AN overview of code division multiple access (CDMA)

Transcription

1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER Wideband CDMA Network Sensitivity Function Savo Glisic, Senior Member, IEEE and Pekka Pirinen, Student Member, IEEE Abstract In this paper, we analyze capacity losses in code division multiple access (CDMA) networks due to imperfections in the operation of the system components. The main result of this work is a systematic mathematical framework for capacity evaluation of CDMA-based networks in fading channels. This should be considered as an alternative tool to extensive simulations being used for these purposes at the moment. The intention is to provide simple approximate relations that simultaneously take into account: multiple access intracell interference (MAI), intercell interference, and near far effect, including different sources of power control imperfections. In addition to this, the efficiencies of the major receiver components are also included in the analysis. A flexible complex signal format is used which enables us to model all currently interesting proposals for wideband CDMA (W-CDMA) standards. The theory is general, and some examples of practical set of channel and system parameters are used as illustration. Further elaboration of these results, including extensive numerical analysis based on the offered analytical framework, would provide enough background for the understanding of W-CDMA system performance in a realistic environment. Index Terms Code division multiple access (CDMA), diversity methods, fading channels, interference suppression, modeling, multiuser channels, nonlinear estimation, sensitivity. I. INTRODUCTION AN overview of code division multiple access (CDMA) can be found in [1] [3]. The CDMA capacity analysis is covered in a number of papers [4] [14]. Gilhousen et al. [4] motivated many researchers to simulate CDMA systems. Their analysis includes voice activity monitoring, sectorization (three sectors), perfect uplink power control, and Gaussian approximation for multiple access interference statistics. The effect of imperfect power control on CDMA capacity has been studied in a number of papers [15] [25]. The conclusion of those references is that CDMA network capacity decreases rapidly as a function of power control error. Power control error is usually modeled as a log-normal random variable. Proper choice of signal propagation parameters is important for studying CDMA network capacity. In general, they can be divided into propagation losses, slow fading (shadowing), and fast fading. Path losses depend on the environment and cell type. Average attenuation grows as a power law of distance. A path loss exponent of four is widely used in the literature. A shadowing effect is usually analyzed at the system level, and the standard model assumes log-normal distribution. Fast fading can be taken into account at the link level as a Manuscript received October 15, 1998; revised February 25, The authors are with the University of Oulu, Telecommunication Laboratory, Oulu FIN Finland ( savo.glisic@ee.oulu.fi; pekka.pirinen@ee.oulu.fi). Publisher Item Identifier S (99) required signal-to-noise ratio (SNR) for the predefined qualityof-service (QoS). The stronger the fading, the more SNR is required for a given required bit-error rate (BER). Influence of these propagation parameters is discussed, e.g., in [25]. The effects of user mobility on the CDMA capacity have been studied in [26]. In that work, the results are based on simulations that take into account shadowing, call statistics, voice activity, cell sectorization, and user mobility. Perfect power control and ideal antenna directivity are assumed. The presented concepts are general, and they can be applied for any asynchronous CDMA cellular networks. Discussion of Erlang capacity in a power-controlled CDMA system is presented in [27]. Similar capacity gains, as reported in [4], are expected in the Erlang capacity as well. Reverse link Erlang capacity under nonuniform cell loading is reported in [28]. The effects of adaptive base station antenna arrays on CDMA capacity have been studied, e.g., in [24], [29], and [30]. The results show that significant capacity gains can be achieved with quite simple techniques. Additional analysis of the outage probability in cellular CDMA is presented in [31] and [32]. Both Nakagami and Rician fadings coupled with log-normal shadowing have been taken into account in the propagation model. Additionally, the voice activity factor is included in [31]. The effects of more sophisticated receiver structures [like multiuser detectors (MUD) or joint detectors] on CDMA or hybrid system capacity have been examined in [33] [37]. Results of [33] show roughly a two-fold increase in capacity, with MUD efficiency equal to 65% compared to conventional receivers. The effect of the fractional cell load on the coverage of the system is presented in [34]. The coverage of MUD- CDMA uplink was less effected by the variation in cell loading than in conventional systems. In [35] and [36], a CDMA system is described joint detection data estimation is used with coherent receiver antenna diversity. This system can be used as a hybrid multiple access scheme with time-division multiple access (TDMA) and frequency-division multiple access (FDMA) components. In [37], significant capacity gains are reported when zero-forcing multiuser detectors are used instead of conventional single-user receivers. In most of the references, it has been assumed that the service of interest is low rate speech. In next generation systems, however, mixed services including high rate data have to be taken into account. This has been done in [38], the performance of an integrated voice/data system is presented. In general, from the literature survey we have presented, it can be seen that capacity evaluation of CDMA networks and comparison of CDMA and TDMA systems has been an important and controversial issue. One of the reasons for such a situation is the lack of a systematic easy-to-follow /99$ IEEE

