Self-Reference Spatial Diversity Processing for Spread Spectrum Communications∗ Daniel Perez-Palomar,´ Montse Najar´ and Miguel Angel Lagunas

International Journal © Urban & Fischer Verlag of Electronics http://www.urbanfischer.de/journals/aeue and Communications

Self-reference Spatial Diversity Processing for Spread Spectrum Communications∗ Daniel Perez-Palomar,´ Montse Najar´ and Miguel Angel Lagunas

Abstract In this paper, the application of three blind (or self- interfering signals by linearly combining the signals re- reference) spatial diversity signal processing methods to Spread ceived at the antenna elements. The design of the beam- Spectrum (SS) communications is described. These methods do former requires some a priori knowledge about the de- not require any kind of side information beyond knowledge of sired signal in order to discriminate it from the inter- the signal structure, in contraposition to methods that depend ference. Depending on the character of this information, on training sequences. Each self-reference method is specifically designed for a par- classical beamforming techniques can be classified into ticular SS transmission scheme and uses a particular signal’s two types. The first one is Time Reference Beamforming structural information. All three methods, however, are derived (TRB), which needs a training sequence that in turn im- under the common goal of finding the optimum beamformer, in plies a loss of spectral efficiency and channel bandwidth the sense of maximum signal to interference-plus-noise ratio, in utilization but yields robust methods. The second type a blind manner. is Spatial Reference Beamforming (SRB), which requires The Code Reference Beamformer for Frequency Hopping sys- the knowledge of the direction of arrival (DOA) of the tems is an approach based on the knowledge of the hopping desired signal, the knowledge of the array geometry, and sequence or code structure of the signal. This method is the strict array calibration. best alternative for array signal processing on this particular SS scheme. Two recently proposed beamforming methods, An alternative to requiring either a spatial or a time which are based on the knowledge of the redundancy struc- reference is Code Reference Beamforming, which can be ture of the desired signal, are described under the common included in the more general category of blind beamform- framework of efficiently using the inherent diversity – either ing. These blind (or self-reference) algorithms exhibit in frequency or time – of two signalling formats, namely, Fre- good behavior in terms of robustness and spectral/channel quency Diversity (FD) SS and DS-CDMA. The former uses efficiency. They are based on the minimization of an ob- frequency diversity, while the latter uses time diversity. The jective cost function which is defined based on certain in- diversity approach presented for FDSS seems to be the best herent structural properties of the desired signal; hence, no choice at the moment. Regarding DS-CDMA, for which many side information, such as a training sequence or the DOA beamforming algorithms have been developed in the literature, the self-reference beamforming is simply an alternative blind of the desired signal, is needed. This implies that self- method that shows very good performance. These diversity ap- reference spatial processing techniques can be applied to proaches were compared via simulations to the standard Time existing systems without the need of any modification of Reference Beamformer (TRB) and showed a performance simi- the emitter (e.g. the uplink channel of a cellular communi- lar to it (with 10% of the bits as a training sequence) even cation system [1]). An important feature of self-reference without the need of any side information whatsoever. beamforming algorithms is that they are not dependent on Keywords Spatial signal processing, Arrays, Beamforming, channel properties or array calibration, which makes them Blind methods, Self-reference, Diversity, Redundancy, Fre- robust methods. It is important to note, on the other hand, quency hopping, CDMA, FDSS, Spread Spectrum that each particular transmission scheme presents a different signal structure and, therefore, requires a specific particular blind method. 1. Introduction Many blind algorithms have been devised exploiting different properties of the signals. They can be divided Array signal processing allows interference rejection ac- into two main groups: deterministic blind beamforming cording to the bearing angles or spatial signatures of the (using the known structure of the signal) and statistical blind beamforming (using statistical properties of the source). All these techniques are also referred to as prop- Received August 2, 1999. Revised May 8, 2000. erty restoral algorithms, because they force the signal estimates to exhibit certain properties that the actual sig- D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas, Universitat Politècnica nals are known to possess. For man-made signals, such de Catalunya (UPC), Department of Signal Theory and Communi- as those encountered in wireless communications, these cations, c/ Jordi Girona, 1-3, Mòdul D5, Campus Nord UPC, 08034 Barcelona, Spain. signal properties are often known with great accuracy, E-mail: [email protected] leading to robust algorithms. ∗ This work was partially supported by the European Comission Some of the most representative deterministic prop- under ACTS Project AC347 SUNBEAM; the Spanish Government erties, Constant Modulus (CM) [2, 3] and Finite Alpha- (CYCIT) TIC98-0412, TIC98-0703; and the Catalan Government bet (FA) (exploited by decision-directed methods [4]), are (CIRIT) 1998SGR 00081, 1999FI 00588. properties exhibited by many modulation schemes. Other

