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Adaptive CDMA networks 12.1 BIT RATE/SPACE ADAPTIVE CDMA NETWORK This section presents a throughput delay performance of a centralized unslotted DirectSequence/Code Division Multiple Acc

Adaptive CDMA networks

12.1 BIT RATE/SPACE ADAPTIVE CDMA NETWORK

This section presents a throughput delay performance of a centralized unslotted DirectSequence/Code Division Multiple Access (DS/CDMA) packet radio network (PRN) usingbit rate adaptive location aware channel load sensing protocol (CLSP)

The system model is based on the following assumptions Let us consider the reverselink of a single-cell unslotted DS/CDMA PRN with infinite population and circle cellcoverage centered to a hub station Users communicate via the hub using different codesfor packet transmissions with the same quality of service (QoS) requirements [e.g thetarget bit error rate (BER) is 10−6] The radio packets considered herein are of mediumaccess control (MAC) layer (i.e MAC frames formed after data segmentations and cod-

ing) Packets have the same length of L (bits) The scheduling of packet transmissions,

including the retransmissions of unsuccessful packets at mobile terminals, is randomizedsufficiently enough so that it is possible to approximate the offered traffic of each user

to be the same, and the overall number of packets is generated according to the Poisson

process with rate λ In the sequel, we will use the following notation:

ζ – the path-loss exponent of the radio propagation attenuation in the range of [2, 5]

r – the distance of a mobile terminal from the central hub that is normalized to the cellradius, thus in the range of [0, 1]

R0 – the primary data rate for given system coverage and efficiency of mobile powerconsumption;

T0 – the packet duration (i.e the time duration needed for transmitting a packet

com-pletely) of the primary rate T0 = L/R0

The cell area is divided into M + 1 rings (M is a natural number representing the

spatial resolution) centered to the hub Let M= {0, 1, , M}; and for all m ∈ M,

r m – the normalized radius of the boundary-circle of ring (m + 1) given by r m= 2−m/ζ,

r0= 1 for the cell-bounding circle and r M+1= 0 for the most inner ring;

R m – the rate of packet transmissions from users in ring (m + 1) given by R m= 2m R0,that is, packets from the more inner ring will be transmitted with the higher bit rate;

Adaptive WCDMA: Theory And Practice.

Savo G Glisic

ISBN: 0-470-84825-1

T m – the corresponding packet duration T m= 2−m T

0 and also the mean service time of a

packet transmission using rate R m

For a fixed packet length L, the closer the mobile terminal to the hub, the higher

is the bit rate and the shorter is the packet transmission time In order to ensure theoptimal operation of transceivers, the packet duration should be kept not too short, forexample, minimum of around 10 ms as the radio frame duration of the 3GPP standards

for WCDMA cellular systems Therefore, a proper trade-off between L, R0 and M is needed For example, with L = 2560 bits, R0= 32 kbps and M = 3, there are four

possible rates for packet transmissions: 32, 64, 128 and 256 kbps with 80, 40, 20 and

10 ms packet duration, respectively In the absence of shadowing, for the same mobile

transmitter power denoted by P from any location in the network, approximated with the spatial resolution described above, the received energy per frame denoted by E is

increasing capacity in the cell The bit-energy Eb= E/L is also constant Let

W – the CDMA chip rate, for example, 3.84 Mcps;

g m – the processing gain of a transmission using rate R m that is given by g m = W/R m;

η – the ratio of the thermal noise density and maximum tolerable interference (N0/I0);

γ m – the local average signal to interference plus noise ratio (SINR), also denotes the

target SINR for meeting the QoS requirements of transmissions with rate R m.The transmitter power control (TPC) is assumed sufficient enough to ensure that thelocal average SINR can be considered as a lognormal random variable having standard

deviation σ in the range of 2 dB Because the transmitter power of mobile terminals in the rate adaptive system is kept at the norm level (denoted by P above), the dynamic

range of TPC can be significantly reduced compared to the fixed rate counterpart for the

same coverage resulting in less sensitive operation Thus, σ of the adaptive system can be

expected to be smaller than that in the fixed rate system Once again, if there were onlynear–far effects in the radio propagation, due to rate adaptation and perfect TPC, SINR

of all transmissions would be the same at the hub However, the required SINR target ofhigher bit rate transmissions in DS/CDMA systems tends to be lower for the same BERperformance due to less multiple access interference (MAI) For example, the simulationresults of Reference [1] show that in the same circumstances the required SINR targetfor 16-kbps transmissions is almost double that of the 256 kbps transmissions Thus, lesstransmitter power is needed for close-in users using higher data rate The rate/space adap-tive transmissions increase the energy efficiency for mobile terminals It will be shownlater that even when the same target SINR was required regardless of the bit rates, theadaptive system still outperforms the fixed counterpart In the sequel, we will use thefollowing notation:

BIT RATE/SPACE ADAPTIVE CDMA NETWORK 423

n= {n m , m ∈ M} is the system state or occupancy vector, where n m is the number of

packet transmissions in progress using rate R m;

w= {w m , m ∈ M} is the transmission load vector, where w m = g−1

m γ m represents the

average load factor produced by a packet transmission with rate R m and target SINR

γ m The higher the bit rate, the more the network resources that will be occupied bythe transmission

c= nw is the system load state representing MAI in the steady state condition.

It has been shown in Chapter 11 that simultaneous transmissions are considered quate, that is, meeting the QoS requirements, if MAI satisfies the following condition:

m∈M

The task of CLSP is to ensure that the condition (12.2) is always satisfied Define

= {n, condition (12.2) is true} the set of all possible system states;

 = {c, c = nw and n ∈
} the set of all possible system load states.

Because of the TPC inaccuracy, the probability that the condition (12.2) is satisfiedand the SINR of each packet transmission is kept at the target level, conditioned on the

steady system load state c and lognormal SINR can be determined as in Chapter 11,

where Q(x) is the standard Gaussian integral function, and σ is the standard deviation

of lognormal SINR in dB This is because the system load state c defined above uses

the mean (target) values of lognormal SINR for calculating the average load factor of

each transmission The Gaussian integral term Q(x) in equation (12.3) represents the

total error probability caused by a sum of lognormal random variable composing theload state

The above analysis implies that in the equilibrium condition, for a given system load

state c, the system will meet its QoS target (e.g actual bit error probability is less than the target BER of 1e-5) with a probability of Pok(c) In other words, it will lose its QoStarget (actual bit error probability is larger than the target BER of 1e-5) with a probability

1− Pok(c) As a consequence, each equilibrium system load state c can be modeled with

a hidden Markov model (HMM) having two states, namely ‘good’ and ‘bad’, which isillustrated in Figure 12.1

good bad

Figure 12.1 Two-state HMM of the system load state.

The stationary probability of HMM state (‘good’ or ‘bad’) conditioned on the system

load state c is given by

Let us introduce two other parameters for analytical evaluation purposes:

Peg – the equilibrium bit error probability over all ‘good’ states of the channel, in whichthe QoS requirements are met The target BER is supposed to be the worst case of

Peg, for example, 1e-5

Peb – the equilibrium bit error probability over all ‘bad’ states of the channel, in which

the QoS requirements are missed to some extent, for example, Peb= 1e − 4 when thetarget BER is 1e− 5 The target BER is therefore the upper bound of Peb

In the perfect-controlled system, Peg= Peband equal to the target BER This tion is widely used in the related publications investigating the system performance on theradio packet level In this section, the impacts of channel imperfection are evaluated in

assump-the context of SINR errors with total standard deviation σ and Pebas a variable parameterrepresenting effects of ‘bad’ channel condition Let

p(c) – the steady state probability of being in the system load state c ∈ ;

Pe – the equilibrium bit error probability of the system for the actual QoS of packettransmissions From the above results, we have

It is obvious that in the perfect-controlled system as mentioned above, Pe is also equal

to the target BER Let

Pc – the equilibrium probability of a correct packet transmission With employment offorward error correction (FEC) mechanism having the maximum number of correctable

BIT RATE/SPACE ADAPTIVE CDMA NETWORK 425

bits Ne(Ne< L and dependent on the coding method; Ne= 0 when FEC is not used),

wherex is the maximum integer number not exceeding the argument.

