Chapter 3: Lognormal Shadowing and Outage Probability

Transcription

1 Chapter 3: Lognormal Shadowing and Outage Probability 3.1 Introduction Mobile stations in any cellular network experience multipath fading and shadowing. Various Base stations of any cluster containing re-usable channels have important bearing towards multipath fading. Fading and shadowing become more critical in assuring a quality of service. Frequent mobility of Mobile stations (MS) adds another dimension. This paper investigates various models proposed to study multipath fading and shadowing. Shadowing has been analysed analytically in [3.1], [3.2] and it is shown to be dependent on location of MS in a cell. Outage in communication due to shadowing is a challenge in assuring service and hence should be reasonably predicted to compensate for the losses. Fig.3.1: Normal Distribution [Internet] Due to limited spectrum allocation, same frequency channels have to be reused in any cellular network. Network coverage area is divided in smaller definite boundary areas known as cell. Each cell has a base transmission station. Also, cells are allocated some channels over which mobile stations are extended services. Hence reuse of channels ensure better spectrum utilizations however, this importantfeature also contributes immensely to interference referred as co-channel interference.shadowing could be modeled as a random process that has log normal distribution. It may also be noted that shadowing may be treated as statistically independent or dependent event. In another approach, it may be desirable to compute the effect of interference on any MS due to various BS present within the re-use distance. Most of the estimations have to

2 be approximated with tighter bounds. 3.2 Fading Fading can be classified as deviation experienced in the signal power. It can also be termed as attenuation in signal power experienced by a signal over certain propagation media. The fading is not constant and may vary with time and geographical position. It is also heavily dependent on radio frequency. Fading is a complex random phenomenon and hencemodeled as a random process. A fading channel is a communication channel that experiences fading. In wireless systems, fadingmay either be due to multipath propagation which is referred to as multipath induced fading, or due to shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow fading Flat fading This process is experienced when channel has adequate bandwidth to accommodate passing signal. Hence, the coherence bandwidth of the channel is larger than the bandwidth of the signal.therefore, all frequency components of the signal will experience the same magnitude of fading Frequency Selective Fading In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth of the signal. Different frequency components of the signal therefore experience varied amount of fading. 3.3 Call Holding Time and Cell Residence Time Performance analysis of cellular systems with Poisson arrivals and exponential Call Holding Times (CHT) adopts the fixed guard channel (GC) scheme. It was analysed by a number of authors [3.3, 3.4, 3.5]. However, there are conflicting results in the literature on the validity of Poisson arrivals and exponential CHT [3.6, 3.7]. Dharmaraja et al. [3.8] presented a performance model with general distributed handoff inter-arrival times and exponential Call Holding Time (CHT). It was shown in [3.9] that actual CHTs are significantly different from the exponential distributions. Wireless technologies such as Universal Mobile Telecommunication Systems (UMTS) and Code Division Multiple Access (CDMA 2000) support voice, video and data traffic that rely on Internet Protocol (IP). TCP/IP traffic has inherent properties of self-similarity and burstiness that cause the correlation in inter-arrival times of the incoming traffic [3.10]. Hence, the popular belief of exponentially distributed CHT and inter-arrival times gets challenged for 3G and beyond cellular networks.

3 Total time of presence of a mobile user or its dwelling in a cell which is called Cell Residence Time (CRT) depends on the mobility of the user, the geographic situation and the handoff scheme used. Hence it should be modeled as a random variable following a general distribution. To assess the realistic performance measures, it is necessary to consider the appropriate probability distributions for call arrivals, CRT and CHT. Markovian arrival process (MAP) can model the call arrivals. It can smoothen total traffic by statistical aggregations [3.10] and allows correlation in the inter-arrival times of the incoming traffic. CHT and CRT can be modeled as random variables with general distributions to capture the effects of various factors such as handovers during a call session, mobility and others [3.16]. Random variables with general distributions make performance analysis of a cell very complex. To proceed further in this regard necessitates further assumptions [3.11]. It is shown in [3.12] that a general distribution can be approximately represented by a set of distributions that is a convolution of different exponential distributions. In [3.13] an analytical model of the wireless networks with voice calls arriving according to MAP was presented. Phase-type distributed CHT and CRT. Similar and burstynature of the voice/video and voice/data traffic have been modeled in [3.14] and [3.15] respectively. 3.4 Received Signal Strength at any MS A MS will receive RF form different BS in range which will traverse through different propagation distance. We may simply put path loss as the difference between transmitted signal power and received signal level. Path loss may heavily depend on shadowing and multipath fading. We may ignore multipath fading if received signal level is averaged over few wavelengths path difference. If we consider N to be No of base station in the cluster; (x, y) denoting location of MS within i th BS coverage area then signal strength from i th BS at a pt(x, y) is given as p(r x, y) = p (r d ) = exp(r mx )2 πσ 2σ2 (3.1) i = 1,2,3, N mx denotes estimated values and is averaged over d i (distance between MS at (x,y) and i th BS) considering the factor Base Transmission power and antenna height &using Okumura prediction