Int. J. Electron. Commun. (AEU)¨ 54 (2000) No. 5, 267−276 1434-8411/2000/54/5-267 $15.00/0 268 D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications signals, known as gated-like signals, have the property of gorithm, a specific method for adaptive arrays using FH not being present on the channel during a certain time signals (assuming knowledge of the FH sequence) based (or at least being present with low power); this allows on the spectral characteristics of the received signals. Fi- anticipative processing to estimate the parameters of the nally, Eken [22] devised a modified sidelobe canceller for scenario free of the desired signal [5–7]. A particular ex- FH signals that needed a priori knowledge of the DOA ample of this type of signal is Frequency Hopping, where of the desired signal. The main drawback of the previous knowledge of the frequency hopping sequence can be approaches is the drop in SINR at hop instants. The rea- used for the anticipative processing [8–10] (see Sect. 2). son for this behavior, as was pointed out in [18, 20], is Another property, the property of diversity, which refers to that changes in signal frequency due to FH modulation the existence of signal replicas along the time, frequency, are seen by the algorithm as changes in the DOA’s, result- code or space axis (usually to combat fading or jamming), ing in discontinuities of the adaptive algorithms’ perform- provides the signal with a redundancy that allows opti- ance. mum beamforming using the replicas as embedded self- The anticipative processing algorithm proposed in [8– references [11–13] (see Sect. 3). 10] and denoted Code Reference Beamformer takes ad- Regarding statistical properties, the most important vantage of the knowledge of the FH sequence at the re- ones are probability density function fitting and statistical ceiver, as in [20], and requires neither temporal nor spa- independence of the sources [14], higher order statistics tial references. The method relies on the possibility of (HOS) [15, 16], and cyclostationary properties [17]. It is the measurement and estimation of the interference-plus- important to note that blind statistical methods usually noise covariance matrix. This property has already been present bad convergence properties, yielding algorithms used by several authors in non FH contexts [5–7]. that are not very reliable. The proposed system, depicted in Fig. 1, is composed Blind beamforming techniques lend themselves to of two parallel processors; both processors begin by de- block or direct implementation (usually based on a gen- hopping the received signal. The first one, called the antic- eralized eigenvector decomposition) and to adaptive al- ipative processor, is used to obtain the interference-plus- gorithms (with a reduced computational load). Clearly, noise covariance matrix, Rin, before the desired signal is adaptive methods are especially suitable for tracking in present. The second one, the on-line processor, performs non-stationary environments. the actual beamforming. In this paper, three blind deterministic beamforming The beamforming part of the on-line processor is made methods, based on the knowledge of the structure of the up of two different stages, corresponding to the two terms = κ −1 κ signal, are described for Spread Spectrum (SS) commu- of the optimum beamvector wopt Rin ad,where is nication systems. Each one is specifically designed for a scalar factor, and ad is the steering vector of the desired a particular SS signalling scheme, but derived from a com- signal. The first stage preprocesses the dehopped received mon framework of diversity aimed at the maximization of snapshot, xol (t), using the inverse of the interference-plus- ( ) = −1 ( ) the Signal to Interference-plus-Noise Ratio (SINR). The noise covariance matrix to obtain x t Rin xol t .The performance of each method is verified via simulations. second stage is devoted to properly weighting the prepro- In Sect. 2, we describe the Code Reference Beamformer cessed signal vector x(t) with the desired steering vec- based on anticipative processing for slow Frequency Hop- tor ad.Sincead is assumed to be unknown, a blind es- ping SS (FHSS). Sect. 3 introduces beamforming techniques based on a general framework of diversity properties. Then, Sects. 3.1 and 3.2 present specific self- reference algorithms based on frequency diversity, for both fast FHSS and Frequency Diversity SS (FDSS), and ANTICIPATIVE PROCESSOR based on time diversity, for Direct Sequence SS (DSSS), Q IF 5 -1 respectively. Finally, in Sect. 4, the conclusions are pre- NBF in estimate sented.

Frequency Synthesizer Q 2. Code reference beamforming for slow fIF+fi+1 Dehopping FHSS . . Q Q Q IF 5 -1 D The addition of spatial diversity processing with an ar- NBF in d [ [ ray to Frequency Hopping Spread Spectrum (FHSS) tech- ol(t) (t) y(t) niques provides a greater capacity for interference rejec- Beamformer Frequency tion. Existing beamformers for the reception of FH modu- Synthesizer lated signals are based on classical techniques of temporal fIF+fi Dehopping or spatial reference beamforming. First, Acar and Comp- ton [18] studied the adverse effects of FH in a time ref- ON-LINE PROCESSOR erence beamformer based on the LMS algorithm. Next, Bakhru and Torrieri [19–21] proposed the Maximin al- Fig. 1. Code Reference Beamformer. D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications 269

