**The God Delusion - Richard G. Howe**

1 The God Delusion by Richard Dawkins Richard G. Howe, Ph.D. Emeritus Professor of Philosophy and Apologetics Southern Evangelical Seminary Vice President ...

International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. network holds the promise of delivering up to 1GBps data rate to end users mostly available at. the macrocell base station the proliferation of mobile devices has lead to very small size hot. spot and therefore require extensive dimensioning of network resources in terms of coverage. These hot spots could be homes trains airports and possibly buses with high data rate wireless. access requirements The range extension with high speed connectivity has been a major point. of interest in LTE advance standard and femtocells very small base stations installable by the. end users have been identified as the most promising potential solution Since femtocells will act. as relays between the end user and the macrocells regular base station with multiple femtocells. expected to cooperate the 4G network can greatly benefit from the ongoing research on the new. communication paradigm of cooperative relay system The deployment of a large number of. femtocells can then be used to improve coverage capacity area and system spectral efficiency. and energy efficiency of the wireless network access system. The cooperative relay communication system takes advantage of the broadcast nature of the. wireless channel to improve the communication between the source node and a destination node. with the aid of one or more relay nodes The system harnesses the new form of spatial diversity. and combat multipath fading thereby improving the spectral efficiency and reducing the. transmission error system outages and transmission power The reduced transmission power of. wireless device femtocell and macrocell effectively lowers the inter and intra macrocell. interference thereby improving both the system and the area spectral efficiency In another. development the cooperative diversity system concept has gained research impetus owing to its. inherent ability to overcome the practical implementation issue of packing a large number of. antenna elements to exploit the benefits of multiple input multiple output MIMO space time. processing techniques in small form factor devices In general there are three cooperative. relaying protocols amplify and forward decode and forward and compress and forward 3 7. The other variations include incremental opportunistic blind and semi blind relays In this. article we advocate the implementation of the amplify and forward protocol on femtocell The. advantages of this include its simplicity lower implementation cost i e relay nodes femtocells. do not have to decode and then re encode the information received prior transmission and. possibly the better privacy The main drawback of the regular cooperative amplify and forward. CAF diversity system which employs the maximum ratio combining MRC or selection. diversity combining SDC at the destination s receiver is that each relay has to transmit on the. orthogonal channels TDMA CDMA Therefore the spectral efficiency is scaled by 1 N 1. where N is the number of relays which reduces the capacity with increasing number of relays In. order to improve this Bletsas et al and Zhao et al 8 11 proposed relay selection method. otherwise known as the opportunistic relaying system ORS Here the best relay is selected prior. to relay to destination transmission to limit the number of orthogonal transmissions to two The. destination would then employ either MRC subsequently referred to as ORS MRC or SDC. subsequently referred to as ORS SDC diversity scheme on the two final diversity paths In. addition to reducing the number of independent transmissions the ORS protocols have been. shown to achieve full diversity just like regular relay system 27. Adaptive transmission is yet another powerful wireless communication strategy for improving the. spectral utilization efficiency wherein the signal constellation size power level and or the coding. rate are matched to the prevailing channel conditions based on the acquired channel side. information CSI on the feedback channel Several articles have investigated the combination of. the link adaptation and the regular cooperative diversity system both from theoretical limit. ergodic capacity and practical implementation using digital modulation schemes perspectives. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. For instance the ergodic capacity of cooperative amplify and forward CAF relay networks with. the limited CSI were derived in 12 19 for different source adaptive transmission policies in a. myriad of stochastic fading environments The performance of practical adaptive digital. modulation scheme with regular relay system was considered in 20 23 The performance of. CAF relay with constant power M QAM adaptive rate transmission when average bit error rate. ABER in Rayleigh fading is constrained to be below a specified target bit error rate BER is. examined in 21 and 22 for fixed and optimum mode switching thresholds respectively In. 23 the performance of discrete rate adaptive M QAM for a single incremental relay in. Nakagami m environment was examined while 22 investigates the performance of a. cooperative decode and forward relay network with five modes adaptive M QAM transmission. in an i i d Nakagami m wireless fading environment All these articles and related references. indicate the advantage of the adaptive cooperative diversity system over the non adaptive and or. the non cooperative system especially at low and medium signal to noise ratio SNR However. the half duplex nature of regular relay system makes the performance worse at high SNRs. With the introduction of ORS in 8 11 several articles have been published on its performance. but mostly focusing on non adaptive system i e fixed modulation Average symbol or bit error. rate ASER ABER performance for ORS MRC scheme over Rayleigh independent and. identically distributed i i d Nakagami m and independent and non identically distributed i n d. Nakagami m fading channels was investigated in 26 27 28 and 29 respectively while 30. investigated ASER of both ORS MRC and ORS SDC scheme over i i d Nakagami m fading. channel Outage capacity for ORS MRC and ORS SDC has been considered in 31 It is. important to note that until now only a few articles have considered the link adaptive ORS. system For instance ergodic capacity with the source adaptation techniques have been. considered in 32 35 for the ORS MRC scheme over Rayleigh fading channel while the variable. rate constant power adaptive M QAM modulation with ORS MRC and ORS SDC schemes over. Rayleigh fading have been considered in 35 36 and 37 respectively Also 38 analyzed the. performance of link adaptive incremental opportunistic relaying over i n d Rayleigh fading. channels However 39 studied the performance analysis of cooperative communication with. only ORS SDC scheme Careful study of the adaptive ORS schemes 32 39 indicates that the. analyses of both the ergodic capacity and the practically achievable spectral efficiency have been. obtained using the probability density function method which can be very tedious and may not. always yield compact solutions, In contrast in this article we develop a new analytical framework based on the marginal MGF. method for evaluating the ASER mean spectral utilization efficiency and outage probability. performance metrics i e since the MGF of total received SNR may be easier to compute or. readily available for CAF relay networks The developed analytical framework is thenused to. analyze and compare the performance of regular MRC SDC opportunistic MRC and SDC CAF. relay schemes that employ constant power adaptive discrete rate M QAM M PSK transmission. The proposed analytical framework is general and can be applied to any arbitrary fade. distribution as long as the MGF of the end to end SNR is available unlike channel specific. derivations in 32 38 For completeness purpose the ergodic capacity with optimal rate. adaptation was also presented Numerical analysis indicates that ORS MRC leads the pack. considering the ergodic capacity and achievable spectral efficiency while the regular MRC is the. best in terms of the outage probability and ASER In the overall the ORS MRC is the best due to. the additional power saving as it consumes only 2 N 1 of the total power consumed by regular. MRC Therefore not only does it perform well as a communication paradigm it also supports. green technology due to its low transmit power requirement Careful literature search indicates. that this is perhaps the first time such comprehensive analysis of regular and opportunistic CAF. relay network with the link adaptation is being reported. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. The remainder of this article is organized as follows In Section 2 the system model is discussed. Section 3 derives the performance metrics for the CAF relay networks with adaptive M QAM M. PSK modulation Selected numerical results are presented in Section 4 Our conclusions are given. in Section 5,Figure 1 Link adaptive cooperative relay networks. 2 SYSTEM MODEL,2 1 TOTAL MGF OF CAF RELAY NETWORKS. In this section we will present the moment generating function MGF of the relayed path of. different cooperative diversity and opportunistic routing protocols that will be utilized in. evaluating the end to end ASER mean spectral efficiency and the outage probability. performance metrics of the proposed network over a myriad of fading channels with the adaptive. M QAM M PSK modulation schemes, 2 1 1 REGULAR COOPERATION CAF RELAYING WITH MAXIMUM RATIO COMBINING. MRC AT THE DESTINATION, In this protocol as shown in Fig 1 source node S which communicates with a destination node D.

