Adaptive Generative Models for Digital Wireless Channels...Adaptive Generative Models for Digital...

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 9, SEPTEMBER 2014 5173

Adaptive Generative Models for DigitalWireless Channels

Omar S. Salih, Member, IEEE, Cheng-Xiang Wang, Senior Member, IEEE,Bo Ai, Senior Member, IEEE, and Raed Mesleh, Senior Member, IEEE

Abstract—Generative models, which can generate bursty errorsequences with similar burst error statistics to those of descriptivemodels, have an immense impact on the wireless communicationsindustry as they can significantly reduce the computational timeof simulating wireless communication links. Adaptive generativemodels aim to produce any error sequences with any given signal-to-noise ratios (SNRs) by using only two reference error sequencesobtained from a reference transmission system with two differentSNRs. Compared with traditional generative models, this adaptivetechnique can further considerably reduce the computational loadof generating new error sequences as there is no need to simulatethe whole reference transmission system again. In this paper,reference error sequences are provided by computer simulationsof a long term evolution (LTE) system. Adaptive generative modelsare developed from three widely used generative models, namely,the simplified Fritchman model (SFM), the Baum-Welch basedhidden Markov model (BWHMM), and the deterministic processbased generative model (DPBGM). It is demonstrated that theadaptive DPBGM can provide accurate burst error statistics andbit error rate (BER) performance of the LTE system, while theadaptive SFM and adaptive BWHMM fail to do so.

Index Terms—Adaptive generative models, error models, bursterror statistics, Markov models, hidden Markov models.

Manuscript received September 3, 2013; revised January 31, 2014; acceptedMay 1, 2014. Date of publication May 16, 2014; date of current versionSeptember 8, 2014. This work was supported in part by the EPSRC and PhilipsResearch Cambridge, U.K.; by the Opening Project of the Key Laboratory ofCognitive Radio and Information Processing, Guilin University of ElectronicTechnology, Ministry of Education under Grant 2013KF01; by the State KeyLaboratory of Rail Traffic Control and Safety, Beijing Jiaotong Universityunder Grant RCS2012K003; by National 863 project in 5G, Ministry of Scienceand Technology, China under Grant 2014AA01A706; by the National NaturalScience Foundation of China under Grant 61222105; by the Beijing MunicipalNatural Science Foundation under Grant 4112048; by the Sensor Networks andCellular Systems Research Center, University of Tabuk; and by the Ministry ofHigher Education in Saudi Arabia. The associate editor coordinating the reviewof this paper and approving it for publication was A. Zajic.

O. S. Salih is with the Department of Aerospace, Electrical and ElectronicEngineering, Faculty of Engineering and Computing, Coventry University,Coventry CV1 5FB, U.K. (e-mail: [email protected]).

C.-X. Wang is with the School of Information Science and Engineering,Shandong University, Jinan 250100, China, the Institute of Sensors, Signals andSystems, School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh EH14 4AS, U.K., and also with the Sensor Networks and CellularSystems Research Center, University of Tabuk, Tabuk 71491, Saudi Arabia(e-mail: [email protected]).

B. Ai is with the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University, Beijing 100044, China (e-mail: [email protected]).

R. Mesleh is with the Sensor Networks and Cellular Systems Re-search Center, University of Tabuk, Tabuk 71491, Saudi Arabia (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TWC.2014.2325028

I. INTRODUCTION

A DIGITAL (time-discrete) channel generally representsthe whole wireless communication chain, including the

transmitter, analog (or physical) channel, and receiver in thecomplex baseband. The input and output of a digital channelare in the digitized form. Because of impairments in wirelesschannels, errors frequently emerge in digital channels. More-over, signal processing in many components of the wirelesstransmission system may add further errors [1]. It is perceivedthat these errors arising from digital wireless channels withmemory are not independent but appear in clusters or bursts.Bursty error sequences can be statistically represented bymathematical channel models called error models [2], whichcan be classified as descriptive [3] and generative [4] models.Descriptive models express the burst error statistics of referenceerror sequences obtained directly from experiments. Generativemodels have mechanisms that can generate error sequenceshaving any required length and burst error statistics similar tothose of reference error sequences. Compared with descriptivemodels, generative models are more efficient as they do notneed to simulate the whole communication system and there-fore can significantly reduce the simulation time of generatingerror sequences. The main applications of error models are toassist in the performance assessment and design of error con-trol schemes and high layer wireless communication protocols[5]–[9]. Error models can characterize error sequences in eitherbit level or packet level [10], [11].

In the literature, there are five main classes of generativemodels. Markov models are the first class of generative modelsconsisting of finite [12]–[17] or infinite states [4] in a chain. TheGilbert-Elliot model [12], [13] was the first finite-state Markovmodel with only two states for generating errors and error-freebits. It produces error sequences with burst error statistics thatdiverge significantly from the desirable ones. An increase inthe number of states can achieve better performance [11], [14],[15]. For example, simplified Fritchman’s models (SFMs) [14],[18], [19] replaced the error-free state of the two-state Markovmodel with a group of error-free states while keeping the onlyerror state. Bipartite models [11] are more advanced Markovmodels, but their complexity is very high in order to achieve asatisfactory accuracy of burst error statistics. The second classis hidden Markov models (HMMs) [20]–[23], which containhidden parameters that can be calibrated through observations.The Baum-Welch (BW) algorithm [24] was mostly used toattune the hidden parameters based on available observations,resulting in the so-called BW based HMMs (BWHMMs).

1536-1276 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

5174 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 9, SEPTEMBER 2014

Compared with finite-state Markov models, HMMs are muchmore complicated due to the huge number of states requiredto train the hidden parameters, which greatly increases thecomputational speed. The third and fourth classes of generativemodels are based on stochastic context-free grammars (SCFGs)[25] and chaos theory [26]–[29], respectively. SCFGs consistof production rules and symbols, each of which is assigned aprobability that controls its behavior. These models are limitedto error bursts with bell-shaped error density distributions.Chaotic generative models cannot describe the desired errorcorrelation function with high accuracy [26]. The final classof generative models is the deterministic process based gen-erative models (DPBGMs) [30]–[32], which utilize the secondorder statistics of fading processes. DPBGMs have proven theirsuperiority over other generative models, e.g., SFM [31] andBWHMM [32].