2 1782 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 mathematical framework for this evaluation. The situation is complicated by the fact that many parameters are involved, and some of the system components are rather complex, resulting into an imperfect operation. The analysis of an advanced CDMA network should in general take all these elements into account, including their imperfections, and come up with an expression for the system capacity in a form that can be used in practice. In this paper, we present such an analysis. The paper is organized as follows. In Section II, a system model is presented. A general framework for capacity evaluation of advanced CDMA networks and performance analysis is presented in Section III. Some numerical results, as illustrations, are presented in Section IV. The results and methodology presented in this paper offer enough tools and data for the careful choice of the system parameters in realistic environments, which are characterized by imperfections. Finally, concluding remarks are presented in Section V. II. SYSTEM MODEL The complex envelope of the signal transmitted by user in the th symbol interval is is the transmitted signal amplitude of user is the signal delay, is the transmitted signal carrier phase, and can be represented as (1) is the number of multipath components of the channel, is the complex coefficient (gain) of the th path of user at symbol interval with index, is the delay of the th path component of user in symbol interval, and is the Dirac delta function. We assume that is the delay spread of the channel. In what follows, indexes will be dropped whenever this does not produce any ambiguity. It is also assumed that. The overall received signal during symbol intervals can be represented as,,, is the frequency downconversion phase error, is a complex zero mean additive white Gaussian noise (AWGN) process with two-sided power spectral density, and is the carrier frequency. The complex matched filter of user will create two correlation functions for each path (4) (2a) (2b) (2c) (2d) (5) (2e) is the estimate of and In (2), and are two information bits in the - and - channel, respectively, is the bit pulse shape, and is the bit offset in the -channel. Parameters and are the th chips of the th user PN codes in the - and -channel, respectively, is the chip shape, and is the chip offset. In practical applications, and will have values either zero or 1/2. Equations (1) and (2) are general, and different combinations of the signal parameters cover most of the signal formats of practical interest. The channel impulse responses consist of discrete multipath components represented as and (6) (7a) (3a) (3b) (7b)

3 GLISIC AND PIRINEN: WIDEBAND CDMA NETWORK SENSITIVITY FUNCTION 1783 are cross correlation functions between the corresponding code components and. Each of these components is defined with three indexes. Parameter and are defined with two indexes. Let the vectors of MF output samples for the th symbol interval be defined as The vector (8d) can be expressed as [39] C C C (8a) (8b) (8c) (8d) (12) (13) C (8e) is a diagonal matrix of transmitted amplitudes Let, in general, correlation matrix with the following partition be a cross is the matrix of channel coefficient vectors C (14) C (15a) (15b) We now define four specific matrices of the form given by (9) with the following notation (9) is the vector of the transmitted data, and C is the output vector due to noise. It is easy to show that, and, is an all-zero matrix of size. Thus, the concatenation vector of the matched filter outputs (8e) has the expression (10a) (10b) R H A d RHAd RHh (16) (10c) (10d) R matrices have elements H C (17a) (11a) A d (17b) (17c) (17d) (11b) (11c) h Ad is the data-amplitude product vector, and is the Gaussian noise output vector with zero mean and covariance matrix R. If we define R ii H A d i (18a) R qi H A d q (18b) (11d) R iq H A d i (18c) R qq H A d q (18d)

