true implying the cross-correlation between user l and user 1, for l >1, will be zero for all user-path-symbol combinations (i<j) . The number of zeros due to the above inequality will be: L2 (K - 1)(Nb + 1)Nb (A- 16) Analysis of the cross-correlation properties between user I and user 1 for i<j reveals cases where the inequality is never satisfied so that no zeros would occur under such circumstances. A similar analysis to the above in the case of i>j gives further: L2 (K - b(Nb + bNb (A- 17) zeros. To this must be added the zeros resulting from the cross- correlation between user I on symbol i with user I on symbolj: LNb(L + b(Nb + 1) (A-18) Giving the total number of zeros as: (K 1) LNb(L+l)( h)+LN6(K-1)(K-2)+L (K-1)(Nh+l)Nh+ 4 (A-l 9) Using the definition of sparseness given above it is straightforward to show < 1 for the above case.

Claims (12)

1. CLAIMS: 1. A common channel interference cancellation processor for

   cancelling common channel interference in a code division multiple access (CDMA) system, the processor comprlsmg: receiving means for receiving a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes; and data extraction means for extracting the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix.
2. 2. A processor according to Claim 1, wherein the received signal r is in the form, or in a form derived from: r = SCAb + n where r is the received signal time sampled over a user data block of N symbols, S is the spreading matrix of the spreading codes of the interfering common channels, C is the channel coefficient matrix of the common channel channelisation codes, A is the received amplitude matrix of the relative amplitudes of the user data symbols, b is the data matrix of the user data symbols, and n is the zero mean Gaussian noise process with variance a2 where is the noise power spectral density.
3. 3. A processor according to Claim 1 or 2, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is the cross-correlation matrix R = SS+ or some derivative thereof, where S is the spreading matrix of the spreading codes of the interfering common channels and S+ is the Hermitian conjugate of the matrix S.
4. 4. A processor according to Claim 1, 2 or 3, wherein the matrix inversion technique includes the elucidation of the matrix by expressing the relationship between the output of the receiving means and the matrix in the form of a linear algebraic equation, Ax = b, where A is a non- singular n by n matrix, b is a vector and x is a vector of unknowns.
5. 5. A processor according to claim 4, wherein the matrix inversion technique includes the elucidation of the matrix A by means of the product LU of an upper triangular matrix U having a diagonal of ones and a lower triangular matrix L having an upper triangular portion containing only zeros.
6. 6. A processor according to claim 5, wherein the matrix inversion technique includes solving the linear equation Lw = b for w, where w = Lab.
7. 7. A processor according to claim 5 or 6, wherein the matrix inversion technique includes solving the linear equation Ux = w for x, where w = L-, b.
8. 8. A method of common channel interference cancellation utilising interference cancellation in a code division multiple access (CDMA) system, the method comprlsmg: receiving a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes; and extracting the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix.
9. 9. A method according to Claim 8, wherein the received signal r is derived from the matrix relationship: r= SCAb + n where r is the received signal time sampled over a user data block of N symbols, S is the spreading matrix of the spreading codes of the interfering common channels, C is the channel coefficient matrix of the common channel channelisation codes, A is the received amplitude matrix of the relative amplitudes of the user data symbols, b is the data matrix of the user data symbols, and n is the zero mean Gaussian noise process with variance a2 where a is the noise power spectral density.
10. 10. A data carrier incorporating a computer program for controlling a common channel interference cancellation processor for cancelling common channel interference in a code division multiple access (CDMA) system, the computer program being operative to receive a transmitted signal incorporating a user data signal and a common channel signal that have been CDMA coded prior to transmission utilising channelisation codes, and extract the user data signal from the transmitted signal utilising known common channel channelisation codes and a matrix inversion technique, wherein the matrix inversion technique is based on an assumption that the matrix to be inverted is a sparse symmetric matrix, and a sequence of processing operations is used to perform the matrix inversion that is significantly less than the number of processing operations that would be required to perform inversion of a corresponding full symmetric matrix.
11. 11. A common channel interference cancellation processor for cancelling common channel interference in a code division multiple access (CDMA) system, the process being substantially as hereinbefore described with reference to the accompanying drawings.
12. 12. A method of common channel interference cancellation utilising interference cancellation in a code division multiple access (CDMA) system, the method being substantially as hereinbefore described with reference to the accompanying drawings.