All the aforementioned traditional generative models[12]–[31] were developed for error sequences corresponding toone digital channel with fixed system parameters and channelconditions, e.g., signal-to-noise ratios (SNRs). If SNRs change,the whole communication system will have to be simulatedagain in order to generate new reference error sequences.Consequently, those traditional generative models will have tobe developed again with modified model parameters in orderto fit the burst error statistics to those of new reference errorsequences. However, for appropriate design and performanceevaluation of error control schemes and high layer protocols, weneed to test transmission schemes with many different channelconditions or SNRs. In this case, using traditional generativemodels are still very time consuming, as numerous referenceerror sequences corresponding to different SNRs have to be firstproduced by the reference communication system. Therefore, itis highly desirable to develop adaptive generative models thatcan utilize the limited (e.g., only 2) available error sequences toattain new error sequences with any SNRs without sacrificingmuch of the accuracy in terms of burst error statistics. To thebest of our knowledge, this has never been done before.

In this paper, we propose three adaptive generative modelsbased on well-known traditional generative models, i.e., SFM,BWHMM, and DPBGM, by adjusting some useful model pa-rameters. Reference error sequences (descriptive models) wereobtained from uncoded long term evolution (LTE) systems.The burst error statistics of newly generated error sequencesusing the three adaptive generative models are compared withthose of reference error sequences. Also, the bit error rates(BERs) of coded LTE systems are compared using referenceerror sequences and new error sequences obtained from thethree adaptive generative models. It is shown that the proposedadaptive DPBGM can provide excellent approximation to thedesired burst error statistics of reference error sequences andthe desired BER of coded LTE systems. However, the adaptiveSFM and the adaptive BWHMM fail to do so.

This paper is organized as follows. Section II defines someterms related to binary error sequences and describes someimportant burst error statistics as performance metrics. Thenovel adaptive procedures for three widely used generativemodels, namely SFM, BWHMM, and DPBGM, are proposedin Section III. Section IV illustrates an LTE simulator which

is used as a descriptive model to derive reference bit errorsequences at certain values of SNR. The burst error statistics arealso compared between different adaptive generative modelsand descriptive models in this section. Finally, conclusions aredrawn in Section V.

II. BURST ERROR STATISTICS

An error sequence of a digital wireless channel can beobtained by comparing the output sequence with the inputsequence. Here, we consider a binary bit error sequence as asequence of “0”s and “1”s, which denote correctly received bitand error bit, respectively.

We can breakdown an error sequence into smaller parts inorder to study its nature and calculate the burst error statistics.Therefore, a number of terms can be defined as follows. A gapis defined as a sequence of consecutive zeros between two ones,having a length equal to the number of zeros [18], [33]. Anerror cluster is a series of errors that occur consecutively. Ithas a length equal to the number of ones [14]. An error-freeburst is defined as an all-zero sequence with a length of at leastη bits, where η is a positive integer [11], [21]. Compared toa gap, an error-free burst has the minimum length of η andis not necessarily located between two errors. An error burstis a series of ones and zeros restricted by “1”s at the edges,and separated from neighboring error bursts by error-free bursts[11], [21]. Clearly, the minimum length of an error burst is one,and the number of consecutive error-free bits within an errorburst is less than η. Hence, the local error density inside an errorburst is greater than 1/η.

In what follows, we list widely used burst error statis-tics available in the literature for characterizing bit errorsequences:

1) G(mg): the gap distribution (GD), which is defined asthe cumulative distribution function (CDF) of gap lengthsmg . This statistic gives some indication of the random-ness of the channel [33].

2) P (0m0 |1): the error-free run distribution (EFRD), whichis the probability that an error bit is followed by at leastm0 error-free bits [14]. The EFRD can be calculatedfrom the GD [33]. Clearly, P (0m0 |1) is a monotonicallydecreasing function of m0 such that P (00|1) = 1 andP (0m0 |1) → 0 as m0 → ∞. This statistic is very usefulto determine the minimum error-free burst length η.

3) P (1mc |0): the error cluster distribution (ECD), which isthe probability that a correct bit is followed by mc ormore successive bits in error [14]. This statistic distin-guishes between the bursty channels and random chan-nels as well, i.e., bursty channels have long error clusters(e.g., 15–20), whereas random channels have short errorclusters (e.g., 1–3).

4) PEB(me): the error burst distribution (EBD), which isthe CDF of error burst lengths me. This statistic helps indesigning the error bursts’ correcting codes [33].

5) PEFB(me): the error-free burst distribution (EFBD),which is the CDF of error-free burst lengths me.This statistic, together with the error burst distribution,

SALIH et al.: ADAPTIVE GENERATIVE MODELS FOR DIGITAL WIRELESS CHANNELS 5175

provides the basis for determining the optimum degree ofinterleaving with respect to a specific code [33].

6) P (m,n): the block error probability distribution (BEPD),which is the probability that at least m out of n bitare in error. This statistic is important for determiningthe performance of Hybrid Automatic Repeat Request(HARQ) protocols [18].

7) ρ(Δk): the bit error correlation function (BECF), whichis the conditional probability that the Δkth bit followinga bit in error is also in error. The BECF is also importantbecause it represents the burstiness of the channel [3], [4].

Burst error statistics are useful statistical means to demon-strate the structural behavior of error sequences obtained fromwireless channels with memory. Consequently, they could helpin the design and evaluation of error control schemes and higherlayer protocols, particularly those very important burst errorstatistics, such as P (m,n) and ρ(Δk). Furthermore, burst errorstatistics are metrics to judge the relative merits of differentgenerative models by comparing them with the descriptivemodel. We will use some of these statistics in Section III todevelop new adaptive generative models, and we will illustrateall of them in Section IV in order to validate the proposedadaptive generative models.

III. ADAPTIVE GENERATIVE MODELS

In the following subsections, we propose three adaptivegenerative models for producing new error sequences with anySNRs from two reference error sequences. The adopted gener-ative models, namely, SFM, HMM, and DPBGM, are widelyknown in the literature and have been applied to many wirelesssystems. The key idea behind an adaptive generative model isto identify a fundamental feature that is used to configure thecorresponding generative model and the trend of the identifiedfeature with different SNRs. Once the trend of the fundamentalfeature of the generative model is found, we can parameterizethe adaptive generative model to generate error sequences atany required SNRs without the need of new reference errorsequences.