via a direct link and through N amplify and forward relays Ri i 1 2 N in two transmission. phases During the initial Phase I S transmits signal x to D as well as to the relays Ri where the. channel fading coefficients between S and D S and the i th relay node Ri and Ri and D are. denoted by s d s i and i d respectively During the second phase of cooperation each of the N. relay nodes transmits the received signal after amplification via orthogonal transmissions e g. TDMA in a round robin fashion and or FDMA Hence the channel usage per source. transmission U N N 1, Now consider that the maximum ratio combiner MRC is employed at a D to coherently. combine all the signals received during Phase I and Phase II the total received SNR at output of. the MRC detector can be shown to be e g 19 20 25,TM R C s d i d. i 1 s i i d 1, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. s i i d s i i d is the harmonic mean SNR a b a b Es No corresponds to the. instantaneous SNRs of link a b Es denotes the average symbol energy and N0 corresponds to the. noise variance, The approximation of 1 is obtained by recognizing that the instantaneous SNR of a two hops. path can be accurately estimated to be the harmonic mean of the individual link SNRs especially. at moderate high SNR regimes 43 Hence it is straight forward to show that the MGF of end to. end SNRis given by, where s and s are the MGFs of the SNR for the S D link and the relayed paths.

respectively The MGF of SNR for single channel reception is readily available in the literature It. has been shown in the literature that the evaluation of the MGF PDF and CDF of i is a daunting. task with existing results limited to Rayleigh fading 41 and Nakagami m 42 fading channels. with integer m and even in such cases the expressions are too complicated and mostly useless for. the system level analysis However it has been shown in 43 that i HM in 1 can effectively. approximate i especially at medium and high SNRs Also in this case the MGF expressions are. still difficult to obtain with the existing results limited to Raleigh fading 44 and i i d Nakagami. m 43 channels Due to this limitation the bounds have been developed for i and it is given by. i UB min s i i d, For instance the closed form formula for the MGF of i UB in a Nakagami channel with i n d. fading statistics is given by 51,mk mj j mk s k mk j 3. 1 mj mk 1 mk,s j k j mk k mj,k s i i d k k j k j k. where q E q corresponds to the mean SNR of link q is the Gamma function and mqis the. Nakagami m fading index, 2 1 2 REGULAR COOPERATION CAF RELAYING WITH SELECTION DIVERSITY COMBINING. SDC AT THE DESTINATION, In this kind of protocol implementation the best route is selected at the destination node based on.

the end to end relay SNR Here in the case of SDC the channel usage per source transmission is. similar to the MRC case i e U N N 1, For this protocol the effective SNR at the output of the SDC detector i e all the signals received. during Phase I and Phase II is given by, TSDC max s d 1 2 N max s d min s 1 1 d min s 2 2 d min s N N d 4. For instance the MGF of TSDC for a special case of independent and identically distributed i i d. Nakagami m fading statistics can be obtained from Appendix A as 45. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. m N N m 1 2 p m,s m m 1 m 5,SDC s 1 sm 1 p,m 1 2 F1 1 m 1 m 1 s 1 2 p m. i1 i2 i2 p j 1 j m 1 s 1 2 p,where 2 F1 is the Gauss hypergeometric function. 2 1 1 CAF RELAYING WITH OPPORTUNISTIC ROUTE SELECTION AND SDC ORS SDC AT. THE SOURCE, The ORS SDC relaying protocol focuses on limiting the number of cooperating relay to one.

