WSEAS TRANSACTIONS on COMMUNICATIONS P. Varzakas
MC/DS-CDMA VERSUS SC/DS-CDMA IN MOBILE RADIO: SPECTRAL EFFICIENCY APPROACH
P.Varzakas
Department of Electronics
Technological Educational Institute of Lamia
3o Km Old Road Lamia-Athens, GR 35100, Lamia
e-mail: [email protected]
Abstract—The spectral efficiency of a multicarrier direct-sequence code-division multiple-access (MC/DS-CDMA) cellular system operating in a mobile radio environment with Rayleigh fading, is investigated. In this work, spectral efficiency is evaluated in terms of channel capacity (in the Shannon sense) per user, estimated in an average sense. It is analytically shown that, under normalized condi- tions and assuming a static model of operation, MC/DS-CDMA spectral efficiency, on downlink, is higher than that of single-carrier direct-sequence code-division multiple-access (SC/DS-CDMA). This result is justified by the combination of path-diversity reception, achieved by a conventional coherent maximal-ratio combining (MRC) RAKE receiver, and physical frequency diversity potential provided, in a fading environment, by frequency-division multiplexing on a set of orthogonal carriers. It is shown that the increase of the carrier frequencies, in the MC/DS-CDMA cellular system, leads to a respective improvement of the spectral efficiency achieved.
Key-Words:-Spectral efficiency, multicarrier modulation, code-division multiple access, cellular sys- tems.
1 Introduction can also be estimated in an average sense while its degradation is anticipated to a certain degree by uti- In the literature, there has been a growing inter- lizing some kind of diversity reception technique, est in broadband transmission over time-variant [3, 4]. This average channel capacity formula would channels due to the inherent diversity potential indeed provide the true channel capacity of the fad- which is provided by the frequency selectivity of ing channel, when the transmitter adapts to the such channels, [1]. Then, a variety of modulation channel variation using a constant-power variable- and coding schemes are investigated in order to fur- rate strategy, [5-8]. ther increase the transmitted data rate for a fixed Spectral efficiency, defined as the transmitted bit-error-rate (BER) value. However, for a time- data rate per unit bandwidth for a specified average variant channel, as it is the case in mobile radio, its transmitted power and fixed BER value, is of prima- capacity, i.e., the maximum rate, at which data can ry concern in the design of future wireless commu- be transmitted with arbitrarily small BER, can be nications systems. Orthogonal frequency-division obtained by finding the best distribution of the multiplexing (OFDM) is a modulation method de- transmitted signal power as a function of the instan- signed in the 1970s, [9]. Based on OFDM principle, taneous signal-to-noise power ratio (SNR) and then MC/DS-CDMA proposed recently and investigated averaging over the SNR distribution, where the in the context of high data rate communication over maximization is subject to the average power con- time-variant channels. Then, in this work, we con- straint, [2]. For a time-variant channel, its capacity sider a MC/DS-CDMA system in which a data se-
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quence multiplied by a spreading sequence modu- special case of the rate region, achievable under the lates N orthogonal carriers rather that a single- respective systems. carrier (SC). Each carrier is spread by the same pseudo-noise (PN) sequence, and each carrier is The analysis covers the base-to-mobile units modulated by the same data symbol; thus this sys- link, i.e., the downlink, also called broadcast chan- tem is analogous to one repetition coding scheme, nel, while a fixed number K of active users per cell, [10]. This transmission technique has a number of that occupy the radio channel simultaneously (fully desirable features, including narrow-band interfer- loaded cellular systems) is assumed for both multi- ence suppression and a lower chip rate than that of a ple-access schemes. However, a variable allocation conventional SC system occupying the same total of users is governed by a birth-death