A. Adaptive SFM (ASFM)

A SFM consists of N -states: one error state and N − 1error-free states. When a SFM transits into the error state, itgenerates a “1” (error bit). When a transition to an error-freestate occurs, the SFM generates a “0” (correct bit). While theSFM is circulating within an error-free state, “0”s are generateduntil a transition to the error state occurs. In this case, the SFMgenerates “1”s again. Transitions between the error-free statesin a SFM are forbidden. The reason for having many statesgenerating “0”s is to generate different lengths of gaps. All thetransitions take place according to assigned probabilities. Theprobability transition matrix T for an N -state SFM is [14]

T =

⎛⎜⎜⎜⎜⎝

P11 0 0 0 P1N

0 P22 0 0 P2N

0 0. . . 0

...0 0 0 PN−1N−1 PN−1N

PN1 PN2 · · · PNN−1 PNN

⎞⎟⎟⎟⎟⎠ (1)

where Pij is the probability of transition from State i to Statej (i, j = 1, . . . , N). Note that States 1, . . . , N − 1 are error-free states, whereas State N is the error state. The transitionsbetween the error-free states are not allowed, i.e., Pij = 0 fori �= j and i, j < N . The elements of T can be determined fromthe EFRD P (0m0 |1) of the reference error sequence accordingto [14]

P (0m0 |1) =N−1∑i=1

PNi

PiiPm0ii , m0 > 0. (2)

The EFRD can also be approximated by the weighted sum ofN − 1 exponentials given by [14]

P (0m0 |1) ≈N−1∑i=1

Aieaim0 . (3)

The parameters Ai and ai can be found by using an optimiza-tion method or a curve fitting technique to match (3) withthe EFRD obtained from the reference error sequence. Conse-quently, the elements of T in (1) are obtained as follows [14]:

Pii = eai , i = 1, . . . , N − 1 (4)

PNi =Ai × Pii, i = 1, . . . , N − 1 (5)

PiN =1− Pii, i = 1, . . . , N − 1 (6)

PNN =1−N−1∑i=1

PNi. (7)

Once the above transition probabilities, i.e., all the elementsof T, are known, an error sequence with any desirable lengthcan be generated. Therefore, the key to generate a new errorsequence with the required SNR from two reference errorsequences for the ASFM is to obtain the EFRD of the newerror sequence, as can be seen from (1)–(7).

Let us suppose that we have two reference error sequences,e.g., X and Y , with two different SNRs in dB, e.g., SNRX

and SNRY , respectively. Without loss of generality, we canassume that SNRY > SNRX . Their EFRDs are denoted asPX(0m0 |1) and PY (0

m0 |1). The task now is to obtain theEFRD PZ(0

m0 |1) for a new error sequence Z with a new SNRin dB, SNRZ .

Fig. 1 shows the EFRDs of some reference error sequenceswith SNRs = 1, . . . , 5 dB. We can see that in the logarithmicscale, the EFRD P (0m0 |1) almost linearly increases with theincrease of the SNR in dB at any given gap length m0, i.e.,

SNRY − SNRZ

SNRY − SNRX=

log10 [PY (0m0 |1)]− log10 [PZ(0

m0 |1)]log10 [PY (0m0 |1)]− log10 [PX(0m0 |1)] .

(8)

After some simple manipulations, we can rewrite (8) as

log10 (PZ(0m0 |1))

= α · log10 [PX(0m0 |1)] + β · log10 [PY (0m0 |1)] (9)

or

PZ(0m0 |1) = [PX(0m0 |1)]α × [PY (0

m0 |1)]β (10)


Fig. 1. The EFRDs of the descriptive model for several SNRs and reproducedEFRDs.

where α and β are defined as

α =SNRY − SNRZ

SNRY − SNRX(11)

β =1− α. (12)

Note that α < 0 if SNRZ > SNRY . Otherwise, α > 0 holds.It is clear that α and β are simply weighting parametersto indicate the linear relationship among log10[PX(0m0 |1)],log10[PY (0

m0 |1)], and log10[PZ(0m0 |1)]. They also imply the

quantity of the characteristics that the new error sequence Zinherits from reference error sequences X and Y .

Fig. 1 also shows the EFRDs of the three newly generatederror sequences with SNRs = 2 dB (using error sequences withSNR = 3 dB and 5 dB, i.e., SNRZ < SNRX ), 4 dB (usingerror sequences with SNR = 3 dB and 5 dB, i.e., SNRX <SNRZ < SNRY ), and 5 dB (using error sequences with SNR =1 dB and 3 dB, i.e., SNRZ > SNRY ), according to (10)–(12).It is clear that the EFRDs of reproduced error sequences canmatch those of reference error sequences with the same SNRvery well, which verifies the proposed adaptive technique, asshown in (8)–(12).

B. Adaptive Baum-Welch Based HMM (ABWHMM)

HMMs [21], [23] employ the idea of Markov models, butuse two stochastic processes. One stochastic process is notobservable but can only be estimated by the other stochasticprocess which produces a sequence of observations. In [21],HMMs were implemented using BW algorithm [20], [24] andthe procedure is briefly explained as follows. The error burstsof the reference error sequence are extracted and numbered.Each error burst is then divided into blocks of L bits. Eachblock is then represented by the number of error bits it contains.For example, when L = 4, the error burst 110011110001 has3 blocks. Hence, that error burst is represented by 3 digits as2 4 1. In this way, the error bursts are converted into a compactformat as vectors, NELh (h = 1, . . . ,NEB , where NEB is thetotal number of error bursts). The largest number in each NELh

vector is called the peak number of errors (PNE). Therefore, wehave h numbers of PNE. In the above example, PNE = 4 holds.

The next step is to classify the error bursts into N disjointclasses (submodels or bursty states) according to

ξ(N− 1) + 1 ≤ PNE ≤ ξN (13)

where ξ is a positive integer. Afterwards, the compact blocksof each state shall be used to train hidden Markov submodelsusing BW algorithm [24]. Each submodel contains one class oferror bursts. BWHMMs have the following parameters:

1) S = {s1, s2, . . . , sN}: the set of states of the model,where N is the number of states in the HMM.

2) V = {v1, v2, . . . , vD}: the set of observable values,where D is the cardinality of the observable values.

3) A = [afl]: the state transition probabilities matrix, whereafl is the probability of transition from State sf toState sl.

4) B = [blk]: the observation probability matrix, where blkis the probability of emitting vk from State sl.

