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Efficiency Comparison Between CDMA and PRMA HS in Low Earth

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Efficiency Comparison Between CDMA and PRMA HS in Low Earth (IILFLHQF\&RPSDULVRQ%HWZHHQ &'0$DQG350$+6LQ/RZ(DUWK 2UELW0RELOH6DWHOOLWH6\VWHPV $QGUHD$EUDUGR*LRYDQQL*LDPEHQH'DYLG6HQQDWL 'LSDUWLPHQWR GL ,QJHJQHULD GHOO¶,QIRUPD]LRQH 8QLYHUVLWj GHJOL 6WXGL GL 6LHQD 9LD 5RPD 6LHQD ,7$/< $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. ,QWURGXFWLRQ 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.
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