H ( ) −1 ( ) timation of this steering vector is adaptively obtained by log-likelihood cost function m n Rin m n (see [10] for maximizing the output SINR [10]: details). If the frequency synthesizer of the anticipative proces- H sor is not perfectly synchronized with the received signal, = = c Rxc − , ad arg max SINR − 1 (1) the estimated interference-plus-noise covariance matrix Q H 1 c∈C c R c in Rin will present a residual contribution from the desired signal. This situation, however, does not prevent the sec- = −1 −1 where Rx Rin Rxol Rin is the correlation matrix of the ond stage from converging to the solution that maximizes preprocessed signal vector x(t),andQ is the number of the SINR at the array output. In [8] it was shown that the antenna elements. convergence rate with leakage of the desired signal into The solution to this problem statement is given by the the covariance matrix can be maintained at the expense of , −1 generalized eigenvector of the matrix pencil Rx Rin an increment in the algorithm misadjustment. This is a key corresponding to the maximum generalized eigenvalue: feature of the procedure’s robustness. In principle, the initial weighting vector used in the = λ −1 , Rxc maxRin c (2) adaptive implementation is randomly chosen or fixed to present an isotropic gain pattern. Nevertheless, this ini- where (λmax − 1) is the maximum SINR. An adaptive im- tialization causes the problem, already observed in the plementation of the computationally expensive eigende- literature, of SINR drops at frequency hop instants. This composition can be found in [8, 10]. arbitrary initialization could be substituted by a good ini- In mobile communications systems, due to the pres- tial estimate of the steering vector of the desired signal ence of fading on the received interferences (and the pos- with the aim of speeding up the convergence of the adap- sible appearance/disappearance of interfering signals), tive algorithm, hence reducing the SINR drops. This can −1 the matrix Rin estimated by the anticipative processor be done by the use of focussing techniques, which convert should be continuously modified in order to track the non- the steering phases estimated in the previous hop to the stationary scenario [10], becoming a discrete-time depen- actual one by simply multiplying them by the frequency −1( ) / dent Rin n . The inverse correlation matrix estimated by ratio fi+1 fi . This allows a prediction of the optimum the anticipative processor is adequate only as an initial- weighting vector for the next hop. Note that this procedure ization of the system. Once it has been transferred to does not require previous knowledge either of the loca- the on-line processor, and after few iterations to achieve tion of the sensors or of the desired direction of arrival. −1( ) convergence of the second stage, Rin n is iteratively up- It is generally accepted, however, that in FH systems the dated (see Fig. 2) using the following recursion: frequency spacing is always set higher than the coherence bandwidth of the mobile channel. Therefore, two consecu- −1( + ) = γ −1( ) + ( − γ) ( + ) H( + ). Rin n 1 Rin n 1 m n 1 m n 1 tive channels will appear as statistically independent, and (3) the same will happen to the generalized steering vectors. This fact, along with the lack of linear dependence on fre- Here m(n) is an estimate of the undesired component of quency of the equivalent steering vector elements, might the incoming snapshot pre-processed by the first stage of be expected to contribute to a degradation of the results the beamformer [10]: achieved with the frequency focussing process. Neverthe- less, simulation results show that it is still adequate to ( ) = ( ) − ( )˜( ) −1 , m n x n g n s n Rin w (4) focus the second stage at the hop instants as a good initialization, since there is always enough residual spatial where s˜(n) is a noisefree regenerated signal that can be ex- information that can be taken into account. tracted from the beamformer output y(n) and g(n) is an In order to show the effectiveness of the method, adaptive coefficient continuously adjusted to minimize the simulations were performed with a uniform linear array (ULA) of 4 sensors with half-wavelength separation with respect to the center frequency (900 MHz) of the hopping band. The following scenario was used: a Gaussian Min- imum Shift Keying (GMSK) signal of interest (DOA of Q [(t) 1 20 degrees and Eb/No = 15 dB) spread over a 50% rela- 5 -1 D Demodulation in G tive bandwidth (assuming slow FH) and two interfering [ (t) and Detection ol y(t) users, also GMSK signals, with bearing angles of −30 {a } and 40 degrees (Eb/No = 15 dB). Each user’s flat-fading P(t) i Q channel was generated with a Laplacian Power Angu- Modulation lar Spectrum ray model with a power Azimuth Spread + - (AS) of 8 degrees [23]. The speed of the users was set to 120 km/h. Q Q 5 -1D 1 The instantaneous SINR evolution with and without g(t) G in ~s(t) adaptation of the first stage is depicted in Fig. 3 along with the optimum values (in the sense of maximum SINR Fig. 2. First stage adaptation for frequency-non selective channels. using the true covariance matrices). It can be noted that 270 D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications

SINR Evolution 25 iii) Code Division Multiple Access (CDMA), the use of a different code (linearly independent and quasi- orthogonal) for each user, overlapping over the time 20 and frequency axes, and iv) Space Division Multiple Access (SDMA), where each user presents a different spatial signature. 15 In the same way, four kinds of diversity can be identi- ﬁed: 10 i) Time Diversity (TD), simple repetition of the signal SINR (dB) in different non-overlapping time slots, e.g., a single user in DS-CDMA or the spontaneous phenomenon 5 of multipath in frequency selective channels2 (efﬁ- ciently utilized by the RAKE receiver [24]),

0 ii) Frequency Diversity (FD), transmission of the same signal in different non-overlapping frequency bands, e.g., FDSS [25] and fast FH, −5 0 500 1000 1500 2000 2500 3000 3500 4000 iii) Code Diversity (CD), transmitting the same signal Iteration with different codes3 or spreading signatures (over- Fig. 3. Instantaneous SINR evolution of the Code Reference lapping over the time and frequency axes) [26], and Beamformer for FH system using frequency focussing. Scenario: iv) Space Diversity (SD), caused by the multipath phe- a desired signal with a DOA of 20◦ and two interfering users nomenon since each ray comes from a different di- ◦ ◦ with DOAs of −30 and 40 (all users GMSK signals with rection of arrival (this diversity can only be exploited / = Eb No 15 dB) received with an array of 4 sensors through a fre- at the receiver by the use of antenna arrays). quency non-selective mobile channel (v = 120 km/h). Dotted line: optimum value. Dash-dotted line: without adaptation of the first Clearly, when diversity is used for transmission of stage. Solid line: with adaptation of the first stage. a signal, the available power has to be distributed over the replicas. Self-replicas can be seen as embedded self-reference the adaptation of the first stage confers the ability to track signals that give rise to the important property of self- the channel variations. A frequency focussing process has prediction, i.e., some replicas of the signal can be pre- been used in both algorithms to reduce the SINR drops at dicted using other replicas [11]. This property has also hop instants. been called the self-coherence property, giving name to the Self-COherence REstoral algorithm (SCORE) [17], which was applied to cyclostationary signals. 3. Diversity-based beamforming for SS Let us assume that there are two available signals, u(t) and v(t), with a correlated desired signal component, d(t), and uncorrelated noise terms, n (t) and nv(t): Diversity-based beamforming combines the use of spatial u diversity at the receiver with other types of diversity inher- u(t) = αd(t) + nu(t), (5a) ent to the signal of interest or to the channel. v( ) = ( ) + ( ), Diversity is a concept closely related to multiplexing. t d t nv t (5b) It refers to the existence of replicas of the same signal, where α is the normalized cross-correlation coefficient be- providing the signal structure with an inherent redun- tween u(t) and v(t). These two signals exhibit the key dancy. Both terms can be lumped together into the more feature property of exact self-prediction. This means that general idea of combining a number of signals – either the it is possible to predict the desired component of one sig- same signal or different signals from different users – in nal using the other one. In other words, we can define such a way that it is always possible to separate them out a prediction error that will be composed only of uncor- again. The combination of these sets of signals or diversity related interference and noise. Therefore, this prediction branches can be done in any of the support axes, namely: error can be used as the objective function to minimize: time, frequency, code and space.1 In the context of multiplexing, these four axes give rise e(t) = u(t) − αv(t), (6) to four types of multiplexing techniques: i) Time Division Multiple Access (TDMA), the use of 2 Note that this diversity resulting from a repetition of time- non-overlapping time slots for each user, delayed replicas of a signal is also commonly referred to as fre- ii) Frequency Division Multiple Access (FDMA), the quency diversity or path diversity in the literature. The former use of non-overlapping frequency bands for each because in the frequency domain it presents a different fading for user, each frequency bin and the latter for obvious reasons. 3 It is important to distinguish the term Code Diversity (replicas of a signal using different spreading codes) from the concept 1 Other support axes could also be considered, such as the polar- of Code Reference (use of the code structure of the signal as ization axis. a reference). D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications 271