5) Π = [πf ]: the initial state probability.

To build the BWHMM submodels, the parameters N, D, andthe set λ = {A,B,Π} must be specified. The value of N can bedecided according to the guidelines in [21]. Given a set of ob-servation sequences (error burst blocks) representing the com-pact error burst Ok = {Ok

1 , Ok2 , . . . , O

kDk}, k = 1, . . . ,K (K is

the number of error bursts in each class), the BW algorithm isutilized to maximize the probability Γ =

∏Kk=1 P (λ|Ok) [21].

In our previous example, O = {2, 4, 1}.Once the optimized transition probabilities are found, error

bursts can be generated from the submodels. To complete thegeneration of new error sequences, the error-free bursts con-catenation to the hidden Markov submodels should be executed.The error-free bursts are represented by one state only. Thetransitions from the error-free state to the other states generateerror bursts with variable structures according to the submodel.However, the transitions from the error burst states to the error-free state generate error-free bursts with different lengths. Botherror-free bursts and error bursts are combined in the end, suchthat an error-free burst is followed by an error burst.

In order to generate new error sequences with any desirableSNRs from two reference error sequences, we should find outthe most important feature of the BWHMM. In fact, errormodels aim to identify the errors and their distribution in theerror bursts, and this is recognized by the NELh vector. FromNELh, we can know the number of errors in each blockfor each error burst. Consequently, from two set of vectorsNELhX and NELhY corresponding to two reference errorsequences X and Y with SNRs in dB as SNRX and SNRY ,respectively, we can obtain NELhZ corresponding to the newerror sequence Z with SNRZ .

Once NELhZ is calculated, the set of steps described beforeto construct the submodels are applicable in the process towardsgenerating the required error sequence. The new error sequenceZ can then be generated directly using NELhZ without theneed for a reference error sequence. Therefore, the key togenerate new error sequences with any required SNRs from tworeference error sequences using the ABWHMM is to obtain theNELhZs of new error sequences.


In order to find NELhZ , we need to first sort each NELhX

and NELhY in a descending order so that the PNE is the lead-ing element in each vector. Secondly, NELhX and NELhY

each should be sorted in the vertical direction with a descendingmanner according to the values of PNE, e.g., the PNE forNEL1X is greater than the PNE for NEL2X . From our investiga-tions, we have found that there also exists a linear relationshipamong NELhX , NELhY , and NELhZ with the decrease ofSNRs in dB. Similar to the derivations in (8)–(12), we canobtain NELhZ from

NELhZ = �α ·NELhX + β ·NELhY �. (14)

Here, �·� denotes the floor function, α and β are given by (11)and (12), respectively. Afterwards, we apply the classificationrule and training procedure to generate new error bursts.

To generate error-free bursts related to the new error se-quence Z, we interpolate two error-free burst distributionsrelated to error sequences X and Y . Moreover, the numberof error-free bursts of Z is obtained by interpolation from thenumbers of error-free bursts of X and Y . Subsequently, theerror-free burst lengths are worked out and substituted withzeros. Eventually, concatenation of new error bursts and error-free bursts is performed to produce the error sequence Z.

C. Adaptive DPBGM (ADPBGM)

The idea of the DPBGM is derived from second-order statis-tics of fading processes [31]. As a matter of fact, some statisticsof bursty errors are related to second-order statistics of fadingenvelope processes. Accordingly, fading processes can be usedto generate error sequences where fading intervals and inter-fading intervals are associated with error bursts and error-freebursts, respectively.

The error burst lengths and error-free burst lengths of areference error sequence can be recorded as vectors calledEBrec and EFBrec, respectively. Let us denote the minimumvalue in EBrec as mB1 and the maximum value as mB2.Subsequently, the lengths me of error bursts satisfy mB1 ≤me ≤ mB2. By analogy, the minimum value and the maximumvalue in EFBrec are denoted as mB1 and mB2, respectively;and the lengths me of error-free bursts satisfy mB1 ≤ me ≤mB1. In order to proceed with the ADPBGMs design, somequantities need to be defined.

1) Nt is the total length of the reference error sequence.2) NEB is the total number of error bursts, which is equal to

the number of entries in EBrec.3) NEFB is the total number of error-free bursts, which is

equal to the number of entries in EFBrec.4) NEB(me) is the number of error bursts of length

me in EBrec. Thus,∑mB2

me=mB1NEB(me) = NEB

holds. Then, the EBD PEB(me) can be calculated byPEB(me) = (1/NEB)

∑me

x=mB1NEB(x).

5) NEFB(me) is the number of error-free bursts of lengthme in EFBrec. Similarly,

∑mB2me=mB1

NEFB(me) =

NEFB holds. Then, the EFBD PEFB(me) is given byPEFB(me) = (1/NEFB)

∑me

x=mB1NEFB(x).

The DPBGM consists of a sampled deterministic processfollowed by a threshold detector and two parallel mappers. The

complex fading deterministic process can easily be approxi-mated and represented by [31], [34]–[37]

ζ(t) = |μ1(t) + jμ2(t)| (15)

where

μi(t) =

Ni∑n=1

ci,n cos(2πfi,nt+ θi,n), i = 1, 2. (16)

Here, Ni is the number of sinusoids, ci,n are gains, θi,n arephases from the realizations of the random generators, andfi,n are the discrete frequencies. To complete the parametriza-tion of the deterministic fading process, the vector Ψ =(N1, N2, rth, σ0, fmax, TA) is required, where rth is the en-velope threshold, σ0 is the square root of the mean power ofμi(t), fmax is the maximum Doppler frequency, and TA is thesampling interval. A subset of Ψ is ψ = (σ0, fmax, TA), and itselements are given by [31]:

σ0 =rth√

2 ln(1 +RB)(17)

fmax =NEB(1 +RB)

Tt

√2π ln(1 +RB)

(18)

TA ≈4σ0

[exp

(r2th

2σ20

)− 1

]√5πrthfmax

√−1 +

√1 + 10qs/3. (19)

The value of RB is the ratio of the mean value of error burstlengths to the mean value of error-free burst lengths. The pa-rameter Tt is the total transmission time of the communicationssystem. The quantity qs is the maximum measurement error ofthe level-crossing rate (LCR).