process imply- system’s bandwidth, [10]. The lower chip rate is a ing a dynamic channel capacity model, [19]. In ad- result of the fact that the entire system’s bandwidth dition, multiple-access interference (MAI) and co- is divided equally among N frequency bands. Re- channel interference (CCI) are considered as gauss- spectively, at the receiver, maximal-ratio combining ian distributed interference, even for small values of (MRC) RAKE reception is employed. number of system's users, [20,21]. However, one question that arises in considering The MC modulation is motivated by Shannon’s the previously described MC/DS-CDMA cellular classical approach of calculating the capacity of a system, is whether or not there is any advantage frequency-selective channel by slicing it to infini- concerning the spectral efficiency achieved, com- tesimal bands, but has been considered rather exten- pared with that of a conventional pure broadband sively in connection to fading, [22-26]. However, it SC/DS-CDMA cellular system. In a conventional must be noticed, that the following approach for the SC/DS-CDMA system, each user bit is transmitted MC/DS-CDMA and SC/DS-CDMA cellular sys- in the form of many sequential chips, each of which tems does not solve the problem of the "capacity is of sort duration, thus having a wide bandwidth. region", i.e., the set of information rates at which Following the methodology described in [11] and simultaneously reliable communication of the mes- [12], in this paper we present a comparison of sages of each user is possible, [27-30], but applies a MC/DS-CDMA and SC/DS-CDMA cellular sys- new method to estimate the channel capacity as- tems, under normalised conditions, been suitable for signed to each user, in an average sense, consider- providing quantitative results for these multiple- ing the system’s inherent diversity potential. Final- access techniques. Then, we analyze the spectral ly, the average spectral efficiency estimated here, is efficiency achieved by MC/DS-CDMA and SC/DS- not the maximum spectral efficiency achieved over CDMA cellular systems operating in an ideal non- such a channel, [31-33], but average channel capaci- fading additive white Gaussian noise (AWGN) and ty represents an optimistic upper bound, in average a Rayleigh fading environment. Previous studies in sense, for applied modulation and coding schemes. spectral efficiency of cellular systems with frequen- The paper is organized as follows. In sections 2 cy reuse were based on a criterion introduced by and 3, MC/DS-CDMA and SC/DS-CDMA cellular Hatfied, [13-15], which only measured the traffic systems are examined, respectively. The numerical loading rather than the throughput intensity. How- results and their comparison are given in section 4. ever, in cellular systems, spectral efficiency is usu- Final conclusions are outlined in the last section. ally measured by the overall throughput per cell per sec per Hz. In contrast to these previous works and following the method described in [16-18], here, the 2 The MC/DS-CDMA case spectral efficiency of the considered cellular sys- In a pure MC/DS-CDMA system, the same us- tems is evaluated in terms of each user’s achievable er’s data symbol is transmitted in parallel over N average channel capacity, meaning the normalized orthogonal carriers frequencies (sub-carriers), each average sum data rate per user. Then, here, the multiplied by a different spreading sequence unique achievable rate region (assuming that all users oper- to each user. Then, the transmitted signal consists of ate at the same data rate and have average transmit the sum of the output of these N "branches". The powers constraint), under Rayleigh fading condi- totally allocated system’s bandwidth WMC/DS, assum- tions, is estimated in an average sense, considering ing no guard band between adjacent frequency the system’s inherent diversity potential. Seen from bands and a strictly band-limited "chip" sequence a multi-user information theory perspective, the as- with bandwidth Wmc/ds=Gp,mc/ds⋅Ws is as shown in sumption that all users share the same rate is only a Figure 1, equal to:
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cellular system. However, in this analysis, we con- sider the case where the receiver for each user’s WMC/DS=N⋅Wmc/ds=N⋅Gp,mc/ds⋅Ws (1) signal does not know the spreading wave forms of the other users or chooses to ignore them in the de- Wmc/ds modulation process. In order to simplify the mathematical descrip- tion, all hexagon cells of the system, are approxi- mated by circular regions of radius R with the same area. Assuming a fourth power law path loss, the fN received signal power Pi,,cl,MC/DS at the cell boundary f1 f2 by i-th user, i=[1,..,12K], will then be:
-4 Pi,,cl,MC/DS=αR (3) WMC/DS=N⋅⋅⋅Wmc/ds
Fig. 1. The spectra of the transmitted signal in a where α is a constant factor, [34]. However, the MC/DS-CDMA system. equal power case is considered, meaning that in the downlink, all mobile units that belong to a certain where Gp,mc/ds is the processing gain (or spreading cell receive equal average signal power from their factor) applied in direct-sequence (DS) transmis- cell site when an appropriate power control scheme sion, Ws is the signal bandwidth and the subscripts is applied. Therefore, for a cellular MC/DS-CDMA ‘MC/DS’ and ‘mc/ds’ refer to MC/DS-CDMA sys- system, Γi,cl,MC/DS for each mobile unit, can readily tem. be determined considering the average MAI power In the following, we consider a cellular MC/DS- and average CCI power resulting from the eleven CDMA system operating in an ideal non-fading co-channel interfering cells as following, [17], AWGN environment with a number K active users per cell. Note that this case is examined here only for theoretical purposes, since it does never appear in practice. Only the average CCI power resulting αR -4 Γ i, cl, MC/DS = 4- + from the eleven co-channel cells of the first domi- ⋅ WN + [ αRK )(1)-( ] 0 mc/ds (4) nant tier is considered significant and all base sta- αR 4- + = tions' and mobile units' antennas are assumed omni- 2 KaR 4- + α RK − 4 + K α R )2.633(6)2(3 4- ] directionals. Clearly, transmission of a user signal P (assumed Gaussian at system input) with arbitrarily = cli MC/DS,, ⋅ WN + (3.3123 1)- ⋅ PK small BER, depends on MAI and CCI level. Thus, 0 mc/ds cli MC/DS,, the channel capacity C required for errorless i,cl,MC/DS transmission of a DS signal of bandwidth Wmc/ds, in N each of the disjoint carrier frequencies, is given where total interference is considered gaussian and, by the Shannon-Hartley theorem when arbitrarily thus, directly incorporated into Shannon-Hartley complex coding and delay is applied, [22,34]: formula and N0 is the power spectral density of the additive white Gaussian noise. However, eq.(4)
does not take into account the voice activity cycle, sector-reuse parameterization, lognormal variations C W og (1l +⋅= Γ ) (2) cli MC/DS,, mc/ds 2 cl,i, MC/DS and a random location model for the users’ posi- tions, as required in describing real commercial sys- tems. In addition, the description of the frequency assignment, in each cell, is beyond the scope of this where Γi,cl,MC/DS, i=[1,..,12K], is the spread -to- work. It must be notice, that inter-carrier interfer- interference plus noise ratio (SINR) received at the ence (ICI) occurs because signal components from mobile unit as it reaches the boundary of a cell, re- one sub-carrier cause interference to neighboring flecting the lowered signal power spectral density sub-carriers. In this paper, the effect of ICI is not due to spreading and the subscript ‘cl’ refers to the considered and, the synchronization, in the recep-
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tion of the DS signals in MC/DS-CDMA cellular W mc/ds (8) MC/DS [WM mc/ds ] 1 =+⋅= + 1 system, is assumed perfect. Thus, for the MC/DS- W CDMA cellular system, eq.(4) can equivalently be coh written in the form:
where is the maximum delay spread or total mul- Γ tipath spread of the Rayleigh fading channel (as- Γ i, cl, MC/DS = (5) sumed known or measurable) and [.] returns the G mc/dsp, + K -(3.3123 1) ⋅ Γ largest integer less than, or equal to, its argument. However, if the bandwidth Wmc/ds is smaller than the coherence bandwidth Wcoh of the Rayleigh fading channel, there will be no inherent diversity poten- where Γ=(Pi,,cl,MC/DS/N0Ws) is the received SNR over tial, and, if fading reduction is seek through diversi- the signal bandwidth Ws. ty techniques, space diversity or a hybrid scheme shall be used. Following eq.(2), the total channel capacity The MC transmission calls for a kind of diversity CMC/DS (in the Shannon sense) for the twelve cells of reception since each single data symbol is transmit- the cellular MC-DS/CDMA system under consider- ted, in parallel, in a different carrier frequency. ation, that is, the total channel capacity available to Since, the bandwidth Wmc/ds is assumed greater than all 12K active users, will be given by the sum of the the coherence bandwidth Wcoh of the Rayleigh fad- individual rates: ing channel, fading will independently affect each of these N orthogonal carrier frequencies, and then physical frequency diversity potential will be ob- tained. Hence, a N carrier MC/DS-CDMA scheme, 12K 12K (6) with MRC can be seen equivalent to a N-branch CMC/DS = ∑C cli MC/DS,, Wmc/ds ∑ og2 1(l +⋅= Γi,cl,MC/DS ) i=1 i=1 space diversity technique. Therefore, the average
channel capacity per user 〈Ci〉cl,MC/DS,Rayleigh, normal- ized over the total system’s bandwidth WMC/DS, used when the information bit is transmitted, is given by: where Γi,cl,MC/DS is given by eq.(5). Since, in prac- tice, Γi,cl,MC/DS, i=[1,..,12K], is well below unity (in linear scale) eq.(6) can be approximated by: C ∞ N −1 i cl , MC/DS, Rayleigh ()γ′ = ()+1log γ′ ⋅ ∫ 2 N WMC/DS ()N !1 ⋅− Γ (9) 0 ()cl,i MC/DS, γ′ exp −⋅ ⋅ γ′)d( C W 121(log K ⋅+⋅= Γ ) (7) MC/DS mc/ds 2 cli MC/DS,, Γ cli MC/DS,,
We now examine the case of a cellular MC/DS- where 〈.〉 indicates average value, the subscript CDMA system operating in a Rayleigh fading envi- ‘Rayleigh’ refers to the Rayleigh fading channel, ronment. We assume that the physical channel of and Γ =〈 γ′ 〉, given by eq.(5), is the average bandwidth W is greater than the coherence cli MC/DS,, mc/ds ′ bandwidth Wcoh of the Rayleigh fading channel. The received SINR γ in each of the N frequencies radio channel is modeled as a slowly fading, time- where the DS signal is transmitted and no correla- invariant and discrete multipath channel and, thus, it tion between the N fading patterns is assumed. appears to be frequency-selective to the transmitted In general, the multipath-intensity profile (MIP) DS signals of bandwidth Wmc/ds. The maximum in an urban Rayleigh fading environment is expo- number MMC/DS of uncorrelated resolvable paths nential, but, here, MIP is assumed discrete and con- ("inherent diversity branches") will be given by, [1]: stant, so that the "resolvable" path model can be considered to have equal path strengths on the aver- age. Furthermore, if path-diversity reception, pro- vided by a MRC RAKE receiver, is also applied to
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the MC/DS-CDMA system, in each carrier frequen- cy, then additional diversity will be achieved.
Hence, the average SINR after path-diversity ap- C cli SC/DS,, W SC/DS 2 (1log +⋅= Γ cli SC/DS,, ) (12) plied, in each of the N carrier frequencies,
Γ cli MC/DS,,pt, , will be given by, [36]: where Γi,cl,SC/DS, i=[1,..,12K], is the spread SINR re- ceived at the mobile unit as it reaches the boundary of a cell, and determined by considering, also in this case, the average received CCI power, as following:
Γ , cli MC/DS,pt, = M MC/DS ⋅ Γ i,cl MC/DS, = (10) Γ M MC/DS ⋅= -4 G mc/dsp, + ()3.3123 K - 1 ⋅ Γ αR Γ i, cl, SC/DS = 4- + 0 ⋅ WN SC/DS + [ αRK )(1)-( ] (13) αR 4- + 4- −4 4- = 0 ⋅ WN SC/DS + [ Kαα + α RK + α .633(6)2(32 RK )2 ] P where the new suffice 'pt' refers to the path-diversity = cli SC/DS,, ⋅ WN + 1)-(3.3123 ⋅ PK reception applied. Then, the spectral efficiency 0 SC/DS cli SC/DS,, SEcl,MC/DS,Rayleigh achieved by the cellular MC/DS- CDMA system operating in a Rayleigh fading envi- ronment and expressed in (bits/sec/Hz) over the to- -4 where it is assumed that Pi,cl,SC/DS=Pi,,cl,MC/DS=αR is tal available system’s bandwidth WMC/DS, is found to be: the user’s average received signal power and the new subscripts ‘SC/DS’ and ‘sc/ds’ refer to SC/DS- CDMA cellular system. Eq.(13) can equivalently be written in the form: C i cl MC/DS,, Rayleigh SE cl , MC/DS, Rayleigh = = W MC/DS ∞ ()γ′ N −1 (11) Γ = ()+1log γ ′ ⋅ ⋅ Γ = (14) ∫ 2 N i cl SC/DS,, G K 1)-(3.3123+ ⋅ Γ 0 ()N 1 ! ⋅− ()Γ cli MC/DS,pt,, sc/dsp, γ′ exp −⋅ ⋅ γ′)d( Γ pt,, cl,i MC/DS where Γ=(Pi,,cl,SC/DS/N0Ws) is the received SNR over signal bandwidth Ws. In the following we consider a cellular SC/DS- where Γ cli MC/DS,, , used in eq.(9), has been changed CDMA system operating in a Rayleigh fading envi- ronment. If the bandwidth WSC/DS is greater than the now to Γ cli MC/DS,,pt, . coherence bandwidth Wcoh of the Rayleigh fading channel, the maximum number MSC/DS of uncorre- lated resolvable paths will be given by, [1]:
3 The SC/DS-CDMA case
WSC/DS In a pure cellular SC/DS-CDMA system, the SC/DS [WM SC/DS ] 1 =+⋅= +1 (15) available radio channel of bandwidth Wcoh
WSC/DS=Gp,sc/ds⋅Ws (where Gp,sc/ds is the proceessing gain applied) is reused in all neighboring cells, while different code sequences use the same radio channel to carry different traffic channels in each of Although the number of resolvable paths MSC/DS these cells. In this case, the channel capacity (in the may be a random number, it is bounded by eq.(15). Shannon sense) required for errorless transmission We now estimate the average channel capacity per user in a SC/DS-CDMA cellular system, as affected of a spread signal of bandwidth WSC/DS will be given by, [17]: by the inherent diversity potential of the DS trans-
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mission. In addition, we assume that all users of the ∞ γ M MC/DS−1 system equally share the average capacity provided ( tm,sc/ds, ) C =WSC/DS 2 +1log γ tm,sc/ds, M ⋅(18) cl SC/DS,, Rayleigh ∫ ()M − !1 ⋅ Γ MC/DS by the entire physical channel of bandwidth WSC/DS 0 MC/DS ()tm,sc/ds, γ and that all users in all cells operate under similar exp −⋅ tm,sc/ds, ⋅ γ )d( Γ tm,sc/ds, Rayleigh fading conditions. Thus, we write: ,sc/ds,tm
Clearly, this channel capacity estimation, is based on the equivalence described above and indi- 1 cates the average total channel capacity that appears C = ⋅ C (16) i cl SC/DS,, Rayleigh 12K cl SC/DS,, Rayleigh at the MRC RAKE receiver output in the form of the average best recovered data rate from all 12K users. However, in general, the performance of the coherent MRC RAKE receiver depends on the where 〈Ci〉cl,SC/DS,Rayleigh is the i-th user’s portion of number of the employed taps and the Rayleigh fad- the totally available average capacity ing channel estimation. If the number of employed taps is less than the resolvable paths' number, the 〈C〉cl,SC/DS,Rayleigh of the channel WSC/DS. Then, consid- ering, a conventional coherent MRC RAKE receiv- receiver performance will substantially be degraded er, the output’s decision variable is identical to the because the power of the remaining "branches" will decision variable which corresponds to the output of appear at the receiver output as self-noise power. In a M-branch space diversity MRC technique, with this work, we consider the optimum operation of the coherent MRC RAKE receiver where the number of M=MSC/DS, [1]. Consequently, the maximal-ratio coherently combining reception of DS spread sig- taps employed is equal to the number MSC/DS of re- nals, achieved by the considered RAKE receiver, is solvable paths as given by eq.(15) and Rayleigh fad- equivalent to a M-branch space diversity MRC ing channel is perfectly estimated. technique and is the optimal diversity scheme as it If we assume that the signal to each user appears provides the maximum output SINR, [36]. There- at the receiver input with the same average spread fore, the probability density function (p.d.f.) of the SINR Γi,cl,SC/DS, then the totally received spread SINR power ratio from all 12K active users will be combined instantaneous SINR γm,t of the spread DS signal over the bandwidth WSC/DS, with no correla- equal to 12K⋅Γi,cl,SC/DS, and Γm,sc/ds,t can be written as: tion among the MSC/DS "branches", will follow the Erlang distribution, [37], i.e., Γm,sc/ds,t =12K⋅ Γi,cl,SC/DS (19)
MSC/DS−1 1 (γ tsc/ds,m, ) MSC/DS γ )(p = ⋅ ⋅ Thus, following eq.(14), tsc/ds,m, MSC/DS MSC/DS −1)!( ()Γ tsc/ds,m, (17)
γ exp ⋅exp − tsc/ds,m, Γ 12 KΓ sc/ds,m, t (20) Γ tsc/ds,m, = )-(3.3123K+ G sc/dsp, 1)-(3.3123K+ ⋅ Γ