4 method. Eq. 3.1 indicates received signal level at any point (x,y) because of a BS. We use Bayes rule to predict pdf of MS at (x,y) as : p(x, y ri) = (, ). (, ) ( ) i = 1,2,3, N (3.2) Here p (x, y) gives the pdf of MS which is located at (x,y) and p (r ) indicated PDF of r i over different values of (x,y). PDF of r i i.e. p (r ) is independent of the MS location (x,y) and hence we may assume : Equation 2thus reduces to : p (x, y) p (r ) = k (constant) p(x, y ri) = k. p(r x, y) 2πσ i = 1,2,3, N = k. exp(r mx )2 i = 1,2,3.. N (3.3) 2πσ Wemay sum up the pdf over all the BS at r = [r 1,r 2,.r N ] p (x, y/r) = K.p (r/x, y)kis any constant. Since r = [ r, r,.. r ] are all statistically independent: p (x, y/r) = k p (x, y/ri) p (x, y/r) = K p (x, y/ri) Hence above statement clearly indicates that pdfof revived signal strength at any MS is product of individual signal strengths of each BS in the cluster.

5 Fig. 3.2: PDF of different signals received at Mobile receiver [Internet] 3.5 Outage probability for any MS As mentioned earlier, shadowing are usually statistically independent however in some cases it may be statistically correlated. Estimation of outage probability requires pdfof sum of lognormal random variables representing the shadowing. Various methods have been suggested in previous literatures to compute correlated as well as statistically independent lognormal RVs. Outage probability can be determined by summing up correlated of normal RVs. As in [3.17], we assume the desired signal S and interfering signal I to correlated. Then X = l n [S] and Y = l n [I] both will be generate a jointly GaussianRV. This may be interpolated as S = e and I = e. The outage probability could be computed by using Wilkinson s approach and [3.18]. 3.6 Shadowing and reuse factor It has been shown in [3.18] that as shadowing becomes more correlated; the reuse factor for any given outage probability also goes up. It is also shown that increase in correlation among the signal and interference, reuse factor decreases. Determining CDF of sum of correlated lognormal RVs is a pre-requisite to predict outage probability.

6 N = 1, 2, 3, 4, 5, 6, 7 (x,y) = location of MS 0 = location of BS r i distance of MS from i th BS i = 1, 2,..N Fig 3.3: Cluster of Seven Cells We may consider outage as a special case where in the power of interfering signals is more than the desired signal power. Over and above that a protection margin is also added to ensure reasonable QoS assurance. Reasonable estimate of outage in presence of shadowing is crucial to all the cellular networks. Re-use distance [3.17] is an indication as to how frequently a channel can be recycled. Smaller reuse distance ensures more reuse of spectrum. However it may indicate higher shadowing due to correlated lognormal interferes. Fig. 3.4 : Rayleigh Fading envelope for 900 MHz [internet]