When the simulation is run, the deterministic process variesin a way that it crosses the threshold with positive and negativeslopes. Second-order statistics of the sampled deterministicprocess, such as the LCR, average duration of fades (ADF),and average duration of inter-fades (AIDF), can be workedout. When the level of the deterministic process is above thatthreshold (inter-fading intervals), an error-free burst is gener-ated. On the contrary, when the deterministic level is belowthe threshold (fading intervals), an error burst is generated. Thelengths of the error-free bursts and error bursts is equal to thenumber of samples counted in inter-fading and fading intervals,respectively. Subsequently, error burst and error-free burst gen-erators are produced as vectors, i.e., EBrec and EFBrec withlength distributions PEB and PEFB , respectively. The tildesign is placed on parameters related to the generative modelto distinguish them from those of the reference error sequence.

Mapping [31] is then employed to adjust the generated errorand error-free burst lengths. This means that mappers modifyEBrec and EFBrec such that NEB(me) = NEB(me) andNEFB(me) = NEFB(me) hold, respectively. Here, NEB(me)is equal to �(Nt/Nt)NEB(me)� or �(Nt/Nt)NEB(me)�+ 1for different error burst lengths me in order to fulfill∑mB2

me=mB1NEB(me) = NEB = �(Nt/Nt)NEB�. Similarly,

NEFB(me) is equal to �(Nt/Nt)NEFB(me)� or�(Nt/Nt)NEFB(me)�+ 1 for different error-free burstlengths me to satisfy

∑mB2me=mB1

NEFB(me) = NEFB =

�(Nt/Nt)NEFB�. To modify EBrec, we first find the


corresponding values 1meand 2me

in EBrec to assure thefollowing conditions [31]:

�2me−1∑

l=�1me

NEB(l) <NEB(me)

�2me∑l=�1me

NEB(l) ≥ NEB(me). (20)

Then,

�2me−1∑

l=�1me

NEB(l) +NEB

( 2me

)= NEB(me). (21)

The same idea applies to EFBrec. It is clear that the mappersrefit l( 1me

≤ l ≤ 2me− 1) samples of the fading process in

each interval to me, which is the required burst length. Aftermapping, error sequences can be obtained by combining theconsecutively generated error bursts with error-free bursts.

Once all the above parameters are known, an error sequencewith any desirable length can be generated. Therefore, the keyto generate a new error sequence Z with any required SNRfrom two reference error sequences X and Y , having differentSNRs, i.e., SNRX and SNRY , is to obtain the parameters ψ,PEB(me), PEFB(me), NEB(me), and NEFB(me) for the er-ror sequence Z from similar parameters of the error sequencesX and Y . Again, our investigations have demonstrated thatthese parameters or burst error statistics will linearly increasewith the increase or decrease of SNRs in dB. Similar to thederivations in (8)–(12), we can obtain ψZ and PEBZ

from

ψZ =α · ψX + β · ψY . (22)

PEBZ=α · PEBX

+ β · PEBY. (23)

respectively, where α and β are given by (11) and (12),respectively.

In order to construct EBrec from PEBZ, we have to know

the total number of error bursts NEB for the error sequenceZ. The number NEBZ

is obtained by interpolating betweenNEBX

and NEBY, given that X and Y have the same length.

Multiplying the obtained number with the extracted PEBZwith

some manipulations related to the CDF gives us the requiredEBrec of Z. Similar procedure can be applied to find EFBrec.In order to apply the mappers, we need to find NEB(me)corresponding to Z by finding PEBZ

as follows:

PEBZ= α · PEBX

+ β · PEBY. (24)

The EBD PEB(me) linearly increases with the increase ofSNRs in dB for any given error burst length me, as clearlyindicated in Fig. 2. Now, we have to work out the total numbersof error bursts NEBZ

for the error sequence Z by interpolatingbetween NEBX

and NEBYgiven that X and Y have the same

length, and then, we find NEB(me). Similar methodology canbe applied to find NEFB(me). Consequently, mappers are usedaccording to (20) and (21) to work out the modified EBrec andEFBrec.

Fig. 2. The EBDs of the descriptive model for several SNRs and reproducedEBD.

Afterwards, we can create error bursts and error-free burstsaccording to the lengths in the modified EBrec and EFBrec.Generating error-free bursts is simple because the lengths of themodified EFBrec can easily be converted to series of zeros,unlike error bursts which contain zeros and ones. Generatingerror bursts involves retrieving their structures from the errorbursts of error sequences X and Y . The retrieved error burstshave the same length me as in the newly obtained EBrec ofZ. Finally, the error bursts and error-free bursts are combinedtogether to construct the new required error sequence Z.

IV. SIMULATION RESULTS AND DISCUSSIONS

To validate our proposed adaptive generative models, we firstneed to obtain reference error sequences, which are essentialto initialize various parameters for the generative models. Weused an uncoded LTE system to obtain the required referenceerror sequences. The performance criteria are the burst errorstatistics defined in Section II. A generative model is better if itsburst error statistics better match those of the descriptive model,particularly the most important statistics such as the BEPDand BECF.

The uncoded LTE system [38] has a burst interleaver, ratematcher, adaptive modulation and coding (AMC), a viterbiequalizer, and a burst deinterleaver. The utilized propagationchannel can be expressed as NAMEx, where x represents thevehicle speed in km/h. NAME here represents the name of theunderlying channel, e.g., a rural area (RA) channel, a typicalurban (TU) channel, or a pedestrian B (PedB) channel. Weused the following channels: RA275, TU3, TU50, PedB5, andPedB10. The received data has a length of 12× 106, and thetransmission rate is Fs = 3450 kb/s. Reference error sequenceswere produced at SNRs of 1 dB, . . ., 7 dB.

By comparing the transmitted error sequence with thereceived one, we work out the bit error sequences. Weuse the three discussed generative models, namely, ASFM,ABWHMM, and ADPBGM, in order to generate new errorsequences of length 15× 106 bits based on the obtained errorsequences from the LTE system. In this paper, we show only the


results of the TU50 channel having SNRs of 2 dB, 3 dB, 4 dB,and 5 dB.

For the ASFM, the fitting of P (0m0 |1) is achieved by usingfive exponentials, and therefore, N = 6 holds. In our experi-ments, no better performance can be accomplished for SFMswith more than six states. After we fit (3) with P (0m0 |1) ofSNRs = 2 dB, 3 dB, and 5 dB, we can obtain the transition ma-trices from which we can generate new error sequences. After-wards, we apply (10)–(12) to calculate the adaptive PZ(0

m0 |1).Once we know the adaptive PZ(0

m0 |1), (1) and (3) can beapplied to generate new error sequences Z.