Chip Sequece where α is, in general, a complex constant. In the follow- Shaping Pulse ing, α = 1 is assumed (case of equal-power and phase- aligned replicas) for simplicity of presentation. γ i,0

ψ ( ) 0 t

γ 3.1 Frequency diversity beamforming for FDSS and i,1 t ψ ( ) fast FHSS 1 t Information Σ Transmitted The Frequency Diversity Spread Spectrum (FDSS) tech- Symbols Signal ... nique was proposed in 1996 [25] as a system to mitigate γ i,Ν−1 the problems of the common spread spectrum techniques, Channel Encoder ψ ( ) namely, vulnerability of Direct Sequence to bandlimited Ν−1 t partial-time (burst) jamming and of Frequency Hopping to partial-band interference. FDSS can be seen as a sim- ultaneous transmission of a signal over different non- Mapper overlapping frequency bands4 (see Fig. 4), providing the ith Block global signal structure with the previously described prop- Fig. 4. Scheme of FDSS signal generation. erty of exact prediction. A detailed comparison between FDSS and DS-CDMA can be found in [27]. A classical TRB can be used to perform a beamform- where u(t) and v(t) are the beamforming output signals ing at the receiver. Nevertheless, since the property of corresponding to snapshots of two different bands: u(t) = H ( ) v( ) = H ( ) exact prediction is clearly present in this particular SS wu xu t and t wv xv t . scheme, we can use a self-reference approach to perform Equation (7) can also be seen as the maximization of blind array processing without the need of side informa- the SINR: tion. In this signalling scheme, there are N available fre- Re {E {u(t)v∗(t)}} quency bands – diversity branches – that can be used. The = , SINR 2 (8) approach taken in [11] consists on using the exact pre- E |u(t) − v(t)| diction between just two diversity branches. Note that the interference is assumed uncorrelated between the selected which is equivalent to the maximization of the following bands, which can be guaranteed if different chip spread- Rayleigh quotient: ing is used on each band (see Fig. 4). The potential beneﬁt ∗ H H 2Re {E {u(t)v (t)}} w R vwv + wv Rv w of using the N diversity branches jointly is not taken into = u u u u , (9) 2 2 H + H account in the present paper (c.f. [28]). The underlying E |u(t)| + |v(t)| wu Ruuwu wv Rvvwv method is equivalent to the cross-SCORE algorithm [17], which yields exactly the same solution. = H where Rij E xixj . The eigenvectors that maximize Note that the beamforming method described here- the quotient of (9) are given by [11]: inafter is completely applicable to fast Frequency Hop- ping, which basically consists of a carrier hopping faster Ruvwv = λmaxRuuwu , (10a) than the symbol period. This can be seen as replicas of = λ , a signal transmitted at different frequency bins at consecu- Rvuwu maxRvvwv (10b) tive time slots. In the case of frequency diversity, since the snapshots and coincide with the solution given by the cross-SCORE of the two diversity branches correspond to different car- algorithm [17]. rier frequencies, which are assumed to undergo indepen- Note that in the covariance matrices of the denomi- dent fading, it is clear that different beamvectors have to natorof(9),Ruu and Rvv, all the signals present in the be used. Once the beamvectors for these two branches scenario appear; whereas the numerator only contains the have been designed, their output signal can be used as desired one, because it is the only correlated signal be- a reference for the rest of the bands using a time reference tween both branches. approach. An adaptive version of the algorithm, called cross- The algorithm is based on the minimization of the coupled LMS, can be found in [11, 29]. Note that an opti- prediction error – difference between the beamformer out- mal joint symbol detection, using the output signal of the puts – with a constraint to avoid the trivial solution: N bands, can be performed taking into account the effect of the beamforming [11]. min E |u(t) − v(t)|2 To test the described beamforming method, Monte- ∗ (7) Carlo simulations were carried out with a uniformly subject to Re {E {u(t)v (t)}} = φ , c spaced linear array of 7 sensors, using a half wavelength separation. The scenario was composed of a BPSK signal 4 The signal transmitted over each band is, in general, a (n,k) of interest (spread over a relative bandwidth of 50% with coded version of the original signal. The trivial repetition channel respect to fc = 900 MHz) with a DOA of 15 degrees and code (n,1) is considered here. 4 interfering BPSK signals present in all the bandwidth 272 D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications

BER of FDSS for Io/No per sensor = 37.495693 dB 0 10

(a)

−1 10

(b)

−2 10 BER

(c)