Additionally the choice of the appropriate route is selected by the source assuming that the relay. with the best transmission parameter is already determined during the route discovery process or. can be accomplished in a distributed fashion among the relays as proposed in 8 Compared to. the regular cooperative diversity protocol discussed above the best route is selected at the source. based on the end to end relay SNR Therefore the statistics of the best route selection is the same. as the selection diversity combining at the destination as the best among N 1 links is being. selected However the channel usage per source transmission in the case is U N 2 i e source. will broadcast the signal to all the relays and destination in first time slot and in the second time. slot one of the best relay amplify and forward the signal to the destination Therefore the. spectral efficiency here does not reduce with the increasing number of relays as in the case of. regular cooperative diversity protocols discussed above i e MRC and SDC only Also the. amount of channel side information and the implementation complexity is highly reduced. 2 1 2 CAF RELAYING WITH OPPORTUNISTIC RELAY SELECTION AND MRC ORS MRC AT. THE DESTINATION, This protocol implementation takes advantage of the half duplex nature of the relay transmission. to achieve better performance than the ORS SDC protocol Here since the source transmits in the. first transmission phase and due to the broadcast nature of the wireless channel the destination. can be close enough to receive this signal before receiving the signal from the relay This is. particularly true in the distributed ORS protocol implementation proposed in 8 Therefore if the. channel side information of both the links is available the received signal can be combined with. the MRC scheme at the destination Note that the transmission channel usage U N 2 each. source transmission but the statistics is slightly different from the pure ORS SDC protocol The. effective end to end SNR of the ORS MRC protocol can be expressed as. TORS MRC s d max 1 2 N s d max min s 1 1 d min s 2 2 d min s N N d 6. The MGF of TORS MRC for a special case of independent and identically distributed i i d. Nakagami m fading statistics can be obtained from Appendix B as 45. ORS MRC s 1 s,p 1 p i i i,1 2 2p j 1 ij s 2p, Hence by utilizing the above mentioned closed form MGFs of the four protocol schemes we can. easily analyse and compare the performance of CAF relay networks in terms of mean achievable. spectral efficiency outage probability and average symbol error rate. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. 2 2CUMULATIVE DISTRIBUTION FUNCTION CDF OF THE TOTAL END TO END SNR. To evaluate the various performance measures the knowledge of the CDF of total effective SNR. T of the CAF relay networks is required Since the analytical CDF expression for the CAF relay. networks is difficult to obtain the alternative is to compute the CDF from the MGF expression in. One of the most efficient frequency inversion method is the Abate s Fixed Talbot method i e. multi precision Laplace transform inversion 16 viz. FX x X r e rx Re e xs k X s k 8, where r 2Z 5 x k k Z s k r k j cot k k k k cot k 1 cot k and positive. integer Z can be chosen to get the desired accuracy Utilizing 8 we can easily compute the CDF. expressions from its respective total MGF expression for the CAF relay networks. 3 ADAPTIVE MODULATION, In this section we develop a new analytical framework based on the marginal MGF for. evaluating the ASER mean spectral utilization efficiency and outage probability performance. metrics It will shown that the mean achievable spectral efficiency of ADR M QAM M PSK and. ASER of CAF relay networks with adaptive source transmission can be expressed in terms of. difference of two CDF terms The ADR M QAM M PSK schemes are first explained followed. by the outage probability the mean spectral efficiency and the average SER analysis. 3 1 ADR M QAM M PSK SCHEMES, In the adaptive modulation techniques the destination node needs only to compute the total.

received SNR select the appropriate transmission rate and feedback this information to the. transmitter In context of CAF relay system the destination node only needs to compute and. convey the information on the total effective received SNR to the source node for it to select an. appropriate transmission rate This results into a higher mean achievable spectral efficiency. without having to sacrifice the error rate performance For this reason and more specifically due. to several other practical advantages of the adaptive rate modulation we consider both the. adaptive M QAM and the M PSK digital modulation schemes in this paper to improve the. performance of the CAF relay networks, In order to simplify the analysis of the adaptive modulation there is a need to express. instantaneous error rate in desirable exponential form similar to the one in the existing literatures. 21 25 Here we employ the exponential type representations of the instantaneous SER for the. M PSK and the M QAM schemes and are respectively given by 40 Table II. b1 s sin 2 M 2b1 s sin 2 M,3 b1 s 3b1 s 6 b1 s 9 b1 s. 2kc1 ka1 e,M 1 k 2 a1c1e, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. where k M 1 M M is the constellation size and parameters a1 0 2938 b1 1 0483. c1 0 5070 are obtained from 40 Table I The above exponential forms particularly facilitate. the averaging of the SER over the fade distribution The resulting average symbol error rate. ASER expression taking advantage of Laplace transform property which can be evaluated as. the weighted sum of the MGF of end to end SNR of fading channel can be expressed as. PM PSK a1 b1 sin2 M c1 2b1 sin2 M 11,3b1 3b1 2 6b1 9b1 12. P M QAM 2ka1,2kc1 ka1 M 1 kc1 M 1 k a1c1 2 M 1,where is the MGF of SNR for single channel.