4 1784 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 then we have (19a) (19b) III. PERFORMANCE ANALYSIS: CDMA SYSTEM CAPACITY The starting point in the evaluation of CDMA system capacity is the parameter, the received signal energy per symbol per overall noise density in a given reference receiver with index. For the purpose of this analysis, we can represent this parameter in general case as (20),, and are power densities of intracell, intercell, and overlay type internetwork interference, respectively, and is thermal noise power density. is the overall received power of the useful signal, and is the information bit interval. Contributions of and to have been discussed in a number of papers [4] [14]. In order to minimize repetition in our analysis, we will parameterize this contribution by introducing (21) In the sequel, we will concentrate on the analysis of the intracell interference in CDMA networks based on advanced receivers using imperfect rake and MAI cancellation. A general block diagram of the receiver is shown in Fig. 1. An extension of the analysis, to both intercell and internetwork interference, is straightforward. A. Multipath Channel: Near Far Effect and Power Control We start with the rejection combiner, which will choose the first multipath signal component and reject (suppress) the others. In this case, (20) for the -channel becomes (22) (shown at the bottom of the page), (for,,, and ) is the power coefficient defined as, is the normalized power level of the received signal, and parameters are in general defined by (5) and (19). stands for averaging with respect to corresponding phases defined by (7). Based on this we have (23) Fig. 1. General receiver block diagram. and normalization A similar equation can be obtained for the -channel too. It has been assumed that all interference-per-path components are independent. In what follows, we will simplify the notation by dropping all indexes so that. With no power control ( ) will depend only on the channel characteristics. In partial power control ( ) only the first multipath component of the signal is measured and used in the power control (open or closed) loop. Full power control ( ) will normalize all components of the received signal and rake power control ( ) will normalize only those components combined in the rake receiver. The ( ) control seems to be more feasible because these components are already available. These concepts for ideal operation are defined by the following equations: (24a) (24b) (24c) (24d) is the number of fingers in the rake receiver. The contemporary theory in this field does not recognize these (22)

5 GLISIC AND PIRINEN: WIDEBAND CDMA NETWORK SENSITIVITY FUNCTION 1785 options, which causes a lot of misunderstanding and misconceptions in the interpretation of the power control problem in the CDMA network. Although is not practically feasible, the analysis including should provide the reference results for the comparison with other, less efficient options. Another problem in the interpretation of the results in the analysis of the power control imperfections is caused by the assumption that all users in the network have the same problem with power control. Hence, the imperfect power control is characterized with the same variance of the power control error. This is more than a pessimistic assumption and yet it has been used very often in analyzes published so far. If we now introduce matrix with coefficients, except for and use notation for the vector of all ones, (22) becomes (25) Compared with (22), the index is dropped in order to indicate that the same form of equation is valid for both, the - and -channels defined by (19). with. Parameter is the carrier phase synchronization error in receiver for the signal of user in path. We will drop index whenever it does not result into any ambiguity. In the sequel, we will use the following notation:, is the estimation of by the receiver, is the relative amplitude estimation error, BER that can be represented as BER (30) and is the carrier phase estimation error. For the equal gain combiner (EGC), the combiner coefficients are given as. Having in mind the notation used so far, in the sequel, we will drop index for simplicity. For the maximal ratio combiner (MRC), the combiner coefficients are based on estimates as (31a) (31b) B. Multipath Channel: Rake Receiver and Interference Cancelling If -fingers rake receiver with combiner coefficients and an interference canceller are used, the SNR will become Averaging (29) gives for EGC (31c) (26) (27) is due to Gaussian noise processing in the rake receiver, and the noise density becomes, due to additional signal processing. Also, we have For MRC, the same relation becomes (32) (28) with being a matrix of size with coefficients, except for, and is efficiency of the canceller. The parameter in (26) called rake receiver efficiency is given as (29) (33) In order to evaluate the first term, we use limits. For the upper limit we have By using this we have (34) (35)