−3 10 u1 u2 v1 v2 u1 u2 v1 v2 u1 u2 v1 v2 Single antenna DIV TRB Theo -1 +1 -1 +1 -1 +1 −4 10 (d) −5 0 5 10 15 20 Eb/No per sensor (dB) Fig. 6. Example of Time Diversity in DS-CDMA: (a) original bit Fig. 5. BER for a receiver with an array of 7 elements of the sequence, (b) bit sequence interpreted as a diversity repetition code, classical TRB, the proposed diversity method and the minimum (c) spread bit sequence using a standard PN, and (d) spread bit theoretical BER (for the array and the single sensor case) using sequence using a fixed redundancy structure (redundant PN). FDSS. Scenario: desired signal with a DOA of 15◦ and 4 interfering signals with DOA’sof0◦, −30◦,50◦ and 80◦ with an / . instantaneous I0 N0 persensorof375dB. Nevertheless, in order to be able to have multiple users overlapping in time and frequency, they have to possess a redundancy structure more sophisticated than a simple (uncorrelated among the two selected bands) impinging repetition scheme. It is compulsory, therefore, to provide from angles of 0, −30, 50 and 80 degrees (Eb/N0 of the replicas with a specific pattern for each user, i.e., 30 dB, 20 dB, 40 dB and 20 dB) respectively, with a total a temporal signature or chip spreading code (see Fig. 6c). I0/N0 = 37.5, with I0 the global interference power per This way, it will be feasible to overlay users, giving rise to sensor. To model the angular spread of the steering vec- the well-known DS-CDMA technique. tors, a Laplacian Power Angular Spectrum with a power The direct application of the previously described al- azimuth spread of 8 degrees was used according to [23]. gorithm in the frequency diversity context consists of tak- The temporal dispersion of the channel was generated ing a couple of chips within one symbol – two temporal with a Pedestrian model as specified by ETSI [30] assum- branches – and use then the exact prediction property. It ing a speed of 3 km/h. is noteworthy that a unique beamvector w is needed in In Fig. 5, the Bit Error Rate (BER) of the proposed this case, because narrowband is assumed and the signals method can be seen compared to that of a classical TRB are considered to be stationary along a symbol period. It (10% as a training sequence) and to the minimum theor- is possible, however, to perform a much better estimation etical achievable BER – either using an array or a single of the desired signal covariance matrix Rd by exploiting antenna. Obviously, the TRB performance depends on the the prediction property among the multiple replicas. As- 2 − / percentage of the bits used as a training sequence. From suming that there are Nc chips per symbol, Nc Nc 2 the simulation results, it can be easily seen that the blind prediction error or cross-correlation terms can be used in- method performs similarly to a TRB with 10% training stead of just two [12], although not all of them will be sequence even though it needs no side information and linearly independent, but rather just (Nc − 1) [31]. therefore presents a higher spectral and bandwidth utiliza- To describe the algorithm, we first define a block tion. snapshot by grouping the snapshots columnwise within QxN a symbol period X(t)= [x1(t), x2(t), ··· , xNc(t)] ∈ C c , where Q is the number of sensors, Nc the number of chips 3.2 Time diversity beamforming for DS-CDMA per symbol (spreading factor), and xk the snapshot corresponding to branch k,defined as: The property of exact prediction can also be used in DS- √ √ NI CDMA communication systems by realizing how, within xk(t) = pdsd,k(t)ad + = pisi,k(t)ai + nk(t), i 1 (11) any symbol, each chip can be predicted from any other – 1 ≤ k ≤ N , assuming knowledge of the spreading code. c The straightforward parallelism of a signal replicated where NI is the number of interfering signals, sd,k(t) along the frequency axis would be a symbol repeated (si,k(t)) refers to desired (ith interfering) temporal signal along the time axis. Actually, a single symbol of dura- with power pd (pi)inbranchk, ad (ai) denotes the de- tion Ts can be interpreted as an implicit repetition of sired (ith interfering) steering vector, and nk(t) represents subsymbols – chips – of shorter period Tc (see Fig. 6a–b). the noise component of the snapshot in branch k. D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications 273