In the ADR M QAM M PSK system the range of the effective received SNR is divided into T 1. fading regions When the fading causes the total received SNR to fall into the n th region n 0. 1 T the constellation size M n 2n is employed for the transmission Also the SNR thresholds. for partitioning of the total received SNR depends on the target SER level Ps The region. boundary n is chosen for the corresponding transmission mode n to be the minimum SNR. required to achieve Ps which can be easily obtained by inverting 9 and 10 for M PSK and M. QAM modulation schemes respectively,1 a1 a12 4c1 PS. b1 sin 2 M n 2c1,a1 a12 4c1 Mn,where n 1 2 3 T and T 1. It is worth to mention here that the two exponential terms are more accurate than the existing. invertible expressions in the literature 46 48 Representative example has been shown in Fig 2. where a comparison has been made between the proposed approximation and the single and two. exponential term approximation in 47 and 48 respectively This figure highlights that our. proposed exponential approximation 11 12 yields a very good estimate of the actual ASER. performance over a wide range of average link SNRs different fading severity indices and for. different constellation sizes It is evident from the figure that the proposed approximation. performs better than 47 and 48 for the M QAM and better than 48 for the M PSK. Therefore for the rest of the analysis in this article the proposed two exponential term. approximation will be utilized, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. 10 32PSK m 1,Avearage Symbol Error Rate,10 4QAM m 1. 5 47 Eq 17,Proposed Method,0 5 10 15 20 25 30,Mean SNR Per Symbol dB.

Figure 2 ASER of M PSK and M QAM over Nakagami fading channels m 1 and 3 without diversity. 3 2 OUTAGE PROBABILITY, When the total received SNR falls below the region boundary threshold 1 1 can be obtained by. setting n 1 in 13 or 14 we cease the transmission because the prescribed target SER. cannot be satisfied even with the smallest constellation size The probability of such an outage. event is given by Pout F 1 where the CDF term can be evaluated efficiently using 8. 3 3 MEAN SPECTRAL EFFICIENCY, The normalized average achievable spectral efficiency for ADR M QAM PSK is given by the. weighted sum of the data rates in each of the partitioned regions 21 25 viz. where p n denotes the transmission mode selection probability i e probability that the total. received SNR falls in the n th partition region,f d F n 1 F n 16. Hence using the appropriate MGF expressions derived in 43 44 49 in 8 we can readily. compute the mean spectral efficiency of the ADR M QAM PSK in a myriad of wireless fading. environments, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. 3 4 ASER OF ADAPTIVE M QAM PSK, The ASER of ADR M QAM PSK can be calculated as the ratio of the average number of error.

bits per transmission divided by the average number of bits per transmission 47 viz. ASERadr 17,n F n 1 F n, where SERn is the average SER in a specific SNR region of n 1 n and can be represented as. where PM is the CEP of the modulation scheme in AWGN channel For the special case of M. PSK scheme we can derive the SERn by substituting 9 in to 18 viz. a exp b sin M c exp 2b sin M f d, a1 b1 sin2 M n 1 b1 sin2 M n c1 2b1 sin2 M n 1 2b1 sin2 M n. and the term e f d in 19 denotes the marginal MGF of the total received SNR. Note that although this quantity is available in closed form for non cooperative system e g 48. similar expressions do not appear to be readily available or generalized for the CAF relay. networks particularly in a generalized wireless fading environment Utilizing 51 Appendix C. we can compute the desired marginal MGF as a difference between two CDF terms of an. auxiliary function viz,SERn a1 F a n 1 F a n c1 F n 1 F n 20. where F a x and F b x in 20 can be evaluated efficiently via 8 but using the MGF formulas. of the auxiliary functions i e s s b sin M and s s 2b sin M Similarly treatment. can also be applied to the M QAM modulation scheme by substituting 10 into 18. Eq 20 allows us to generalize the evaluation of ASERadr over arbitrary multipath shadowing. fading as long as the MGF of SNR of fading channel is available This is in sharp contrast with. channel specific PDF methods in 32 34 which limited their analysis to Rayleigh fading channel. 4 NUMERICAL RESULTS, In this section selected numerical results are provided for the normalized mean achievable. spectral efficiency outage probability and ASER performance metrics of CAF relay networks. with both the adaptive discrete rate M QAM and M PSK digital modulation schemes In. particular we are comparing the performance of four distinct cooperative diversity and. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. opportunistic routing protocols i ORS MRC ii ORS SDC iii MRC and iv SDC over the. i i d Nakagami fading environment including special case of Rayleigh fading Moreover the. ergodic capacity analysis with the optimal rate adaptation policy is also presented for the. theoretical performance limit of the above protocol schemes To generate plots the mean link. SNRs are chosen arbitrarily as s 1 s 2 s 3 1 d 3 d s d Es N0 and the fading indexes 2 d. on the each links is chosen as m 3 unless states otherwise For the ADR system the target. SER of 10 3 is arbitrarily chosen, Fig 3 illustrates the ergodic capacities of the ORA policy using four different protocols i e.