6 1786 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 and the first term becomes [40] For the lower limit we use and the first term becomes (36) (37) (38) For a signal with - and -components, the parameter should be replaced by (39) is the information in the interfering channel ( or ), and is the cross correlation between the codes used in the - and -channels. For small tracking errors, this term can be replaced by (40) for a single signal component and (41b) (41c) for a complex ( and ) signal structure. In a given receiver, components and correspond to and. Parameter includes both amplitude and correlation functions. In (41a), and are amplitude and phase estimation errors. The canceller will create, and the power of this residual error (with index dropped for simplicity) would be (42) stands for averaging with respect to and. Parameter corresponds to. This can be represented as (43) the notation is further simplified by dropping the subscript. By using (40) in (31) (39), similar expressions can be derived for the complex signal format. From this equation, we have (44) C. Interference Canceller Modeling: Nonlinear Multiuser Detectors For the system performance evaluation, a model for the canceller efficiency is needed. Linear multiuser structures might not be of much interest in the next generation of mobile communication systems, the use of long codes will be attractive. An alternative approach is nonlinear (multistage) multiuser detection that would include channel estimation parameters too. This would be based on interference estimation and cancellation schemes (OKI standard-is-665/itu recommendation M.1073 or UMTS proposal recently defined by ETSI) [41], [42]. In general, if the estimates of (19) are denoted as and, then the residual interference after cancellation can be expressed as and By expanding as and averaging gives For zero mean (45) (46) (47) is the carrier phase tracking error variance. For the complex ( and ) signal structure, cancellation efficiencies in the - and -channels can be represented as (19c) index spans all combinations of and.by using (19c), each component in (28) can be obtained as a corresponding entry of. To further elaborate these components, we will use a simplified notation and analysis. After frequency downconversion and despreading, the signal from user received through path at the receiver would have the form (41a) (48a) (48b) So, in this case, the canceller efficiency is expressed in terms of amplitude, phase, and data estimation errors. These results should be now used for analysis of the impact of the large scale of channel estimators on overall CDMA network sensitivity. The performance measure of any estimator is the parameter estimation error variance that should be directly used in (48) for the cancellation efficiency and (31) (40)

7 GLISIC AND PIRINEN: WIDEBAND CDMA NETWORK SENSITIVITY FUNCTION 1787 for the rake receiver. If joint parameter estimation is used based on ML criterion, then the Cramer Rao bound could be used for these purposes. For the Kalman type estimator, the error covariance matrix is available for each iteration of estimation. If each parameter is estimated independently, then for carrier phase and code delay estimation errors, a simple relation SNR can be used SNR is the SNR in the tracking loop. For the evaluation of this SNR, the noise power is in general given as. For this case, the noise density is approximated as a ratio of the overall interference plus noise power divided by the signal bandwidth. The loop bandwidth will be proportional to is the fading rate (Doppler). The higher the, the higher the loop noise bandwidth, the higher the equivalent noise power. If interference cancellation is performed prior to the parameter estimation, is obtained from, defined by (28). If parameter estimation is done without interference cancellation, the same is used with. In addition to this E. Outage Probability The previous section completely defined the simulation scenario for the system performance analysis. For the numerical analysis, further assumptions and specifications are necessary. First of all, we need the channel model. The exponential multipath intensity profile (MIP) is a widely used analytical model realized as a tapped delay line [46]. It is very flexible in modeling different propagation scenarios. The decay of the profile and the number of taps in the model can vary. Averaged power coefficients in the multipath intensity profile are (53) is the decay parameter of the profile. Power coefficients should be normalized as (54) [43] (49a) is the code delay estimation error, and. For noncoherent estimation we have For, the profile will be flat. The number of resolvable paths depends on the channel chip rate, and this must be taken into account. We will start from (26) and look for the average system performance for, is the system processing gain, and is the system bandwidth (chip rate). The average SNR will be expressed as (55) (49b) and are the zeroth and first order Bessel functions, respectively, and is the SNR. Now, if we accept some quality of transmission, BER, that can be achieved with the given SNR, then with the equivalent average interference density, the SNR will be D. Approximations If we assume that channel estimation is perfect, the parameter becomes (50) for DPSK modulation, is the SNR, and for CPSK. So, we have To evaluate the outage probability [4] BER MAI (56), we need to evaluate for DPSK (51) for CPSK (52) For large,, and for small, in a DPSK system, we have and. This can be presented as, is given by (26). Bearing in mind that depends on, the whole equation can be solved through an iterative procedure starting up with an initial value of,. Similar approximations can be obtained for and. From a practical point of view, an attractive solution could be a scheme that would estimate and cancel only the strongest interference (e.g., successive interference cancellation schemes [44], [45]). is given as MAI MAI (57) (58) It can be shown that this outage probability can be represented by the Gaussian integral (59)

