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$EVWUDFW This paper deals with the spectral efficiency comparison between &RGH 'LYLVLRQ 0XOWLSOH $FFHVV (CDMA) and a modified version of 3DFNHW 5HVHUYDWLRQ 0XOWLSOH $FFHVV (PRMA), called 350$ ZLWK +LQGHULQJ 6WDWHV (PRMA-HS), in a /RZ (DUWK 2UELW  0RELOH 6DWHOOLWH 6\VWHP (LEO-MSS). The same Rice channel model, available bandwidth, source and channel coding, energy per bit, satellite antenna system and satellite constellation altitude have been assumed in both cases. A performance analysis of both CDMA and PRMA-HS has permitted to evaluate their spectral efficiency. We have obtained that PRMA-HS has not a satisfactory performance when the fading margin is low, especially if also the Rice factor is low. Whereas CDMA maintains a certain capacity also for low fading margin values.


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The 8QLYHUVDO 0RELOH 7HOHFRPPXQLFDWLRQV 6\VWHPV (UMTS) will encompass a terrestrial cellular component and a satellite one integrated at the system level. This paper focuses on the comparison of 0HGLXP $FFHVV &RQWURO (MAC) protocols for /RZ (DUWK 2UELW ± 0RELOH 6DWHOOLWH 6\VWHPV (LEO-MSSs). In particular, 'LUHFW 6HTXHQFH - &RGH 'LYLVLRQ 0XOWLSOH $FFHVV (DS- CDMA) and a modified version of 3DFNHW 5HVHUYDWLRQ 0XOWLSOH $FFHVV (PRMA), called 350$ ZLWK +LQGHULQJ 6WDWHV (PRMA-HS), are considered [1]. We refer to a satellite system where cells are fixed on the earth and satellite antenna spot-beams are steered to point to the same area on the earth as long as possible. We neglect cell changes of 8VHU 7HUPLQDOV (UTs) during call lifetime. The efficiency comparison between CDMA and PRMA-HS is made with the same channel model, bandwidth, source and channel coding, energy per bit, satellite antenna system, constellation altitude. We have considered only on/off voice sources, with talking and silent phases exponentially distributed and mean values W = 1 s, W = 1.35 s, respectively [2]. The efficiency parameter is [1]: η = 0PD[ 5E / : bit/s/Hz, where : is the total one-way bandwidth of the system, 5E is the voice source bit rate before channel coding, 0PD[ is the maximum number of voice users per cell. With PRMA-HS, the bandwidth : is divided among cells according to a reuse factor . [3]; whereas, the same bandwidth : is used in all the cells with CDMA. The success/failure of a packet transmission can be modeled as the outcome of a comparison between the instantaneous %LW (QHUJ\ WR 1RLVH-,QWHUIHUHQFH 5DWLR, (V/1RW , and a threshold value

(V/1RW | th: the packet is successfully decoded if the instantaneous (V/1RWÃ is above (V/1RW | th;

1 otherwise, the packet is lost [4]. Such model relies on two assumptions: (L) the fading process is slow enough so that the channel can be considered constant during a packet time; (LL) the relationship between the instantaneous (V/1RW and the bit error probability is close to a step function. Even if these conditions are not strictly satisfied, the threshold model may be used as well [4]. This model will be considered in this paper, where packet errors are due to outage events. A convolutional channel code protects transmissions and allows a low (V/1RW | th value before decoding. The UMTS satellite channel has been studied in [5], where measures for different outdoor scenarios are presented. We refer here to /LQH 2I 6LJKW (LOS) propagation conditions that are typical of suburban and rural scenarios [5]; accordingly, a Rice channel model is considered. The / low-pass impulse response of a frequency-selective fading channel is α(τ;W) = ∑ α (W)δ (τ −τ ) , O=1 O O where δ(W) is the Dirac delta function, αO(W) and τO, O = 1,…., / are the tap weight coefficients and the relative delays, respectively. The first tap may be considered as the superimposition of a constant and a complex Gaussian contribution, while the other taps may be modeled as Gaussian independent complex random processes. Let βejφ denote the constant direct path component and ( 2 ) L / ΩL = ( α L , = 1,…., the mean square envelope of the multipath components. The Rice factor / of the channel is .5 = β 2 /∑ Ω . L=1 L


7KH350$+6SURWRFRO

Each PRMA-HS carrier is divided into time intervals, i.e., VORWV with duration 7V; 1 slots form a IUDPH with duration 7I . The transmission of voice is organized in packets transmitted in 7V. Each packet contains user information bits and a header. The number of slots per frame is [2]:

  VORWV 7 57FI and I (1) 1   7V = 1 57VI  +Y  IUDPH where 5FÃ is the channel bit rate, 5V is the source bit rate after channel coding, +Y is the header length in bits of a packet and x is the highest integer less than or equal to [.