Thus, with respect to CLSP, the hub senses the channel load (i.e MAI, in general,

or the number of ongoing transmissions for the fixed rate system) and broadcasts thecontrol information periodically in a forward control channel Users having packets tosend should listen to the control channel and decide to transmit or refrain from thetransmission in a nonpersistent way The feedback control is assumed to be perfect, that

is, zero propagation delay and perfect transceivers in the forward direction The impacts ofsystem imperfection, such as access delay, feedback delay and imperfect sensing have beeninvestigated in Chapter 11 for the fixed rate systems with dynamic persistent control Let

G – the system offered traffic G = λT0 (the average number of packets per normalized

T0 ≡ 1) is kept the same for both adaptive and fixed rate systems for fair comparison

purposes In the adaptive system, G ≡ λ is distributed spatially among users that are in

different rings

For m∈ M, let

λ m – be the packet arrival rate from ring (m + 1), which is dependent on λ and the spatial user distribution (SUD) having the probability density function (PDF) f (r, θ ) In general, λ m is given by

For instance, let us assume that the SUD is uniform per unit area in the mobility

equilib-rium condition Thus, λ m can be determined by

12.1.1 Performance evaluation

Fixed-rate CLSP

The performance characteristics of the unslotted CDMA PRN using fixed-rate CLSPunder perfect TPC is given in Chapter 11 Herein, we consider the system with imperfectTPC Define

n– the number of ongoing packet transmissions in the system or the system state;

p n – the steady state probability of the system state n;

Psucc – the equilibrium probability of successful packet transmissions;

S – the system throughput as the average number of successful packet transmissions per

T0;

D – the average packet delay normalized by T0;

Using the standard results of the queuing theory for Erlang loss formula [3] with the

number of servers set to the channel threshold C0, the arrival rate of λ and the normalized service rate of 1/T0 ≡ 1, we have for the steady state solutions:

p n= C G n /n!0

The second factor is the equilibrium probability of correct packet transmissions Pc given

by equation (12.7) with a modification of equation (12.6) as given below:

BIT RATE/SPACE ADAPTIVE CDMA NETWORK 427

The system throughput is given by

The average packet delay is decomposed into two parts: Db the average waiting time of

a packet for accessing the channel including back-off delays and Drthe average residenttime of the given packet from the instant of entering to the instant of leaving the system

successfully Formally, the average packet delay (normalized to T0) is given by

Rate adaptive CLSP

This system, as mentioned above, can be modeled with a multirate loss network model

It is well known that the steady state solutions of such a system have a product form [2]given by

where p(n) is the steady state probability of having n transmission combination in the

system, n∈
; α m is the offered traffic intensity from ring (m + 1) using rate R m Thus,

α m = λ m T m , where λ m and T m are defined above

For large state sets, that is, large M and C0, the cost of computation with the above mulas is prohibitively high This problem has been considered by many authors, resulting

for-in elegant and efficient recursion techniques for the calculation of the steady system load

state and blocking probabilities The steady state probability p(c) of system load state

c ∈  defined above can be obtained by using the stochastic knapsack approximation

where Pc is given by equation (12.7) with Pe given by equation (12.6) and B m is the

packet blocking probability of transmissions using rate R m from ring (m+ 1)

Note that G = λT0≡ m∈Mλ m because of normalized T0 ≡ 1 The average packet delay

of this system, similar to equation (12.18), can be obtained by

arrival rate from ring (m+ 1) is given in equation (12.6) For the second scenario, the

BIT RATE/SPACE ADAPTIVE CDMA NETWORK 429

Table 12.1 System parameter summary [4] Reproduced from Phan, V and Glisic, S (2002)

Unslotted DS/CDMA Packet Radio Network Using Rate/Space Adaptive CLSP-ICC’02, New York,

May 2002, by permission of IEEE

and max tolerable interference

1e − 5 target BER

‘good’ condition

‘bad’ condition

packet arrival rate from ring (m + 1) is given by λ m = λ(r m − r m+1) with r m= 2−m/ζ

and r M+1= 0 as defined above This one-dimensional uniform SUD is often used formodeling the indoor office environment in which users are located along the corridor

or the highway The target SINR is set to 3 dB for all transmissions regardless of thebit rates This is not taking into account the fact that higher bit rate transmissions needsmaller target SINR for the same QoS than the lower bit rate transmissions The loadfactor introduced by the transmission is therefore linearly increasing with the bit ratethat is compensated by shortening the transmission period with the same factor Because

of this, under perfect-controlled assumption (Peb= Peg set to target BER as explainedabove), the fixed rate CLSP system could have slightly better multiplexing gain thanthe adaptive counterpart for the same offered traffic resulting in slightly better through-put as shown in Figure 12.2 In reality, the BER is changing because of the randomnoise and interference corrupting the packet transmissions The throughput characteris-tic of the fixed system worsens much faster than that of the adaptive system because

it suffers from higher MAI owing to larger number of simultaneous transmissions andlonger transmission period Further, when the transmission is corrupted, longer trans-mission period or packet length could cause a drop of the throughput performance andwasting battery energy (Figures 12.2 and 12.6) In any case, the adaptive system hasmuch better packet delay characteristics than the fixed counterpart (Figures 12.2–12.7).The same can be expected for the throughput performance in real channel condition or