For the ABWHMM, we extract the error bursts from errorsequences with SNRs = 3 dB and 5 dB. Then, we divideeach error burst into blocks with L = 20 bits and obtain theNELh vectors. We apply (14) afterwards to obtain the NELhZ

vectors. A Baum-Welch training process was then applied toNELhZ after classifying it into a satisfactory number of states.The number of classes N is 7 in our example, and the numberof substates is considerably large. Finally, the generated errorbursts are concatenated with the generated error-free bursts inorder to produce the full required error sequence.

In order to proceed with the ADPBGM, we need to find thevector Ψ. The value of qs was chosen as 0.01. For the error se-quences with SNRs = 2 dB, 3 dB, and 5 dB, NEB = 428418,69706, and 122474 and RB = 8.43, 5.24, and 2.09, respec-tively. Consequently,Ψ=(9,10,0.09,0.0425,34.9 kHz,8.33 μs)for SNR = 2 dB, Ψ = (9, 10, 0.09, 0.0470, 36.8 kHz, 5.43 μs)for SNR = 3 dB, and Ψ = (9, 10, 0.09, 0.0599, 40.9 kHz,4.97 μs) for SNR = 5 dB. For the new required error sequenceZ, the vector ΨZ can be obtained by (22). Then, we findNEB(me) and the modified NEB(me) for the error sequenceZ with the aid of (23) and (24). Similarly, NEFB(me) and themodified NEFB(me) can be found.

Eventually, the error bursts and error-free bursts are com-bined to construct entailed error sequences Z. The bit structurein the new error bursts is retrieved from the two reference errorsequences X and Y based on the error burst lengths.

In the following, we focus on simulations where SNRZ is be-tween SNRX and SNRY due to limited space. However, otherSNR values are applicable to our adaptive models, as shownin Figs. 1 and 2. Here, we produce an error sequence Z withSNR = 4 dB from reference error sequences X with SNR =3 dB and Y with SNR = 5 dB (first scenario, Figs. 3–7). Wealso produce an error sequence Z with SNR = 4 dB fromerror sequences X with SNR = 2 dB and Y with SNR = 5 dB(second scenario, Figs. 8–11). This means that α = β = 0.5for the first scenario and α = 1/3 and β = 2/3 for the secondscenario. The second scenario investigates the impact of furtherdistancing the SNRs of error sequences X and Y from the SNRof error sequences Z. We compare the burst error statistics oferror sequences Z, obtained from both scenarios, with thosestatistics obtained from the reference error sequence of the LTEsimulator having SNR = 4 dB. In terms of parametrization, thevalue of η can be found from Fig. 1 when the curve is tendingto turn, and it was chosen to be 20.

Figs. 3–11 illustrate various burst error statistics of thedescriptive model and adaptive generative models such as theECDs (Figs. 3 and 11), BEPDs (Figs. 4 and 8), BECFs (Figs. 5

Fig. 3. The ECDs of the descriptive model, generative models, and threeadaptive generative models (SNR = 4 dB obtained from 3 dB and 5 dB).

Fig. 4. The BEPDs of the descriptive model, generative models, and threeadaptive generative models (SNR = 4 dB obtained from 3 dB and 5 dB,n = 50).

Fig. 5. The BECFs of the descriptive model, generative models, and threeadaptive generative models (SNR = 4 dB obtained from 3 dB and 5 dB).

and 9), EBDs (Figs. 6 and 10), EFRDs (Fig. 1), and GDs(Fig. 7). Figs. 3–7 omit the comparison between the DPBGMand the ADPBGM since the DPBGM gives approximate resultsto the descriptive one [31]. In general, the ADPBGM shows


Fig. 6. The EBDs of the descriptive model, generative models, and threeadaptive generative models (SNR = 4 dB obtained from 3 dB and 5 dB).

Fig. 7. The GDs of the descriptive model, generative models, and threeadaptive generative models (SNR = 4 dB obtained from 3 dB and 5 dB).

Fig. 8. The BEPDs of the descriptive model, ASFM, and ADPBGM(n = 50).

the best fit to the descriptive model. This is clear for all theburst error statistics, except a small mismatch at the end ofthe curve of the ECD (see Fig. 3) and the BEPD (see Fig. 4).The second best generative model is the ASFM, althoughits burst error statistics considerably mismatch those of theADPBGM. However, the ASFM and the SFM fit each other.The ABWHMM results are slightly worse than those obtainedusing the normal BWHMM procedure.

Fig. 9. The BECFs of the descriptive model and ADPBGM.

Fig. 10. The EBDs of the descriptive model and ADPBGM (n = 50).

Fig. 11. The ECDs of the descriptive model and ADPBGM.

In Figs. 8–11, we omit the results of the ABWHMM be-cause its burst error statistics do not match those of theBWHMM. Fig. 8 shows the BEPDs of the descriptive model forSNRs = 3 dB, 4 dB, and 5 dB, as well as the BEPDs of theADPBGM and the ASFM for SNR = 4 dB obtained from twoscenarios, i.e., from SNRs = 3 dB and 5 dB and SNRs =2 dB and 5 dB. It is found that distancing the SNRs that arerequired to produce the new error sequence can deteriorate the


Fig. 12. The coded BER of the descriptive model and three adaptive genera-tive models.

performance of the ADPBGM. On the other hand, the ASFMis not affected by distancing the reference SNRs, althoughthe general performance of the ASFM is not satisfactory (farfrom the descriptive model). In Figs. 9–11, we illustrate theBECFs, EBDs, and ECDs of the descriptive model for SNRs =3 dB, 4 dB, and 5 dB, as well as those of the ADPBGM forSNR = 4 dB obtained from two scenarios, respectively, whileneglecting the results for ASFM and ABWHMM. It is clear thatthe ADPBGM is slightly affected by changing the values of αand β. Fig. 12 shows the BER performance of the coded LTEsystem using the original error sequence (descriptive model)and newly generated error sequences using three adaptive gen-erative models. Note that the new error sequences Z of the threegenerative models were obtained from two neighboring errorsequences X and Y with SNRs distancing 1 dB from the SNRof error sequences Z, i.e., α = β = 1/2. It is apparent that theADPBGM outperforms the ASFM and the ABWHMM in termsof fitting the coded BER performance.