The PRMA-HS protocol uses a slow speech activity detector to avoid that slots are allocated to UTs during silent pauses [2]. When a talkspurt begins, the related UT enters the FRQWHQGLQJ VWDWH (CON): the UT attempts to transmit the first packet on an available slot with the permission probability S. An error-free feedback channel broadcast by the satellite informs all the UTs within a cell about the state of each slot (i.e., idle/reserved). A transmission attempt made by a UT on an idle slot is successful if no other UT has made a contemporary transmission attempt (the capture effect is neglected) and if the packet of the UT has been successfully decoded at receiver. Otherwise, the transmission fails and the UT must reschedule its attempt. When a UT has successfully transmitted, it obtains the reservation of a slot per frame. The UT knows the outcome of its transmission through the feedback channel after a 5RXQG 7ULS SURSDJDWLRQ 'HOD\ (RTD). In a conventional PRMA scheme a UT waits for this outcome; whereas, PRMA-HS allows that a UT attempts other transmissions also during RTD. Hence, PRMA-HS permits a faster reservation mechanism, so allowing a high UT capacity in LEO-MSSs [6], close to that of PRMA in terrestrial cellular systems, where RTD << 7V. The first successful attempt of a UT is recorded by the satellite in a database to ignore any subsequent successful

2 attempt made by the same UT while it waits for the outcome of the reservation. A UT in the CON state discards a packet from its buffer if the delay to transmit correctly this packet exceeds a maximum value, 'PD[ = 32 ms [2]. The voice transmission quality with PRMA- HS is measured by the packet loss probability 3ORVV due to either packet dropping in the contending phase or packet error during the reservation phase. It is required 3ORVV ≤ 1% for an acceptable speech quality [2]. Let SH denote the packet error probability due to outage and 3GURS the packet dropping probability for a delay greater than 'PD[. Errors within a packet are correlated, because the Doppler shift [5] IG = Y0ÃI/F (where Y0 is the maximum user speed, I is the transmission frequency, F is the light speed) multiplied by the bit transmission time (i.e., 1/5F) is lower than 0.1 [4]. In particular, for Y0 = 20 km/h, I = 2 GHz and -3 5F = 765 kbit/s, we have IG = 2.2 kHz and IG/5F ≈ 2.9x10 . Moreover, we assume that packet errors are slot-by-slot independent, if IG 7V > 0.2 [4]; this condition is fulfilled, because we will use 7I = 15 ms and 1 = 21 slots/frame. Then, we have also independent packet errors from frame to frame (i.e., IG 7I > 0.2) in the reservation phase. For the Rician fading channel considered in this paper, the fading term λ2 may be modeled as a non-central χ2 random variable with 2 degrees of freedom, unit mean and non-centrality parameter β2 = .5 / (1 + .5), where .5 is the Rice factor. A power control scheme is considered in order to compensate for different propagation attenuations experienced by the users spread on the area covered by the same satellite. Let ) denote the fading margin and let ,(V(.) denote the mean signal to interference ratio with a resource reuse among spot beams characterized by a cluster with . cells [3] Without interference, the instantaneous (V/1RW at the satellite is ) (V/1RW |th 2 2 -1 -1 λ ; with interference, the instantaneous (V/1RW | th becomes λ / [) (V/1RW | th + ,(V(.)]. 2 -1 -1 Finally, the outage probability is SH = 3URE{λ / [) (V/1RW | th + ,(V(.)] < (V/1RW | th} = 2 -1 3URE{λ < ) [1 + ) (V/1RW | th ,(V(.)]]}. Owing to the constraint on 3ORVV, we assume that the transmission parameters are set so that SH < 1%. For the PRMA-HS case, a frequency non-selective channel is considered for LEO-MSSs; this assumption is realistic for the maximum delay spread considered in [5](typically, 180 - 250 ns) and for 5F < 2 Mbit/s. The packet loss probability is:

3ORVV = 3GURS + (1− 3GURS )SH (2)

We consider RTD always equal to its maximum value, 57'PD[, (conservative assumption) and 57'PD[ = 7I - 7VÃÃ(i.e., 57'PD[ = 1 - 1 slots). Hence, when a UT makes a successful transmission attempt on an idle slot it knows the outcome of its transmission before the beginning of the same slot in the next frame. In the packet header a special (QG2I7DONVSXUW (EOT) flag is used to notify to the satellite that the present packet is the last one of a talkspurt, so that the satellite releases the reservation of this slot in the next frame. We model the behavior of a UT by the Markov chain in Fig. 1, where $ is the probability that a UT attempts to transmit on a slot; 8 is the probability that a transmission attempt is successful; σ is the probability that a silent gap ends within 7V γ is the probability that a talkspurt ends during 7V; γI is the probability that a talkspurt ends within 7I; σI is the probability that a new talkspurt starts in 7I. Accordingly,

γ ()− γ N σ − ()σ 1 f = 11 - and I 1 1 (3)

3 SH

1 (1 – SH) (1 – σI) WAIT 0 WAIT N-1 SH γI (1 – SH) σI 1 - γI

1 RES 0 RESN-1

γIÃ(1 – SH)

γ $Ã8Ã(1 -Ãγ)

SIL CON 1 HINN-1 HIN1 σ

1 - σ (1 - $8) (1 -Ãγ)

Fig. 1: UT state diagram with PRMA-HS.

As soon as a UT generates the first packet of a talkspurt, it goes from SIL to CON. When a transmission attempt is successful, the UT enters the hindering states from HINN - 1 to HIN1 that model the delay to know the positive outcome of the transmission attempt. In the hindering states, the UT may continue to attempt transmissions on idle slots even if it has already obtained a reservation. In the HIN1 state, the UT receives a positive acknowledgement and it enters the loop from RES0 to RESN-1. During this phase if a packet error occurs, no packet retransmission is considered. However, if the EOT packet is not correctly received, the satellite can not release the reservation: at the next frame, the related UT knows from the feedback channel that it still has a reservation; then, the UT must retransmit the EOT packet. The states from WAITN-1 to WAIT0 model these situations: the UT retransmits its last packet when it is in WAIT0; the UT remains in the WAIT loop until the EOT packet is correctly received. Consequently, the UT goes to SIL. If the satellite channel causes frequent packet errors, so that the EOT packet must be sent many times, it is also possible that a new talkspurt begins when the old reservation is still active; in this case, the UT enters the loop from RESN-1 to RES0 when the first packet of the new talkspurt is correctly received by the satellite on the reserved slot. In Fig. 1 the backward transition from CON to SIL refers to the drop of a talkspurt before obtaining a reservation. Let 5 denote the total number of UTs with a reservation; 6, the number of UTs in the SIL state; &, the number of UTs in the CON state; +L, the number of UTs that will receive a positive acknowledgment after L - 1 slots; 5L, the number of UTs with a reservation on the L-th future slot; :L, the number of UTs with still a reservation on the L-th future slot due to previous EOT packet errors. Accordingly, 5 results to be:

R = R* + H (4) where: 1ÃÃ 1 − 1 and (5) + ∑ + L 5 * = ∑ 5L + :L LÃ Ã1 L = 0

4 Moreover, we must have: 5 + 6 + & = 0 (6) where 0 denotes the number of simultaneous voice conversations per PRMA-HS carrier.

$ is the probability that a slot is not reserved and that a UT obtains the permission to transmit:  5  $ = 1−  S (7)  1 

A UT in the CON state, which attempts a transmission on a slot, obtains a reservation if no other

UT (in CON or HINi states) attempts to transmit on the same slot and if the packet has been correctly received. Therefore, probability 8 results to be:

0, IRU & = 0 DQG ∀ + 8 = ()− S (8) 1 H  & + + − ()1 − S 1, IRU & > 0 DQG ∀ +

We use the (TXLOLEULXP 3RLQW $QDO\VLV (EPA) for the PRMA-HS analysis [2]. The equilibrium values of state variables, denoted by small letters, are real non-negative numbers obtained by equating the inflow and the outflow for each state of the diagram in Fig. 1:

K = K = ...... K1Ã = K HINi for L = 1, . . ., 1 – 1(9)

U = ...... U1 = U RESi for L = 1, . . ., 1 - 2 (10)

UÃ = U + K RES0 (11)

Z = Z = ...... Z1ñÃà = Z WAITi for L = 0, . . ., 1 - 2 (12)

Z U SHγI  ZSHÃÃ WAITN-1 (13)

σ V = γI (1 - SH) U + Z (1 - SH) (1 - σI) + γ F SIL (14)

U = (1 - γIÃ) U + ZσIÃ(1 - SH) RESN-1 (15) σ V = γ F + D X F (1 - γ) CON (16)

Since the total number of active UTs is 0, from (6) we have:

V + F + (1 - 1)U + U + (1 – 1)K + 1 Z = 0 (17) In (16), the terms D and X are obtained from (7) and (8) by substituting the equilibrium values to &, 5 and +: F, 1 U + 1 K  1 Z and (1 –1)K, respectively. D = (1 – U – K – Z) S (18)

0, IRU F = 0 DQG ∀ K  ()1 −1 K (19) X ()()1− SH  1− S , IRU F < 1 DQG ∀ K  F+()1 − K− ()1− S 1 1 , IRU F ≥ 1 DQG ∀ K

The system (9)-(19) can be simplified in the following one with unknown variables F and K:  1 []γ + ()− S ()−γ  1 I 1 H 1 I  γ  ) ()F , K  + K  1+ F 0 (20) σ γ ()− S ()− σ S σ  I 1 H 1 I H   

 γ I + ()1− SH ()1−γ I  X SF(1−γ )1− K − K 0 (21) γ ()− S ()− σ S  I 1 H 1 I H 

5 For each couple (F , K) which fulfils (20),(21) we obtain the corresponding values V, U and Z: K + γ F S K V = , Z = H K , U = − K (22) σ ()1− SH ()1− σ I SH γ I ()1− σ I SH

Equations (20)-(22) are equal to the corresponding ones in [6], if SH = 0. Equation (21) can be numerically solved with the Gauss-Newton recursive method. The system (20),(21) must have a single solution for a correct PRMA-HS behavior [6]. This condition is verified if 0 is below a value which is typically beyond the maximum value to guarantee 3ORVV ≤ 1%. The discarded packets which affect 3GURS are for UTs in the CON state (Fig. 1); under the assumption SH < 1%, we neglect the packets that may be dropped in WAITi states due to many subsequent packet errors when a new talkspurt is generated. Since 3GURS ≤ 1%, we neglect the transition from CON to SIL (Fig. 1). We consider 3GURSÃ(&, +, 5 ) conditioned on 5 UTs which know to have a reservation, + UTs in hindering states and & UTs in the contending state. We refer to a tagged UT which arrives in the CON state where other & UTs are already present. This UT successfully transmits on a slot with probability 3V that accounts for four independent events: (L) the slot is available; (LL) the tagged UT has the permission to transmit; (LLL) only the tagged UT transmits on this slot; (LY) the packet sent by the UT has been successfully decoded.

 5*++  &+ + 3 ()&,+,5 * = 1−  ()()1− S S 1− S (23) V  1  H

The time in slots spent by a UT in the CON state to obtain a reservation given & + 5 has the following geometric distribution 3&21ÃÃ with parameter 3V [2],[6]:

M − 1 M 3&21 ()()&,+,5* = 3V 1− 3V for = 1, 2, ….. (24)

Probability 3GURS(& + 5 ) is computed according to the basic analysis shown in [2]:

' γ ()1− 3 3 ()& + 5 = I V (25) GURS , , * 1 1 − ()1−γ I ()1− 3V

In the case + + 5 = 1, 3V = 1 and (24) is not valid; by taking the limit for 3V → 1 in (25), we have 3GURSÃ(&, +, 5 ) = 1. From the Bayes rule, the joint probability distribution Θ(& + 5 ) is:

Θ()()()()&, +, 5* = Θ & | +, 5* Θ + | 5* Θ 5* (26) where Θ(5 ) is the probability that 5 UTs know to have a reservation, Θ(+ _ 5 ) is the probability that + UTs are in hindering states given 5 and Θ(& _ + 5 ) is the probability that & UTs are in the contending state given + and 5 .