8 1788 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 Fig. 2. Capacity (K 0 ) versus the number of rake fingers for EGC ( =0:25). and are the mean value and the standard deviation, respectively, of the overall interference. From (55), we have for the system capacity with ideal system components (60) Due to imperfections in the operation of the rake receiver and interference canceller, this capacity will be reduced to (61) and are now replaced by real parameters and that take into account those imperfections. The system sensitivity function is defined as IV. NUMERICAL EXAMPLES (62) (63) (64) In this section, we present some numerical results for illustration purposes. The results are obtained for a channel with exponential multipath delay profile with decay factor. The number of paths is. The system parameters are chosen from UMTS recommendation: processing gain (24 db), the required SNR has been set to (3 db), bit rate kbit/s, and chip rate Mchips/s. BPSK modulation is assumed. For all illustrations, the maximum SNR in the first rake finger with perfect intracell interference cancellation is normalized to 3.2 (5 db). Parameter estimation is made before interference cancellation (worst case). Cancelling efficiency for maximum capacity is calculated according to (52). When estimation errors are included, cancelling efficiencies follow (46). Carrier phase tracking error variance is assumed to be SNR. For MRC, the amplitude estimation error is approximated from (49b) to follow SNR. In Fig. 2, we present network capacity (61) versus the number of rake fingers for the EGC and. One can see that for the number of fingers, the capacity starts to decrease due to imperfections in the parameter estimation. The situation is more critical if the fading rate is higher. The same parameter for is presented in Fig. 3. The signal component in each finger is now stronger so that there will be a constant increase in capacity if the number of fingers is increased. Once again, the capacity is lower if the fading rate is higher. In the case of MRC, capacity versus the number of rake fingers for is shown in Fig. 4. Like in Fig. 2, the capacity decreases with due to parameter estimation errors, but this is much less critical than in the case of EGC. The same parameter for is shown in Fig. 5. Like in Fig. 3, the signal component in each finger is now stronger so that there will be constant increase in capacity if the number of fingers is increased. Also, like in Fig. 3, the capacity is lower if the fading rate is higher.