Regarding the simulation time, obtaining a reference errorsequence with a length of 12 million bits can take more than10 hours. Generating an error sequence with the same lengthusing generative models can take just a few minutes or sec-onds [31]. However, it takes adaptive generative models a fewseconds to generate many new error sequences. Therefore,adaptive generative models are very efficient in terms of savingthe simulation time as we can simply use two reference errorsequences to produce many new error sequences.

V. CONCLUSION

Adaptive generative models are highly desirable becausethey can generate new error sequences with any channel con-ditions (or SNRs) utilizing limited available reference errorsequences. Compared to descriptive models and traditionalgenerative models, adaptive generative models can significantlyreduce the computational time when we need a huge number oferror sequences for the purpose of evaluating the performanceof a digital communication system. In this paper, we haveproposed three adaptive generative models, i.e., ADPBGM,ASFM, and ABWHMM. To validate our proposed adaptive

algorithms, we have used uncoded LTE system to obtain afew reference error sequences at various SNRs. It has beenillustrated through simulations that the ADPBGM can well fitthe descriptive model and the DPBGM in terms of both bursterror statistics and fitting the BER performance of the codedLTE system. The ASFM and the ABWHMM give poor bursterror statistics compared to those of the descriptive model.However, the ASFM is superior to the ABWHMM regardingmost of the burst error statistics. It has also been found thatthe burst error statistics of the ASFM match those of the SFM,while the burst error statistics of the ABWHMM do not matchthose of the BWHMM.

REFERENCES

[1] J. G. Proakis, Ed., Digital Communications, 4th ed. New York, NY,USA: McGraw-Hill, 2001.

[2] H.-H. Hung and L.-J. Chen, “An analytical study of wireless error modelsfor bluetooth networks,” in Proc. AINAW, Okinawa, Japan, Mar. 2008,pp. 1317–1322.

[3] P. M. Crespo, R. M. Pelz, and J. Cosmas, “Channel error profiles forDECT,” Proc. Inst. Elect. Eng.—Commun., vol. 141, no. 6, pp. 413–420,Dec. 1994.

[4] L. N. Kanal and A. R. K. Sastry, “Models for channels with memoryand their applications to error control,” Proc. IEEE, vol. 66, no. 7,pp. 724–744, Jul. 1978.

[5] M. Zorzi, R. R. Rao, and L. B. Milstein, “ARQ error control forfading mobile radio channels,” IEEE Trans. Veh. Technol., vol. 46, no. 2,pp. 445–455, May 1997.

[6] M. Zorzi and R. R. Rao, “Perspectives on the impact of error statisticson protocols for wireless networks,” IEEE Pers. Commun., vol. 6, no. 10,pp. 32–40, Oct. 1999.

[7] G. Mazzini, “Queue system with smart ARQ on Markov channel forenergy efficiency,” in Proc. IWCMC, Jun. 2005, pp. 546–551.

[8] L. Badia, N. Baldo, M. Levorato, and M. Zorzi, “A Markov frameworkfor error control techniques based on selective retransmission in videotransmission over wireless channels,” IEEE J. Sel. Areas Commun.,vol. 28, no. 3, pp. 488–500, Apr. 2010.

[9] L. Badia, “On the effect of feedback errors in Markov models for SRARQ packet delays,” in Proc. IEEE GLOBECOM, Honolulu, HI, USA,Dec. 2009, pp. 3745–3750.

[10] C. Jiao, L. Schwiebert, and B. Xu, “On modeling the packet error statisticsin bursty channels,” in Proc. IEEE LCN, Tampa, FL, USA, Nov. 2002,pp. 534–541.

[11] A. Willig, “A new class of packet- and bit-level models for wire-less channels,” in Proc. IEEE PIMRC, Lisbon, Portugal, Sep. 2002,pp. 2434–2440.

[12] E. N. Gilbert, “Capacity of a burst-noise channel,” Bell Syst. Tech. J.,vol. 39, no. 5, pp. 1253–1265, Sep. 1960.

[13] E. O. Elliot, “Estimates of error rates for codes on burst-noise channels,”Bell Syst. Tech. J., vol. 42, no. 5, pp. 1977–1997, Sep. 1963.

[14] B. D. Fritchman, “A binary channel characterization using partitionedMarkov chains,” IEEE Trans. Inf. Theory, vol. IT-13, no. 2, pp. 221–227,Apr. 1967.

[15] H. S. Wang and N. Moayeri, “Finite-state Markov channel—A usefulmodel for radio communication channels,” IEEE Trans. Veh. Technol.,vol. 44, no. 1, pp. 163–171, Feb. 1995.

[16] F. De Rango, F. Veltri, and S. Marano, “Channel modeling approachbased on the concept of degradation Level discrete-time Markov chain:UWB system case study,” IEEE Trans. Wireless Commun., vol. 10, no. 4,pp. 1098–1107, Apr. 2011.

[17] K. Fukawa, H. Suzuki, and Y. Tateishi, “Packet error rate analysis usingMarkov models of signal-to-interference ratio for mobile packet systems,”IEEE Trans. Veh. Techol., vol. 61, no. 6, pp. 2517–2530, Jul. 2012.

[18] F. Swarts and H. C. Ferreira, “Markov characterization of digitalfading mobile VHF channels,” IEEE Trans. Veh. Technol., vol. 43, no. 4,pp. 977–985, Nov. 1994.

[19] A. Semmar, M. Lecours, J. Y. Chouinard, and J. Ahern, “Characterizationof error sequences in UHF digital mobile radio channels,” IEEE Trans.Veh. Technol., vol. 40, no. 4, pp. 769–776, Nov. 1991.

[20] W. Turin, Digital Transmission Systems: Performance Analysis andModeling. New York, NY, USA: McGraw-Hill, 1999.


[21] J. Garcia-Frias and P. M. Crespo, “Hidden Markov models for burst errorcharacterization in indoor radio channels,” IEEE Trans. Veh. Technol.,vol. 46, no. 6, pp. 1006–1020, Nov. 1997.

[22] O. S. Salih, C.-X. Wang, and D. I. Laurenson, “Double embedded pro-cesses based hidden Markov models for binary digital wireless channels,”in Proc. IEEE ISWCS, Reykjavik, Iceland, Oct. 2008, pp. 219–223.