Since slots are independently reserved, a binomial distribution is considered for Θ(5 ):  1  Θ ()5 =   S 5* (− S )1 −5* , 5 ∈ [0 , 1] (27) *   U 1 U  5 * where the probability that a slot is reserved, SU , is obtained by equating the mean value of 5 from (27) to its equilibrium value:

−1 SU = U + K1 + Z (28)

The distribution Θ(+ _ 5 ) is binomial, since the UTs in hindering states have an independent

6 behavior (the maximum value of + can not exceed 1 - 5 or 1 – 1). Hence, we have:

min()1−5*,1 −1  + ()1 −5 1 − + Θ()+ 5   S () S min *, 1  + ∈ [] ()1−5 1 − (29) | *   K K 0 min *, 1  +  where SKÃ is obtained by equating the equilibrium value of + to its expected value: ()1 − K S = 1 (30) K 1 1 ()()1− SU − 1− SU

As shown in [6], we consider a truncated geometric distribution for Θ(& _ +  5 ):

S ()− S & IRU & < 0 − + − 5 0 1 0 , *  Θ ()& + 5 = ()− S & IRU & = 0 − + − 5 (31) | , *  1 0 , *  RWKHUZLVH 0 , where S is derived by equating the expected value of & to its equilibrium value. We have the -1 following approximated solution [6]: SR ≈ (F + 1) .

Finally, we remove the conditioning in 3GURS(&  + 5 ) given by (25) with the exception of 3GURS(&  + 5 ) = 1, for 5  + 1 as follows:

1 min ()1 −5* , 1 −1 0 − + − 5* − 1 (32) 3GURS ∑∑ ∑3GURS ()& , + , 5 * Θ ()()()& | + , 5 * Θ + | 5 * Θ 5 * 5* = 0 + = 0 & = 0

In (32) the sum on & is up to 0 - + - 5 - 1, because at least one UT is in the SIL state to enter the CON state. For a set of system parameter values (i.e., 5F, 5V, +Y, 7I and S) we compute 3ORVV from (2) and (32) for given values of both SH and 0; the PRMA-HS carrier FDSDFLW\, 00.01, is obtained as the maximum value of 0 which allows 3ORVV ≤ 1%. The PRMA-HS performance depends on S and 7I, once 5F, 5V and +Y have been selected. We assume 5F = 765 kbit/s, 5V = 32 kbit/s, +Y = 64 bits as in [6] and 1/2 rate convolutional encoder, so that 5E = 16 kbit/s.
Following the approach outlined in [6], we obtain the optimized values S = 0.5 and 7I = 15 ms (for SH from 10-4 to 10-2) that have been used in the following study. This value of S is greater than that used in [6] to compensate for the unsuccessful attempts due to packet errors; the 7I value is unchanged. Without packet errors, PRMA-HS attains a capacity of 39 UTs/carrier; whereas, the capacity -3 decreases to 37 UTs/carrier for SH = 5x10 . The PRMA-HS spectral efficiency is: 0 5 ELW 0.01 E (33) η 350$−+6 . 5F V +] where we consider one PRMA-HS carrier per cell and a modulation with bandwidth 5F.


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We refer to a typical DS-CDMA system, where 0 users per cell share the up-link satellite channel with a set of Gold codes of length *, where * is the spreading factor. If each user transmits at a channel bit rate of 5V bits/s, and : is the available bandwidth, we have * = :/5V. Assuming the same channel encoding strategies as in the PRMA-HS case (i.e., 1/2 rate encoder), we have a channel bit rate 5V = 25E, where 5E is the voice source bit rate (i.e., 16 kbit/s). The same