7 3.7 Multi-Hop Retransmission In a divergent approach [3.19], concept of multi-hop relaying was suggested by a cooperative macro diversity system. Diversity is an effective method to negate shadowing. In this concept,any MS may be served by many BS. However, power transmitted by the MS is effective to nearest BS only and has least impact to the farthest BS. In order to address this issue, idea of multi hop cooperation has been mooted. This envisages relay of information from source via intermediate BS acting as relay point, to destination. This ensures longer reach of wireless channel and is found suitable in reducing effects of shadowing. Fig. 3.5 : Diversity Model To Counter Shadowing A circular cellular structure sectored into threesectors. Sectors are assumed to have three BS at vertices as shown in fig 3.2. Cell is sub-divided into three sectors each having one BS, with sectored antennas. Every sector has one intermediate relay station (IRS). IRS is used to relay messages to their respective BS in case where MS is not co-located within their sectors. IRS can simply amplify the signal received from MS or on the other hand it may regenerate and retransmit the MS signal to corresponding BS. MS as shown in figure, can communicate with BS1 directly, however uses IRS2 and IRS3 to relay its message to BS2 and BS3 respectively. It is assumed that MS cannot communicate to BS2 and BS3 directly as its transmitted power is not sufficient to reach there. MS loc at a K can communicate with BS1 and BS2 directly however needs IRS3 to communicate with BS3. Performances of two hop relay system have been compared with conventional single hop system and it has emerged that under the influence of shadowing, multiple hop system outperforms.

8 It was shown that multi hop system has shown approx 2-4 db improvement over conventional setup under similar average BER. This improvement in performance is attributed to reduction in path loss due to shadowing. Performance of multi-hop system also degrades as shadowing increases; however, it still does better as compared with single hop system. Hence effect of shadowing can be offset at the cost of increased complexity of the system. Reuse distance is defined as the distance between the centers of nearest co-channel cells. Considering Rician fading, reuse distance could be dependent on components of desired signal and interfering signals. Normalized ruse distance could be defined as : D= d is reuse distance and r is the radius of cell. As shown in [3.22], reuse distance could be determined by ratio of distances to the desired station d 0 and interfering stations d I as D= = 1 + ( ) Since we consider hexagonal sized cells, it can be seen from [3.23] that cluster sizes can be related to reuse distance as under: S = S can be determined as S= i 2 +j 2 +ij where i&j are shown as under: Fig 3.6 : Cluster Showing Reuse Distance

9 i&j are positive integers. For case shown in fig.3.3 i=2 & j=1 Hence S=7. As S and D are dependent on desired and interfering signals; it can be inferred that cluster size can be optimized depending on operating conditions. Parameter Name [Unit) Value Cluster Size 19 Number of BS 19 Number of Cells 49 Antenna ht MS/BS 1.5/30 Carrier Frequency 24 Hz Bandwidth 5 MHz Channel Reuse 1 Table 3.1: Parameters of system level Simulator used in [3.18] 3.8 Results and Discussion In cellular network, fading is deviation of the attenuation that a signal experiences over certain propagation media. The fading may vary with time, geographical position or radio frequency. Hence fading is often modeled as a process. Afading channel is also a communication channel that experiences fading. In wireless systems, fading may either be due to multipath propagation, referred to as multipath induced fading, or due to shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow fading.as we discussed in this chapter, it is extremely difficult to compute lognormal shadowing due to composite fading phenomenon Approximation for Shadowing Computing exact amount of fading or predicting the nature of shadowing due to composite fading is extremely difficult. However, there are different approximation approaches available which put strict bounds. In [3.20],fourdifferent approaches have been discussed towards estimating the resultant log normal distribution. Approximation methods resort to recursive evaluation using numerical analysis methods and matching cumulates or joint moments. Four different approaches to compute CDF of independent lognormal RVs could be classified as:

10 Wilkinson s, Schwartz &Yeh s, Schleher s Farley s approach Shadowing Bounds Itis seenthat Wilkinson s approach is much simpler to use and it provides very accurate results in case of CDF < 0.1. Reference [3.7] discussed sum of independent lognormal random variables. A modified power lognormal distribution was suggested in [3.21] and it was shown to be simpler and more effective in cases where σ 2 i(variance) are same and only µ i differ. It may also be possible to model desired signal as Rician faded while co-channel interferers are modeled as Rayleigh faded. It is assumed in [3.8] that desired signal will have line of sight (LOS) where as co-channel interferers may not have LOS. A more generalized form of outage probability to show lognormal shadowing and fast Rician fading was presented in [3.22]. It was shown that lognormal only shadowing cases could be considered as special cases where in Rician fading has also been considered for LOS Lognormal Interferers and Reuse Distance Signals arriving at any mobile station can be modeled as correlated lognormal interferers. Estimation of outage probability due to correlated interferers could be modeled as Rician and lognormal random variables. Outage probability had to be estimated within tighter bounds due to computational complexity. Wilkinson formula has been quoted in this chapter. It is important to see that increased correlation among interferes demands higher reuse distance. However, smaller reuse distance ensures more re-use of spectrum. Hence, tradeoff between correlated shadowing and reuse factor is established.