The first step consists of polarizing the block snap- ture within each symbol. This can be done by the use of shot so that the desired signal is fully correlated whereas a fixed redundancy matrix G applied on a PN-frame basis: neither the interferences nor the noise are (assuming long PN sequences, i.e., time-varying codes). This is achieved = T , by multiplying the block snapshot by the synchronized rpnq G pnq (17) spreading sequence of the desired user (PN synchroniza- N x1 tion is assumed), c(t) ∈ C c : ∈ CNx1 where the original PN frame, pnq ,istrans- formed into the redundant and longer PN frame, rpn ∈ Xpol(t) = X(t) · diag(c(t)) , (12) q CMx1, using the redundancy matrix, GT ∈ CMxN, with − where diag(v) is a diagonal square matrix containing vec- R (M N) the number of redundant chips. The redun- tor v along its main diagonal. dancy structure considered herein is simply the repetition In the polarized snapshots, the desired signal is of certain chips with a possible change of sign so that the fully correlated: s pol (t) = s (t), whereas the interfering finite alphabet is kept (as can be seen from Fig. 6d where d,k d the matrices used have been defined according to Fig. 7). { pol ( ) pol,∗( )}=δ δ users still remain uncorrelated: E si,k t sj,l t ij kl , The redundancy matrix has to be properly designed so that which can be guaranteed due to the time-varying nature the desired auto- and cross-correlation properties of the of the spreading codes. Since the desired signal is the original PN sequences are not destroyed (see [31] for de- only one correlated among the time branches, Rd and tails). Furthermore, if different users have to coexist, the Rx(received signal covariance matrix) can be estimated redundancy structures for all of them have to be jointly de- as [12]: signed so that each presents a zero cross-correlation with respect to any other user’s structure. To this end, exten- Nc Nc = 1 pol( ) pol,H ( ) sive search methods have to be used and, therefore, small Rd E xl t xm t (13) values of R are easier to handle (c.f. [31]). Nc(Nc − 1) l=1 m=1 m=l The receiver will make use of a parity check matrix, MxR Rx1 H ∈ C to define an error eq ∈ C : Nc = 1 pol( ) pol,H ( ) , Rx E xk t xk t (14) Nc = = T = T − T = − , k 1 eq H yq Hu Hv yq uq vq (18) which can be compactly expressed as ∈ CMx1 where yq contains the desired modulated RPN sig- , 1 pol pol H nal plus noise and interferences (defined on a frame basis). Rd = E X (t)IX˜ (t) , (15) Nc(Nc − 1) The matrices Hu and Hv can be seen as matrices that ex- tract two different sets of diversity elements, u and v, from 1 pol pol,H . Rx = E X (t)X (t) , (16) the redundant vector, y (see Fig. 7) Note that the previ- Nc ously described method using the implicit redundancy of spreading codes is a particular case of this general scheme where the matrix I˜ ∈ CNcxNc is defined as I˜ = 1 − I,being with the specific redundancy matrix G = I (with no ex- 1 the all-one matrix and I the identity matrix. The final plicit redundancy, i.e., R = 0andM= N). formulas for the estimation of the desired and total co- In the same way as for the frequency diversity scheme, variance matrices (15) and (16), which have been derived the beamforming algorithm for time diversity is based on from a viewpoint of chip-level cross-correlation properties the maximization of the SINR: using the key feature of exact prediction, are equivalent to those found by Suard et al. in [7] from a matched filtering Re E uT v∗ perspective. SINR = q q , (19) Nevertheless, this method based on exact prediction E e 2 properties requires time signature or PN synchronization. q In some adverse situations, spatial filtering is needed before complete synchronization is achieved, so that beamforming helps the synchronization stage. For these cases,  1 0 0 0 0 0   1 0 0 0 0 0 0 0 it is necessary to devise an alternative diversity scheme  0 1 0 0 0 0 +7 = X   able to work without global PN synchronization. −1 0 0 0 0 0 0 1 0 0 0 0 0 0   The alternative scheme proposed in [13] works by in- 0 0 −1 0 0 0 0 0 7  0 0 1 0 0 0 +7 = * = Y   troducing an explicit fixed redundancy structure over the  0 0 0 1 0 0 0 0 0 0 0 0 0 1   time-varying spreading codes – long PN sequences – con-  0 0 0 0 1 0   tained in each symbol. Therefore, only symbol timing is 0 0 0 0 0 1 +7*7 = needed ( a requirement far more relaxed than the global    0 1 0 0 0 0 long PN sequence synchronization needed in the previ-   ous method). The underlying idea consists of generating Fig. 7. Example of redundancy and check-parity matrices G a modified PN sequence so that it presents a fixed struc- and H. 274 D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications

BER of DS−CDMA with Io/No per sensor = 25.580297 dB 0 which is equivalent to the maximization of the following 10 Rayleigh quotient: T ∗ H 2Re E uq vq w (Ruv + Rvu) w −1 = , (20) 10 2 2 wH (R + Rvv) w E uq + vq uu = H H where R E X H H X and X is a block snap- −2 ij q i j q q 10 shot matrix containing the snapshots of the whole frame BER columnwise. Note that only the desired signal is present in the nu-

−3 merator of (20) because it is the only correlated signal in 10 both branches (recall that, for this to be true, the G’sof Single antenna RPN all the users must be jointly designed to present a zero TRB PN cross-correlation with respect to any other user struc- Theo

−4 ture [31]). The denominator of (20) contains all the signals 10 −5 0 5 10 15 20 present in the scenario. Thus, the desired and global co- Eb/No per sensor (dB) variance matrices can be deﬁned as Rd ∝ (Ruv + Rvu) and Fig. 8. Uncoded BER of the different methods (TRB+DD using R ∝ (R + Rvv). x uu 10% as training sequence, PN-based, RPN-based) along with the Once the matrices Rd and Rx have been estimated, ei- theoretical minimum BER – for the array and the single antenna ther using the implicit or explicit redundancy structure, case. The scenario was involved of a desired signal with DOA of the beamvector that maximizes the SINR is given by the 15◦ and 4 interfering signals with DOA’sof0◦, −30◦,50◦ and 80◦ generalized eigenvector w corresponding to the maximum (Eb/No of 30 dB, 20 dB, 40 dB and 20 dB) respectively. Nc = 1023 generalized eigenvalue: and SF = 31.