7 bandwidth is available for both PRMA-HS and DS-CDMA. Thus, if a reuse factor . and a channel bit rate 5F are adopted for PRMA-HS, the whole bandwidth is : = .5F in the case of a single carrier per cell. With CDMA, a packet is transmitted in a time 7I. Errors in a packet are correlated, because the Doppler shift IG multiplied by the bit transmission time (i.e., 1/5V for CDMA) is below 0.1 [4]. In particular, for Y0 = 20 km/h, I = 2 GHz and 5V = 32 kbit/s, we have IG = 2.2 kHz and IG/5V ≈ 0.06. Moreover, we consider independent packet errors under the condition IG 7I > 0.2 [4], that is fulfilled for 7I = 15 ms. According to [5], the
bandwidth of the transmitted signal may be greater than the coherence bandwidth of the channel (e.g., assuming . = 7 and 5F = 765 kbit/s for PRMA-HS, we have a bandwidth : = .5F = 5.35 MHz for CDMA, which is comparable to the coherence bandwidth of the LEO satellite channel).
However, since the reflected paths in [5] have levels well below the direct path, their impact on the RAKE receiver performance is negligible. Let us assume an optimum single-user receiver on the satellite. According to the standard Gaussian approximation [7], the SNIR at the satellite is: ( λ2 6 = (34) 1 W 1 W 20 0, 1 0, + int ) ( * V WK 3 where 0LQW is the number of interfering users (assuming a single-cell system) and ) is the fading margin introduced in Section II.

A packet error occurs when (V/1RW is below the threshold (V/1RW | th; accordingly, SHÃÃ is:

  0 (   2 1  2 int V  (35) SH = 3URE. λ < 1+ )  )  3* 1    0,W WK 

The fading term λ2 may be modeled as a non-central χ2 random variable with 2 degrees of 2 freedom, unit mean and non-centrality parameter β = .5 / (1 + .5). Probability SH in (35) may be numerically evaluated, once 0LQW in the case of a multi-cell system is identified. In a CDMA system, the inter-cell interference may be modeled by considering a suitable number of users which must be added to the users in the same cell [8]. We assume that only α% of the call duration time is of real talking (typically αC = 42%). Moreover, we envisage that each spot uses a given circular polarization; hence, interfering signals from adjacent cells are reduced by the cross-polarization isolation factor ρ = (1 + 1/$[)/2; a typical value of $[ is 10 dB. Hence, we obtain the
equivalent number of interfering users per cell to be used in (35) as 0LQWÃ = α [0ερ + (0 - 1)]. Finally, the CDMA spectral efficiency is: 0 ELW PD[ (36) η&'0$ 2* V +] where 0PD[ is the maximum value of 0 so that 0LQW = α [0ε ρ + (0 - 1)] gives SH < 1% in (35).


(IILFLHQF\&RPSDULVRQV

In the following comparisons we have assumed the optimized parameter values of the PRMA-HS system. Due to both the selected value 7I = 15 ms and the assumption 7I = 57'PD[ - 7V, we refer to a satellite constellation altitude of 780 km with a minimum elevation angle of 10° [6].

8 For a fair comparison between CDMA and PRMA-HS, we must consider that the interference in the PRMA-HS case depends on the frequency reuse .; whereas in the CDMA case, the interference comes from both the current cell and adjacent ones. The value of . for PRMA-HS and the value of ε for CDMA depend on the transmission techniques, the carrier frequency and the satellite antenna system. The satellite antenna model shown in [9] has been considered with parameters GD = 2 m, 7 = 10 dB, S = 2. Moreover, different circular polarizations have been used in adjacent cells with $[ = 10 dB. With this antenna system,
ε and ,(V(.) have been obtained by assuming a perfect power control that compensates for different distances and antenna gains. The value obtained for ε is about equal to 0.9; ,(V(.) has been derived for typical . values: that is, ,(V(. = 7) = - 34 dB and ,(V(. = 12) = - 38 dB.
Probabilities SH for both

CDMA and PRMA-HS have been numerically evaluated. The (V/1RW | th value
has been set to 6 dB
so as to have a good performance
with 1/2 rate convolutional code. Figs. 2 and 3 show the spectral efficiency obtained from the theoretical analysis presented in previous Sections. The PRMA-HS curves are for . = 7 and . = 12; the same total bandwidth in the CDMA case is obtained respectively in the cases : = 75F and : = 125F. From Figs. 2 and 3, η&'0$ does not depend on the available bandwidth. Fig. 2 compares the efficiency of CDMA and