ORS MRC ORS SDC SDC and MRC To generate the plots we have used the following. generalized expressions in terms of the MGF of end to end SNR of CAF relay networks 11. C O RA 1 1,U N ln 2 0 y, Expression 21 indicates that the ORA capacity evaluation requires only the knowledge of the. MGF of SNR of the fading channel By substituting the total MGF of the above mentioned. protocols into 21 we can easily generate the curves as shown in the figure From the figure we. can observe that the performance of the opportunistic relay scheme i e ORS MRC and ORS. SDC is better than the regular cooperation i e MRC and SDC respectively This improvement. in the performance of the ORS scheme is due to the utilization of the two orthogonal slots for the. total transmissions compared to the three slots in the regular cooperation Moreover it is. interesting to note that the authors in 28 compares the ergodic capacities of the CAF relay. network using best relay selection and the regular MRC scheme However their framework does. not lend itself to the analysis of the ORS SDC or the SDC case whereas our framework. encapsulates the performance of all the four protocols. Normalized Channel Capacity C B bits sec Hz,0 5 10 15 20. Figure 3 Ergodic channel capacities of the optimal rate adaptation ORA policy with two cooperative. relays N 2, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. Fig 4 shows the comparison in terms of spectral efficiency of the different cooperative diversity. and the opportunistic routing protocols with the adaptive M PSK modulation It is worth to. mention that for a single relay case the ORS MRC gives the same performance as the MRC. scheme while the ORS SDC scheme also gives the same performance as the SDC scheme. However as the number of relay increases ORS MRC performs better than the regular MRC. protocol at medium and high SNRs while the ORS SDC protocol performs better than the regular. SDC protocol throughout the SNR range This is because irrespective of the number of relays in. the participation the total channel usage for the ORS MRC and the ORS SDC is kept constant at. two time slots per source transmission whereas the channel usage for MRC and SDC schemes. increases with increasing number of relays Moreover to further improve the spectral efficiency. we incorporate the adaptive M PSK modulation scheme compared to fixed modulation schemes. in the previous literatures to adapt the transmission rate with the varying channel conditions It is. evident from Fig 4 that by increasing the maximum constellation size transmission modes in. the ADR M PSK directly translates into improved spectral efficiency However this. improvement is achieved at the expense of the increased ASER see Fig 5 In summary the link. adaptive ORS MRC scheme gives the best overall performance Hence it can be concluded that. the ORS MRC protocols are recommended for the cooperating nodes at the tactical edge or at the. cell boundary where the received signal strength is weak. 1 8 ORS SDC T 4, Normalized Average Spectral Efficiency bits sec Hz. 0 5 10 15 20 25 30,SNR Es No dB, Figure 4 Comparison of different cooperative diversity and opportunistic routing protocols with adaptive.

M PSK modulation T 3 and 4, Fig 5 illustrates the average symbol error rate ASER of a CAF relay network with the adaptive. M PSK modulation using T 3 and 4 We observe that the ASER of the MRC scheme is the. lowest whereas the ORS SDC scheme is the highest This is due to the availability of the total. N 1 diversity paths in the MRC scheme However this is achieved at the expense of the power. efficiency as the ORS SDC and the ORS MRC requires only 1 N 1 and 2 N 1 of the total. power of the regular MRC scheme respectively, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. Average Symbol Error Rate,10 ORS MRC,0 5 10 15 20 25 30. SNR Es No dB, Figure 5 Average symbol error rate of a CAF system with different cooperative diversity and opportunistic. routing protocols using adaptive M PSK modulation T 3 and 4. Normalized Average Spectral Efficiency bits sec Hz. 0 5 10 15 20 25 30,SNR Es No dB, Figure 6 Comparison of different cooperative diversity and opportunistic routing protocols with adaptive.