where Γm,sc/ds,t=〈γm,sc/ds,t〉 is the totally received aver- age spread SINR value in the m-th, Then, combining eqs (16) and (18), the spectral m=[1,…,MSC/DS], diversity branch from all 12K us- efficiency SEcl,SC/DS,Rayleigh achieved by a cellular ers, MSC/DS is obtained from eq.(15) and the sub- SC/DS-CDMA system operating in a Rayleigh fad- scripts ‘t’ and ‘m’ refer to the totally received aver- ing environment and measured in (bits/sec/Hz) over age spread SINR from all users and to the m-th di- the total system’s bandwidth WSC/DS, is found to be: versity branch, respectively. Thus, an expression for the average capacity C of the chan- c SC/DS,, lRayleigh nel WSC/DS can be written as:
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C Note that all integrals are calculated numerically, i cl SC/DS,, Rayleigh SE = = cl SC/DS,, Rayleigh W as they can not be expressed in closed form. Fur- SC/DS thermore, considering K=10 as an indicative value 1 = ⋅ (21) (in real cellular systems the actual number K of us- M SC/DS 12 ()MK SC/DS − !1 ()Γ tsc/ds,m, ers per cell is of the order of 50). Then, the spectral ∞ efficiencies achieved on the downlink, M SC/DS −1 γ +1log ⋅ ()+1log ⋅ γγ exp −⋅ ⋅dγ SE and SE (given by eqs ∫ 2 Γ cl,MC/DS,Rayleigh cl,SC/DS,Rayleigh 0 c/ds, tm.s (11) and (21) respectively) in a Rayleigh fading en- vironment are plotted against Γ (expressed in dB) in Figure 2. As it can readily be seen, for cellular op- eration in a Rayleigh fading environment and under normalized conditions, MC/DS-CDMA offers al- where the notation for the combined instantaneous ways higher spectral efficiency, expressed in SINR γm,sc/ds,t, used in eq.(18), has been changed to γ (bits/sec/Hz), than that of a cellular SC/DS-CDMA and the SINR value Γm,sc/ds,t is given by eq.(20). system. In addition, one must notice that, in all cas- However, the so derived SEcl,SC/DS,Rayleigh value repre- es plotted in Figure 2, as Γ increases to infinity, the sents an average value following the average chan- spectral efficiency of each of the considered cellular nel capacity per user
Wmc/ds=1.25MHz and assuming the following val- ues:
(i) signal bandwidth: Ws=30KHz,
(ii) number of users per cell for both cellular sys- (b) tems: K=10, (iii) total multipath spread of the urban Rayleigh fading channel: =3µsec, Spectral efficiency (bits/sec/Hz) (iv) number of "inherent diversity branches" of MC/DS-CDMA cellular system:
M MC/DS = Wmc/ds ⋅ +1][ =4, Γ (dB) (v) number of "inherent diversity branches" of SC/DS-CDMA cellular system: SC/DS = WM SC/DS ⋅ +1][ =31, and Fig 2. Spectral efficiency in (bits/sec/Hz) on down- (vi) number of carrier frequencies in cellular link in a Rayleigh fading environment: (a) cellular MC/DS-CDMA system: N=8 (so that MC/DS-CDMA system, (b) cellular SC/DS-CDMA
WMC/DS=N⋅Wmc/ds). system.
However, this holds only for small values of N, because, for increased values of N, the system’s
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spectral efficiency is limited by the total interfer- cellular MC/DS-CDMA system with path-diversity ence power. Then, the relationship between the reception provided by a MRC RAKE receiver, has spectral efficiency SEcl,MC/DS,Rayleigh on downlink of always an advantage in spectral efficiency over cel- cellular MC/DS-CDMA system, as given by lular SC/DS-CDMA, especially, when a large num- eq.(11), and the number N of carrier frequencies, is ber of carrier frequencies are used. Consequently, shown in Figure 3, for Ws=30KHz, K=10, =3µsec, the cellular MC/DS-CDMA system is shown to be Γ=15dB (keeping in all cases WMC/DS=10MHz since another good alternative in the situation of the cellu- WMC/DS=N⋅Gp,mc/ds⋅Ws). lar network evolution from the cellular SC/DS- CDMA to an advanced CDMA system. However, the increased number of carrier frequencies and path-diversity applied in each of them, in MC/DS- CDMA, adds serious complexity to the system. Fi- nally, a simulation process must be described ana- lytically, in order to compare with the theoretical results of this paper. We are still working on this, for a future paper, but results are not yet derived due to complicated system’s parameters.
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