Rdw = λmaxRxw , (21) based method is clearly inferior to those two methods. The = /(λ−1 − ) yielding SINRmax 1 max 1 . Adaptive implementa- difference of performance between the PN and RPN based tions of the computationally expensive calculation of the methods is due to the number of cross-correlation terms generalized eigenvector can be found in [10, 13]. per symbol used (R = 2 for RPN vs. 465 (30 indepen- To evaluate and compare the methods presented using dent) for PN); it has to be remembered, however, that the the implicit and explicit redundancy, Monte-Carlo sim- RPN approach allows beamforming before global PN syn- ulations were performed with a uniformly spaced linear chronization. It can be concluded from the results that the array of 7 sensors, using a separation of half wavelength. choice of the algorithms has to be based on a trade-off be- A simple and suboptimum single-user detector consisting tween performance and the amount of side information to of a matched filter was used after beamforming. The sce- be transmitted – with the consequent reduction of spectral nario involved was a BPSK signal of interest with a DOA efficiency and bandwidth utilization. of 15 degrees and 4 interfering BPSK signals impinging from angles of 0, −30, 50 and 80 degrees (Eb/No of 30 dB, 20 dB, 40 dB and 20 dB) respectively, with a total 4. Conclusions I0/N0 = 25.6, with I0 the global chip-level interference power per sensor. Gold sequences of length Nc = 1023 and SF = 31 were utilized (for the RPN case, R = 2was In this paper, three blind spatial diversity array signal used). To model the angular spread of the steering vectors, processing methods for Spread Spectrum (SS) techniques a Laplacian Power Angular Spectrum with a power az- have been described. Each method was specifically de- imuth spread of 8 degrees was used according to [23]. The signed for a particular SS signalling scheme. temporal dispersion of the channel was generated with The Code Reference Beamformer using anticipative a Pedestrian model as specified by ETSI [30] with a speed processing was derived for slow FHSS to maximize the of 3 km/h. SINR. Its performance was shown via simulations in In Fig. 8, the performance of the proposed methods a non-stationary environment. It was able to track the sce- is shown in terms of BER. The uncoded BERs for both nario in an adaptive fashion, with a performance, in terms the implicit (PN-based) and explicit (RPN-based) time- of SINR, quite close to the optimum theoretical value. redundancy methods, for the classical TRB (10% as This self-reference beamforming method appears to be the a training sequence) aided with a decision directed (DD) best alternative for array signal processing applied to slow approach during the data transmission, and the mini- FHSS. mum theoretical BER – for both the array and single Two diversity-based beamforming algorithms were antenna case – are depicted. It can be seen how the PN- described for the frequency and time axes and were de- based method outperforms the TRB and is just about rived under a common framework of redundancy proper- 1 dB worse than the theoretical minimum BER. The RPN- ties. They were shown to yield maximum SINR and were D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications 275 compared via simulations to the classical TRB. These [10] Najar,´ M.; Mestre, X.; Lagunas, M. A.: Two-stage code ref- self-reference beamformers, despite the lack of side infor- erence beamformer for the reception of frequency hopping mation, achieved a performance quite similar to TRB. For modulated signals. Accepted at Eurasip Signal Processing. FDSS, the described self-reference method seems to be [11] Lagunas, M. A.; Perez-Neira,´ A. I.; Amin, M. G.; Vidal, J.: the best choice to perform beamforming at the receiver. Spatial processing for frequency diversity schemes. IEEE For DS-CDMA, however, there is a wide range of avail- Trans. Signal Processing 48 (Feb. 2000), 353–362. [12] Palomar, D. P.; Lagunas, M. A.: Self-reference beamform- able algorithms in the literature and the presented self- ing for DS-CDMA communication systems. Proc. IEEE reference method is simply a blind alternative; a choice of ICASSP-2000, Istanbul (Turkey), June 5-9, 2000, Vol. V, algorithm would depend on a trade-off between perform- 3001–3004. ance and amount of side information. [13] Perez-Palomar,´ D.; Lagunas, M. A.: Blind beamforming for The beamforming methods presented herein are based DS-CDMA systems. Proc. Fifth Bayona Workshop on on structural inherent properties of the signals and do not Emerging Technologies in Telecomm. (Sept. 1999), 83–87. need any external reference or side information; there- [14] Pope, K. J.; Bogner, R. E.: Blind signal separation. I. Lin- fore, they present a good spectral efficiency and channel ear, instantaneous combinations. Digital Signal Processing 6 bandwidth utilization. They do not make any assumption (January 1996), 5–16. regarding the steering vectors or spatial signatures of the [15] Lathauwer, L. D.; Moor, B. D.; Vandewalle, J.: Independent component analysis based on higher-order statistics only. signals and, consequently, they are robust and do not re- Proc. IEEE Signal Processing Workshop on Statistical Signal quire array calibration. Array Processing (1996), 356–359. [16] Gönen, E.; Mendel, J. M.: Applications of cumulants to array processing-part III: Blind beamforming for coherent signals. IEEE Trans. Signal Processing 45 (September 1997), 2252– Acknowledgement 2264. [17] Agee, B. G.; Schell, S. V.; Gardner, W. A.: Spectral self- The authors wish to thank Dana Brooks and the anonymous re- coherence restoral: A new approach to blind adaptive signal viewers for their helpful comments on the manuscript. extraction using antenna arrays. Proceedings of the IEEE 78 (April 1990), 753–767. [18] Acar, L.; Compton, R. T.: The performance of an LMS adaptive arraywithfrequencyhoppedsignals.IEEETrans.onAerospace References and Electronic Systems AES-21 (May 1985), 360–371. [19] Bakhru, K.; Torrieri, D. J.: The maximin algorithm for adap- [1] Goldberg, J.; Pagès, A.; Lagunas, M. A.; Fonollosa, J.; tive arrays and frequency-hopping communications. IEEE Vazquez,´ G.: Experimental results for an SDMA mobile Trans. on Antennas and Propagation AP-32 (September communications antenna array system. Proceedings of 1984), 919–928. the Int. Symp. on Signal Processing and its Applications [20] Torrieri, D. J.; Bakhru, K.: Frequency compensation an adap- ISSPA’96 (August 1996), 455–458. tive antenna system for frequency-hopping communications. [2] Treichler, J. R.; Larimore, M. G.: New processing techniques IEEE Trans. on Aerospace and Electronic Systems AES-23 based on the constant modulus adaptive algorithm. IEEE (July 1987), 448–467. Trans. on Acoustics, Speech and Signal Processing ASSP-33 [21] Torrieri, D. J.; Bakhru, K.: An anticipative adaptive array (April 1985), 420–431. for frequency-hopping communications. IEEE Trans. on [3] Gooch, R.; Lundell, J.: The CM array: an adaptive beam- Aerospace and Electronic Systems AES-24 (July 1988), former for constant modulus signals. Proc. IEEE ICASSP’86 449–456. (1986), 2523–2526. [22] Eken, F.: Use of antenna nulling with frequency-hopping [4] Swindlehurst, A. L.; Daas, S.; Yang, J.: Analysis of a decision against the follower jammer. IEEE Trans. on Antennas and directed beamformer. IEEE Trans. on Signal Processing 43 Propagation AP-39 (September 1991), 1391–1397. (December 1995), 2920–2927. [23] Pedersen, K. I.; Mogensen, P. E.; Fleury, B. H.: A stochas- [5] Viberg, M.: Sensor array processing using gated signals. tic model of the temporal and azimuthal dispersion seen at IEEE Trans. on Acoustic, Speech and Signal Processing the base station in outdoor propagation environments. IEEE ASSP-37 (March 1989), pp. 447–450. Trans. on Vehicular Technology, Accepted: to appear in the [6] Souloumiac, A.: Blind source detection and separation using May 2000 issue. second order non-stationarity. Proceeding of the IEEE Int. [24] Proakis, J. G.: Digital communications. 3rd ed. McGraw-Hill, Conf. on Acoustic, Speech and Signal Processing ICASSP- 1995. 95 (May 1995), 1912–1915. [25] Kaleh, G. K.: Frequency-diversity spread-spectrum commu- [7] Suard, B.; Naguib, A. F.; Xu, G.; Paulraj, A.: Performance nication system to counter bandlimited gaussian interference. of CDMA mobile communication systems using antenna ar- IEEE Trans. on Comm. 44 (July 1996), 886–893. rays. Proc. IEEE Int. Conf. on Acoustic, Speech and Signal [26] Weerackody, V.: Diversity for the direct-sequence spread Processing ICASSP-93 (April 1993), IV153–IV156. spectrum system using multiple transmit antennas. Proc. [8] Najar,´ M.: Conformador de haz de referencia por codigo´ de ICC’93, Geneva, Switzerland, May 1993. 1775–1779. dos etapas: aplicacion´ a la recepcion´ de señales con mod- [27] Papproth, E.; Kaleh, G.: A CDMA overlay system using ulacion´ de saltos frecuenciales. Dissertation. Polytechnic frequency-diversity spread spectrum. IEEE Trans. on Vehic- University of Catalonia (UPC), October 1996. ular Technology 48 (March 1999), 397–404. [9] Mestre, X.; Najar,´ M.; Lagunas, M. A.: Two-stage code refer- [28] Palomar, D. P.; Lagunas, M. A.: Optimum self-reference spa- ence beamformer in mobile communications. Proceedings of tial diversity processing for FDSS and FH communication the IEEE Int. Conf. on Acoustic, Speech and Signal Process- systems. Proc. EUSIPCO-2000, Tampere, Finland, Sept. 5-8, ing ICASSP-98 (May 1998), 3309–3312. 2000. 276 D. Perez-Palomar,´ M. Najar,´ M. A. Lagunas: Self-reference Spatial Diversity Processing for Spread Spectrum Communications