M MQAM modulation T 5 consisting of two relays, Fig 6 shows the spectral efficiency performance comparison of the four cooperative diversity and. the opportunistic routing protocols with the ADR M QAM modulation scheme with T 5 This. figure highlights the influence of the channel fading severity on the performance of the link. adaptive cooperative system While the performance trend among the protocols is similar to the. one obtained in Fig 4 Fig 6 in particularly shows that as the channel condition improves the. International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. achievable spectra efficiency improves To the best of our knowledge this effect has never been. reported in the earlier literature and it also demonstrates the versatility of our mathematical. 10 ORS SDC,Outage Probability 10,0 5 10 15 20 25,SNR Es No dB. Figure 7 Probability of outage of a CAF system with different cooperative diversity and. opportunistic routing protocols using adaptive M PSK modulation T 3 Note that for N 1 the. ORS MRC and MRC whereas for any values of N ORS SDC and SDC schemes are the same. Figure 7 depicts the outage probability as a function of SNR at the target SER of 10 3 and it. highlights the benefit of the cooperative diversity to maximize the performance of the wireless. communication system From figure 7 we conclude the following important observations First. we notice that the case with cooperative diversity i e N 3 evidently outperforms the case with. N 1 Second the outage probability with the MRC protocol has a better performance than all the. other protocols similar to the case in fig 5 for the ASER analysis with the MRC protocol This. performance gain is due to the additional diversity path offered by all the relays and direct path in. the system but still at the expense of the power efficiency. 5 CONCLUSIONS, This paper analyzes the performance of cooperative amplify and forward CAF relay networks. that employ the adaptive M ary quadrature amplitude modulation M QAM M ary phase shift. keying M PSK digital modulation techniques in the Nakagami m fading channel model In. particular we present and compared the analysis of the CAF relay networks with different. cooperative diversity and opportunistic routing protocols such as Maximal Ratio Combining. MRC Selection Diversity Combining SDC Opportunistic Relay Selection with Maximal. Ratio Combining ORS MRC and Opportunistic Relay Selection with Selection Diversity. Combining ORS SDC We advocate a simple yet unified numerical approach based on the. marginal moment generating function MGF of the total received SNR to compute the average. symbol error rate ASER mean achievable spectral efficiency and the outage probability. performance metrics These analytical frameworks and results will facilitate the choice of. cooperation protocol and configurations that can be employed in the design and deployment of. femtocells, International Journal of Computer Networks Communications IJCNC Vol 8 No 3 May 2016. APPENDIX A, This section provides the derivation for the MGF of end to end SNR of CAF relay system with.

SDC protocol at the destination This is also applicable to the ORS scheme with SDC at the. destination, The CDF of the end to end SNR given in 4 can be expressed as. F SDC F s d r 1 F r F s d r 1 1 1 F s r 1 F r d A 1. where F s d F and F are the CDFs of the source to destination source to relay and. relay to destination links respectively, The effective MGF can then be evaluate using the differentiation property of the Laplace. transform via a single integral expression,SDC s s e s F s d r 1 F r d. F s d r 1 1 1 F s r 1 F r d d, For special case of independent and identically distributed i i d Nakagami m channel the MGF. can be reduced to 30,s s e 1 1 e,T 0 m p 1 p j 1 i j.

i1 i2 i2 p, where G is the lower incomplete gamma function and i. Using the identity 52 Eq 6 455 2 after few algebraic manipulations the closed form MGF. expression can be obtained as shown in 5,APPENDIX B. This section provides the derivation for the MGF of end to end SNR of ORS CAF relay system. with MRC protocol at the destination, The effective MGF of 6 can be evaluated using the addition and differentiation properties of the. Laplace transform via a single integral expression given by.

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