11 References [3.1] R Prasad and K Kegel, Improved assessment of interference limits in cellular radio performance, IEEE Trans on veh Tech. vol VT-40, PP , May [3.2] A.A. Abu-Dayya and N C Beaulien, Outage probabilities of diversity cellular systems with cochannel interference in Nakagami Fading, IEEE Trans. on Veh-Tech., vol VT-41 PP , Nov [3.3] D. Hong, S.S. Rappaport, Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and nonprioritized handoff procedures, IEEE Transactions on Vehicular Technology 35 (3) (1986) [3.4] G. Haring, R. Marie, R. Puigjaner, K.S. Trivedi, Loss formulas and their applications to optimization for cellular network, IEEE Transactionson Vehicular Technology 50 (3) (2001) [3.5] R. Ramjee, R. Nagarjan, D. Towsley, On optimal call admission control in cellular networks, ACM/Baltzer Wireless Networks Journal 3 (1) (1997) [3.6] S.H. Choi, K. Sohraby, Analysis of a mobile cellular system with handoff priority and hysteresis control, in: Proceedings INFOCOM 2000, 2000, pp [3.7] S. Dharmaraja, K.S. Trivedi, D. Logothetis, Performance modeling of wireless networks with generally distributed handoff inter-arrival times, Computer Communications 26 (2003) [3.8] A. Jayasuriya, D. Green, J. Asenstorfer, Modelling service time distributions in cellular networks using phase-type service distributions, in: IEEE International Conference Helsinki, Finland, vol. 2, 2001, pp [3.9] A. Klemm, C. Lindemann, M. Lohmann, Traffic modeling of IP networks using the batch Markovian arrival process, Computer Performance Evaluation/TOOL, 2002, pp [3.10] M. Rajaratnam, F. Takawira, Non-classical traffic modeling and performance analysis of cellular mobile networks with and without channel reservation, IEEE Transactions on Vehicular Technology 49 (2000) [3.11] Takayuki Osogami, MorHarchol-Balter, Closed form solutions for mapping general distributions to quasi-minimal PH distributions, Performance Evaluation 63 (6) (2006)

12 [3.12] A.S. Alfa, W. Li, A homogeneous PCS network with Markov call arrival process and phase-type cell residence time, Wireless Networks 8 (2002) [3.13] M. Chatterjee, S.K. Das, G.D. Mandyam, Performance evaluation of voice-data integration for wireless data networking, in: International Conference on Networking, LNCS, July, 2001, pp [3.14] F. Houeto, S. Pierre, Quality of Service and performance issues in multi-service networks subject to voice and video traffics, Computer Communications 28 (2005) [3.15] A.S. Alfa, PCS networks with correlated arrival process and retrial phenomenon, IEEE Transactions on Wireless Communications 1 (4) (2002) [3.16] A A Abu-Dayya and N C Beaulien, Outage probabilities in presence of correlated lognormal interferers, Queen s Tech Report 9302, Mar [3.17] A A Abu-Dayya and N C Beaulien, Outage probabilities in presence of correlated lognormal interferers, Queen s Tech Report 9302, Mar [3.18] A A Abu Dayya and N C Beaulien, Correlated by normal interferers and outage probabilities, IEEE Pac Rim [3.19] Weijun Cheng, LaiboZheng and Jian dong Hu, Performance analysis of cooperative macro-diversity in Rayleigh-lognormal composite fading, IEEE , [3.20] Normanc.Beaulien, Adnan A Abu-Dayya and Peter J.Mclane, Estimating the distribution of a sum of independent lognormal random variables, IEEE Trans. on communications, vol.43, No.12. Dec [3.21] Sebastian S Szyskowicz and HalimYanikomeroglu, Fitting the Modified-Power- Lognormal to sum of independent lognormal distribution, IEEE GLOBECOM 2009 proceedings. [3.22] TjengThiangTjhung, Outage probability for lognormal-shadowed Rician Channels, IEEE Trans. on vehicular technology. Vol.46 No.2 May [3.23] W.C Jakes, Microwave Mobile communication, New York Wilely.