0 10 20 30 40 50 60 70 80 0

Figure 12.2 Effects of channel imperfection on the throughput performance (two-dimensional

uniform SUD, ζ = 3, σ = 2 dB, L = 2560 bits, Peg = 1e − 5).

System offered traffic

Fixed perfect-ctrl system Adaptive perfect-ctrl Fixed bad-BER = 5e − 4 Adaptive bad-BER = 5e − 4 Fixed bad-BER = 1e − 3 Adaptive bad-BER = 1e − 3

Figure 12.3 Effect of channel imperfection on the packet delay performance (two-dimensional

uniform SUD, ζ = 3, σ = 2 dB, L = 2560 bits, P = 1e − 5).

BIT RATE/SPACE ADAPTIVE CDMA NETWORK 431

Figure 12.4 Effects of SUD on the performance trade-off (ζ = 3, σ = 2 dB, L = 2560 bits,

Figure 12.5 Effects of propagation model on the performance trade-off (two-dimensional

uniform SUD, σ = 2 dB, L = 2560 bits, P = 1e − 5, P = e − 4).

0 5 10 15 20 25 30 35 40

Figure 12.6 Effects of packet length on the performance trade-off (two-dimensional uniform

SUD, ζ = 3, σ = 2 dB, Peg= 1e − 5, Peb = 5e − 4).

Fixed with 3 dB SINR std dev.

Adaptive with 3 dB SINR std dev.

Figure 12.7 Effects of TPC inaccuracy on the performance trade-off (two-dimensional uniform

SUD, ζ = 3, L = 2560 bits, P = 1e − 5, P = 5e − 4).

MAC LAYER PACKET LENGTH ADAPTIVE CDMA RADIO NETWORKS 433

even in ideal channel condition if the advantage of less SINR for higher rate is taken intoaccount For example, according to Reference [1], target SINR is 1.5 dB for 256 kbps,

2 dB for 128 kbps, 2.5 dB for 64 kbps and 3 dB for 32 kbps The numerical results forsuch advantages are not presented in this chapter because of limited space Overall, theadaptive system outperforms the fixed counterpart Figures 12.4 to 12.7 show the effects

of design and modeling parameters on the performance characteristics The adaptive

sys-tem is sensitive to the SUDs (Figure 12.4) and path-loss exponent ζ (Figure 12.5) In

the rate/space adaptive systems, spatial positions of the clusters formed by mobile usersaffect the overall throughput-delay improvement, whereas performance of the fixed ratecounterpart is less sensitive to user population profile or does not depend on it given thatTPC is perfect These effects could be desirable if the advantage of less SINR for higher

rate was taken into account That more users are put to more inner rings depending on ζ

and SUD boosts up the rate and reduces the time of communications, resulting in better

throughput-delay performance One should keep in mind that larger ζ also causes much

larger dynamic range of transmitter power, especially for the fixed system that degradesthe TPC performance, significantly resulting in more erroneous packet transmissions thusworse system performance Figure 12.7 shows the effects of the standard deviation of

lognormal SINR (σ ) that represents the TPC errors Although the adaptive system can

be expected to have better TPC performance and thus smaller σ , the same value of σ is

used for both systems in the numerical examples

The throughput-delay performance of unslotted DS/CDMA PRNs using adaptive CLSP is evaluated against the fixed rate counterpart The combination of CLSPand adaptive multirate transmissions not only provides a significant performance improve-ment but also increases the flexibility of access control and reduces the uncertainty ofthe unslotted DS/CDMA radio channel Once again, one should be aware that because

rate/space-of equation (12.1) the system is more environment friendly and reduces the level rate/space-ofinterference in the surrounding cells too

12.2 MAC LAYER PACKET LENGTH ADAPTIVE

CDMA RADIO NETWORKS

Impacts of packet length on throughput-delay performance of wired/wireless networkshave been extensively investigated in the open literature The packet length optimizationproblem based on numerous factors is also well elaborated Let us revisit a standard for-mula (12.7) for the probability of correct packet transmission determining the throughputcharacteristic