[29] Lagunas, M. A.; Perez-Neira,´ A. I.: Cross-coupled LMS for Montse N´ajar received the Electrical quadratic constrained ﬁlter design. ICECS’99, Cyprus, Sept. Engineering degree and the Ph. D. from 5-9, 1999. 839–842. the Polytechnic University of Catalonia [30] ETSI: Selection Procedures for the Choice of Radio Trans- (UPC), Barcelona, Spain, in 1991 and mission Technologies of the UMTS (UMTS 30.03). Tech. 1996, respectively. Since 1997 she is an Rep. TR101 112, v3.2.0,ETSI (1998). Associate Professor at the Polytechnic [31] Perez-Palomar,´ D.; Lagunas, M. A.: Temporal diversity on University of Catalonia, Barcelona, Spain, DS-CDMA communication systems for blind array signal where she teaches undergraduate courses processing. Submitted to Eurasip Signal Processing (2000). in Analog and Digital Communications and graduate courses in Digital Signal Processing. Her current research interests include Mobile Communication Systems, Space Division Multiple Access (SDMA) and Blind Multiuser Detection.

Miguel Angel Lagunas was born in Madrid 1951. Telecommunications En- gineer in 1973 (UPM Madrid), Ph. D. Telecom. (UPB Barcelona). From 71–73 was research assistant at the Semiconduc- tor Lab. (ETSIT, Madrid), 73–79 teacher assistant in Network Synthesis and Semi- conductor Electronics, 79–82 Associate professor on digital signal processing, Daniel P´erez-Palomar was born in since 1983 full professor teaching courses Barcelona, Spain, on April 1975. In 1998, in signal processing, array processing and he received a degree in Telecommunica- digital communications. 81–82 Fullbright post-doc grant Univer- tions Engineering from the Polytechnic sity of Boulder (Colorado). Project leader of high speed SCMA University of Catalonia (UPC), Barcelona, (87–89) and ATM (94–95) cable network. Co-director of the ﬁrst Spain. During 1998 he stayed with the projects for the European Spatial Agency and the European Union Signals and Systems Research Group of providing engineering demonstration models on smart antennas for the Department of Electronic Engineer- satellite communications using DS and FH systems (86) and mo- ing at King’s College London. He joined, bile communications GSM (Tsunami, 94). 86–89 Vice-president afterwards, the Communication Signal for Research (UPC), 95–96 Vice-Secretary General for Research Processing Group of the Department of (Cicyt-Spain). Fellow Member 1997. Member at large of Eurasip Signal Theory and Communications at the Polytechnic University (90). Elected member of the Academy of Engineers of Spain (98). of Catalonia (UPC), where he is currently working on his Ph.D. as His research activity is devoted to spectral estimation, adaptive a Research Assistant. His primary research interests include array systems and array processing. His technical activities are in ad- signal processing, multiuser detection, communication over MIMO vanced front-ends for digital communications combining spatial channels, spread spectrum techniques and fuzzy logic systems. with frequency-time and coding diversity.