PRMA-HS for .5 = 7 dB. For low ) values, the η350$+6 curve is interrupted, because the PRMA-HS scheme can not guarantee the 3ORVV requirement. Whereas, CDMA maintains a given efficiency also for low ) values. For high ) values PRMA-HS attains a better efficiency; the saturation of η350$+6 for high )Ã values is due to the fact that the PRMA-HS performance is limited by the collisions which restrict the maximum number of users per cell. Fig. 3 presents the spectral efficiency comparisons for .5 = 10 dB. Fig. 3 shows efficiency values higher than those in Fig. 2 for CDMA and also for PRMA-HS with low ) values; this is due to the fact that the channel allows lower SH values. CDMA attains a good performance for low ) values; for sufficiently high ) values the CDMA performance is between those of PRMA-HS . = 7 and PRMA-HS . = 12. We have also verified that if a more directive antenna and/or a different antenna model are considered, lower ε values are possible with a significant impact on η&'0$. A similar impact is not present for η350$+6. Moreover, we have verified a low dependence of η&'0$ on the altitude.

Whereas, η350$+6 depends on the satellite altitude through both ,(V(.) and RTD [6]. In Figs. 2- 3, we have selected the best satellite altitude for PRMA-HS. If a higher satellite altitude is considered, η350$+6 reduces, whereas η&'0$Ã remains practically unchanged. We have η350$+6 ≈ 0.045 bit/s/Hz for ) = 11 dB, .5 = 7 dB, . = 12, 2000 km satellite altitude with 57'PD[ = 30 ms. In the case previously considered in Fig. 2, we have η350$+6 ≈ 0.059 bit/s/Hz.


&RQFOXVLRQV

This paper presents a preliminary study on the efficiency comparison between CDMA and PRMA-HS in LEO-MSSs. A Rice channel and a typical antenna model have been used to analytically evaluate the spectral efficiency for PRMA-HS and CDMA. We have found
that PRMA-HS has not a satisfactory performance for low fading margin values, especially when the Rice factor is low. This limit is not present with CDMA, that achieves a good efficiency behavior for low fading margin values.
A further study is needed to consider different satellite antenna systems and integrated voice and data traffics.

9 Fig. 2:
PRMA-HS versus CDMA efficiency comparison for .5 = 7 dB.

Fig. 3: PRMA-HS versus CDMA efficiency comparison for .5 = 10 dB. 5HIHUHQFHV [1] S. Cacopardi, and F. Frescura, F. Martininno, “Complex CDMA Versus FDMA/SCPC for Low and Medium Rate Applications for Fixed Satellite Services”, ,QWÃ-RXUQDOÃRIÃ6DWÃ&RPP, pp. 23-34, Vol. 14, 1996. [2] S. Nanda, D. J. Goodman, U. Timor, “Performance of PRMA: a Packet Voice Protocol for Cellular Systems”, ,(((Ã7UDQVÃRQÃ9HKÃ7HFK, Vol. 40, No. 3, pp. 584 - 598, Aug. 1991. [3] V. H. MacDonald, “The Cellular concept”, %HOOÃ6\VWÃ7HFKÃ-, Vol. 58, pp. 1-41, Jan. 1979. [4] Michele Zorzi, Ramesh R. Rao, Laurence B. Milsteinà “Error Statistics in Data Transmission over Fading Channels”, ,(((Ã7UDQVÃ&RPP, Vol. 46, No. 11, pp.1468-1477, Nov. 1998. [5] H. Bischl, A. Jahn, E. Lutz, “Wideband Channel Model for UMTS Satellite Communications”, &267à  7'   [6] E. Del Re, R. Fantacci, G. Giambene, S. Walter, “Performance Analysis of an Improved PRMA Protocol for Low Earth Orbit Mobile Satellite Systems”, ,(((Ã7UDQVÃRQÃ9HKÃ7HFK., Vol. 48, No. 3, pp. 985-1001, May 1999. [7] Robert K. Morrow, “Accurate CDMA BER Calculations with Low Computational Complexity”, ,(((à 7UDQV &RPPXQ, Vol. 46, No 11, pp.1413-1417, Nov. 1998. [8] Y. Ishikawa, N. Umeda, “Capacity Design and Performance of Call Admission Control in Cellular CDMA Systems”, ,(((Ã-6$&, Vol. 15, No. 8, pp. 1627-1635, Oct. 1997. [9] F. Vatalaro, G. Emanuele Corazza, C. Caini, C. Ferrarelli, “Analysis of LEO, MEO, and GEO Global Mobile Satellite Systems in the Presence of Interference and Fading”, ,(((Ã-6$&, Vol. 13, No. 2, pp. 291-300, Febr.1995.

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