It is easy to see from the equation that the smaller L makes the better Pc In order to

have Pc as close to 1 as possible for optimum throughput-delay performance, PeLneeds

to be very small compared to max (Ne, 1) In radio transmissions, SINR that is dependent

on transmitter power, path loss and MAI, dominates Pe In the bad channel conditions,

Pe can be relatively large and may require impracticably small L in order to meet the

performance requirements; otherwise throughput can drop to zero because all packets getcorrupted Meanwhile, mobile terminals are wasting battery energy for having to transmiterroneous packets

On the other hand, in order to reduce the overhead and improve the goodput, L should

be large This can be seen from the formula for normalized goodput [5],

R0 – the bit rate for packet transmission;

H – the length of protocol overhead, that is, the total length of packet header and packettail in (bit)

Equations (12.7) and (12.29) are the basis for the derivation of optimum packet lengthand packet length adaptation However, in order to obtain comprehensive and applicableresults, further research efforts are required For the last decade, there have not been manypapers actually elaborating the packet length adaptation problem for PRNs Reference [6]presents a simulation-based study of throughput improvement for a stop-and-wait auto-matic repeat request (ARQ) protocol using packet length adaptation in mobile packetdata transmission The channel estimation for the adaptation mechanism is based on thenumber of positive/negative acknowledgements (ACK/NACK) This is a learning-basedadaptive process on the data link layer; thus the adaptation can happen even when the

radio channel is in good conditions or vice versa owing to the bias of the learning toward

actual conditions of unreliable radio channel Reference [5] exploits equations (12.7) and(12.29) as such with no FEC capability to adopt adaptation mechanisms based on estima-tions of BER or frame error rate (FER) Results are supported by physical measurementswith Lucent’s WaveLAN radio No comprehensive channel modeling, derivations andadaptation mechanisms are given despite the fact that equation (12.7) may not be accu-rate to apply for different fading environments and long-packet applications as targetedwith maximum-transmission-unit TCP/IP link in Reference [5] Technical reasons behindthe applicability of equation (12.7) are elaborated in, for example, References [7–11].The bottom line is that, for robust adaptation, instead of using the uncorrelated formula(12.7), the correlation between channel conditions and packet length in time domain needs

to be considered Moreover, in less correlated fading environments, using suitable FECchannel coding can be a more effective solution Reference [12] presents a broad adaptiveradio framework for energy efficiency of the battery in mobile terminals including packetlength adaptation Similar to Reference [5], Lucent’s WaveLAN radio is used to provideresults Although Reference [12] provides valuable insights into adaptive radio problems,

no comprehensive mechanisms are given that affect the accuracy and the practicality

of the analysis We should also add here that References [5,6,12] consider the case ofnoncontention packet access, that is, a single connection-oriented radio link The packetdelay characteristic and the throughput delay trade-off are ignored in References [5,6] Inaddition to providing an overview of the existing work in this section, we consider theheavily correlated flat fading, where the error-correcting coding has not yet been effective.Packet length adaptation is used for a multiple access unslotted CLSP/DS-CDMA channel

MAC LAYER PACKET LENGTH ADAPTIVE CDMA RADIO NETWORKS 435

in order to improve the system throughput delay performance and the energy efficiency

of mobile terminals

The adaptation criteria are to eliminate the impacts of fading for an optimal trade-offbetween throughput, average packet delay and goodput Two alternative strategies arepresented: (A1) keeping the packet length as large as possible to avoid degradation of thegoodput while fulfilling the specified QoS requirement, for example, Packet Error Rate(PER); (A2) maximizing the goodput The correlation between fade duration statistics andpacket duration in time domain over a flat Rayleigh-fading channel is studied to ensurethe robustness and the practicality of adaptation mechanisms The chapter also presentscomprehensive modeling and analysis tools, taking into account impacts of imperfectpower control and user mobility

12.2.1 Unslotted CLSP/DS-CDMA packet radio access

This section considers the packet radio access in the uplink of a single-cell unslottedDS-CDMA PRN using CLSP with infinite population and circle coverage around a hubstation Mobile users communicate via the hub using different sequences and fixed bit

rate R0 for packet transmissions with the same QoS requirement Further, the followingassumptions are made without loss of generality