9 GLISIC AND PIRINEN: WIDEBAND CDMA NETWORK SENSITIVITY FUNCTION 1789 Fig. 3. Capacity (K 0 ) versus the number of rake fingers for EGC ( =0). In Fig. 6, we present CDMA network sensitivity function versus the number of rake fingers for EGC and. For larger, the sensitivity (percentage of lost capacity) is increased due to imperfections in the parameter estimation process. The situation is more critical for faster fading. The same parameter for is presented in Fig. 7. The network becomes now more sensitive when increases due to the weaker signal components in rake fingers with higher indexes. In the case of MRC, CDMA network sensitivity function versus the number of rake fingers for is shown in Fig. 8. Very much the same behavior as in Fig. 6 is demonstrated, except that the sensitivity is slightly higher due to additional errors in the combiner coefficient estimation. Finally, if, the same parameter is shown in Fig. 9. The sensitivity function is now lower because the contribution of the weaker signal components is reduced proportionally. As a general conclusion, one can see that capacity for the EGC (Fig. 2) is lower than for the MRC (Fig. 4) due to the inferior combining scheme. On the other hand, the sensitivity for the MRC (Fig. 9) is higher than for the EGC (Fig. 7) because the former is using estimated (with errors) signal phases and amplitudes in the combiner. At the same time, EGC has all combining coefficients equal to one, and the only estimated parameters (with errors) are signal phases. V. CONCLUSION In this paper, we have presented a systematic analytical framework for the capacity evaluation of an advanced CDMA network. This approach provides a relatively simple way to specify the required quality of all system components. This includes multiple access interference canceller and rake receiver, taking into account all their imperfections. A variety of schemes can be included as explained in (48). The system performance measure is the network sensitivity function representing the relative losses in capacity due to all imperfections in the system implementation. Some numerical examples are presented for illustration purposes. These results are obtained for a channel with the exponential multipath delay profile with the decay factor. It was shown that for the fading rate of Hz, as much as 70% of the system capacity can be lost due to the imperfections of the rake receiver and interference cancellation operation. A variety of results is presented for different channel decay factors, fading rates and number of rake fingers. In general, under ideal conditions, the system capacity is increased if the number of fingers is increased. At the same time, one should be aware that the system sensitivity is also increased if the fading rate and number of rake fingers are higher. The results and the methodology presented in this paper offer enough tools and data for a careful choice of the system parameters in a realistic environment imperfections are present. ACKNOWLEDGMENT The authors are grateful to the anonymous reviewers for their comments and suggestions to improve the overall quality of the paper. The authors would also like to thank Mr. M. Hämäläinen at the Telecommunication Laboratory and Centre for Wireless Communications, University of Oulu, Oulu, Finland, for the help with the graphics.

10 1790 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 Fig. 4. Capacity (K 0 ) versus the number of the rake fingers for MRC ( =0:25). Fig. 5. Capacity (K 0 ) versus the number of rake fingers for MRC ( =0).

11 GLISIC AND PIRINEN: WIDEBAND CDMA NETWORK SENSITIVITY FUNCTION 1791 Fig. 6. CDMA network sensitivity function versus the number of rake fingers for EGC ( =0). Fig. 7. CDMA network sensitivity function versus the number of rake fingers for EGC ( =0:25).

12 1792 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 1999 Fig. 8. CDMA network sensitivity function versus the number of rake fingers for MRC ( =0). Fig. 9. CDMA network sensitivity function versus the number of rake fingers for MRC ( =0:25).

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From , he was a Visiting Scientist at the Cranfield Institute of Technology, Cranfield, U.K., and at the University of California at San Diego, San Diego, CA, from He has been active in the field of spread spectrum and wireless communications for 20 years, and he has published a number of papers and five books. He is consulting in this field for industry and government. Dr. Glisic has served as Technical Program Chairman of the 3rd IEEE International Symposium on Spread Spectrum Techniques and Applications (ISSSTA 94), the 8th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC 97), and the IEEE International Conference on Communications (ICC 01). He is the Director of IEEE ComSoc MD programs. Pekka Pirinen (S 97) was born in Oulainen, Finland on March 4, He received the M.S. degree and the Lic. Tech. degree in electrical engineering from the University of Oulu, Finland, in 1995 and 1998, respectively. He is currently a graduate student at the Infotech Oulu Graduate School pursuing the Ph.D. degree. Since 1994, he has been with the Telecommunication Laboratory and Centre for Wireless Communications, University of Oulu, first as a Research Assistant and later as a Research Scientist, on various spread spectrum and CDMA research projects. His main research interests include multiple access protocols, capacity evaluation, and wireless networks in general.