User data are coded and segmented into information blocks Then a header that containsaddress, control information and error-correcting control fields is added to each block to

form a radio packet, which is sent over the air toward the hub For a packet length L (bit) including a constant H (bit) of the protocol overhead, define

T – the packet duration, T = L/R0 (ms), also referred to as the packet length in

time domain Thus, T is proportional to L for a given constant bit rate R0 In practical

implementations, for example, according to radios of current 3GPP standards, T should be kept between Tminand Tmaxand should take the value of one or multiples 10-ms periodsfor effective operation of CDMA radios for long-packet duration applications

In this CLSP system, similar to the model described in Section 12.1, the hub is sible for sensing the channel load (number of ongoing transmissions) and rejecting furtherincoming packets when the load is reaching a certain channel threshold by forcing users

respon-to refrain from the transmission with feedback control The hub broadcasts the controlinformation periodically in a forward control channel Users having packets to send willlisten to the control channel and decide to transmit or refrain from the transmission in

a nonpersistent fashion Thus, the ‘hidden terminal’ problem of distributed carrier sensemultiple access (CSMA) systems can be avoided The feedback control is assumed to

be perfect, that is, zero propagation delay and perfect receiving in the forward direction.The impacts of system imperfection, such as access delay, feedback delay and imperfectsensing have been investigated in Chapter 11 for a nonadaptive, perfect power-controlsystem The channel threshold or system capacity, defined as the maximum number ofsimultaneous packet transmissions is given by equation (12.8)

The traffic model is based on the assumption that the scheduling of packet sions including retransmissions of unsuccessful packets at mobile terminals is randomizedsufficiently enough so that the overall number of packets is generated according to the

transmis-Poisson process with rate λ Let us define

n– the system state, that is, the number of ongoing packet transmissions in the

sys-tem The CLSP is responsible for keeping n under C0 However, because of imperfectpower control, characterized by a lognormal error of average SINR with standard devi-

ation σ (dB), the equilibrium probability that n simultaneous transmissions are not

cor-rupted by the system outage state (i.e target SINR is kept) can be given by modifyingequation (12.3)

Pok(n) = 1 − Q



C0− E[MAI|n]

√Var[MAI|n]



( 12.30)

where E[MAI |n] = n exp[(εσ )2/2] and Var[MAI|n] = n exp[2(εσ )2] and C0 is given by

equation (12.8), ε = ln(10)/10, and Q(x) is the standard Gaussian integral.

This equation represents the interference-limited nature of DS-CDMA systems The

smaller L makes the shorter packet transmission duration T = L/R0 and thus the smaller

number of simultaneous transmissions n for a given packet arrival rate λ and bit rate R0.This improves the system outage probability and therefore can be used for adaptationstrategy as well However, in this section CLSP is used to compensate MAI To simplifythe analysis, we assume that all packet transmissions hit by the system outage state areerroneous with Probability 1

12.2.2 Fading model and impacts on packet transmission

Let us assume that the system operates at 2.4-GHz carrier frequency [industrial scientificand medical (ISM) band] with omnidirectional antenna, 64-kbps packet transmission and

64 spreading factor The user speed is in the range of 0 to 4 ms−1, which means that itmay take at least 32 ms for the user to travel the distance of one wavelength, and themaximum Doppler frequency is up to 32 Hz This radio channel is modeled as a flatRayleigh-fading channel, where the fading process is heavily correlated according to thecorrelation properties presented in References [7,11] For a certain fade margin, depending

on the packet duration T (one or multiple of 10 ms), several fades may occur during the

packet transmission period To determine the probability of correct packet transmission

as well as the packet length adaptation criteria, one needs to consider the impacts of fadeand interfade duration statistics, and packet lengths The correlation between them in timedomain is illustrated in Figure 12.8 Let us use the following notation:

tf – the fade duration, that is, the period of time a received signal spends below a threshold

voltage R, having PDF g(tf) and mean tf avrg

tif– the interfade duration, that is, the period of time between two successive fades, having

PDF h(tif) and mean tif avrg

tfia – the fade interarrival time, that is, the time interval between the time instants that

two successive fades occur: tfia= tf+ tif, having PDF s(tfia) and mean tfia avrg.For a Rayleigh-fading channel, it has been shown in numerous papers [9,13,14] that

tf avrg and tif avrg can be approximated as