[23] M. U. Ilyas and H. Radha, “Modeling, estimating and predicting thepacket-level bit error rate process in IEEE 802.15.4 LR-WPANs us-ing hidden Markov models,” in Proc. CISS, Baltimore, MD, USA,Mar. 18–20, 2009, pp. 241–246.

[24] L. R. Rabiner, “A tutorial on hidden Markov models and selected appli-cations in speech recognition,” Proc. IEEE, vol. 77, no. 2, pp. 257–286,Feb. 1989.

[25] W. Zhu and J. Garcia-Frias, “Stochastic context-free grammars and hid-den Markov models for modeling of bursty channels,” IEEE Trans. Veh.Technol., vol. 53, no. 3, pp. 666–676, May 2004.

[26] E. Costamagna, L. Favalli, and P. Gamba, “Multipath channel model-ing with chaotic attractors,” Proc. IEEE, vol. 90, no. 5, pp. 842–859,May 2002.

[27] E. Costamagna, L. Favalli, P. Gamba, and P. Savazzi, “Block-error prob-abilities for mobile radio channels derived from chaos equations,” IEEECommun. Lett., vol. 3, no. 3, pp. 66–68, Mar. 1999.

[28] E. Costamagna, L. Favalli, P. Savazzi, and F. Tarantola, “Long sequencesof error gaps derived from chaotic generators optimized for short ones inmobile radio channels,” in Proc. IEEE VTC-Fall, Los Angeles, CA, USA,Sep. 2004, pp. 4250–4254.

[29] A. Köpke, A. Willig, and H. Karl, “Chaotic maps as parsimonious bit errormodels of wireless channels,” in Proc. IEEE INFOCOM, San Francisco,CA, USA, Mar. 30–Apr. 3, 2003, pp. 513–523.

[30] C. X. Wang and M. Pätzold, “A generative deterministic model for digitalmobile fading channels,” IEEE Commun. Lett., vol. 8, no. 4, pp. 223–225,Apr. 2004.

[31] C.-X. Wang and W. Xu, “A new class of generative models for burst-errorcharacterization in digital wireless channels,” IEEE Trans. Commun.,vol. 55, no. 3, pp. 453–462, Mar. 2007.

[32] Y. He, O. Salih, C.-X. Wang, and D. Yuan, “Deterministic process basedgenerative models for characterizing packet-level bursty error sequences,”Wireless Commun. Mobile Comput., 2013, DOI:10.1002/wcm.2356, to bepublished.

[33] S. Tsai, “Markov characterization of the HF channel,” IEEE Trans.Commun. Technol., vol. COM-17, no. 1, pp. 24–32, Feb. 1969.

[34] W. C. Jakes, Ed., Microwave Mobile Communications, 2nd ed.Piscataway, NJ, USA: IEEE, 1994.

[35] C.-X. Wang, M. Pätzold, and D. Yuan, “Accurate and efficient simula-tion of multiple uncorrelated Rayleigh fading waveforms,” IEEE Trans.Wireless Commun., vol. 6, no. 3, pp. 833–839, Mar. 2007.

[36] C.-X. Wang, D. Yuan, H.-H. Chen, and W. Xu, “An improved determinis-tic SoS channel simulator for efficient simulation of multiple uncorrelatedRayleigh fading channels,” IEEE Trans. Wireless Commun., vol. 7, no. 9,pp. 3307–3311, Sep. 2008.

[37] M. Pätzold, C.-X. Wang, and B. O. Hogstad, “Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelatedRayleigh fading waveforms,” IEEE Trans. Wireless Commun., vol. 8,no. 6, pp. 3122–3131, Jun. 2009.

[38] C. Mehlführer, M. Wrulich, J. C. Ikuno, D. Bosanska, and M. Rupp,“Simulating the long term evolution physical layer,” in Proc. EUSIPCO,Glasgow, U.K., Aug. 2009, pp. 1471–1478.

Omar S. Salih (S’07–M’14) received the Ph.D. de-gree in electrical and electronic engineering jointlyfrom the Institute of Sensors, Signals, and Systems,Heriot-Watt University, Edinburgh, U.K., and theInstitute of Digital Communications, University ofEdinburgh, Edinburgh.

He is currently an Assistant Lecturer withthe Department of Aviation, Aerospace, Electricaland Electronic Engineering, Coventry University,Coventry, U.K. His main research interests are indigital channel modeling, propagation and channel

characterization, 4G and 5G cellular systems, DSP applications to wirelesssystems, resource allocation and load balancing, and adaptive antennas forwireless systems.

Cheng-Xiang Wang (S’01–M’05–SM’08) receivedthe B.Sc. and M.Eng. degrees in communicationand information systems from Shandong University,Jinan, China, in 1997 and 2000, respectively, andthe Ph.D. degree in wireless communications fromAalborg University, Aalborg, Denmark, in 2004.

Since 2005, he has been with Heriot-Watt Univer-sity, Edinburgh, U.K., where he became a Professorin 2011. He is also an Honorary Fellow with theUniversity of Edinburgh and a Chair/Guest Professorwith Shandong University and Southeast University,

Nanjing, China. He was a Research Fellow with the University of Agder,Grimstad, Norway, from 2001 to 2005; a Visiting Researcher with SiemensAG-Mobile Phones, Munich, Germany, in 2004; and a Research Assistant withTechnical University of Hamburg-Harburg, Hamburg, Germany, from 2000 to2001. His current research interests include wireless channel modeling andsimulation, massive MIMO, green communications, cognitive radio networks,vehicular communication networks, and 5G wireless communications. He hasedited one book and published one book chapter and over 200 papers in refereedjournals and conference proceedings.

Prof. Wang served or is currently serving as an Editor of eight internationaljournals, including the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY(2011-) and the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS(2007–2009). He was the leading Guest Editor of the IEEE JOURNAL ONSELECTED AREAS IN COMMUNICATIONS, Special Issue on Vehicular Com-munications and Networks. He served or is serving as a TPC member, a TPCChair, and a General Chair for over 70 international conferences. He receivedthe Best Paper Awards from IEEE Globecom 2010, IEEE ICCT 2011, ITST2012, and IEEE VTC 2013-Fall. He is a Fellow of the IET, a Fellow of theHEA, and a member of EPSRC Peer Review College.

Bo Ai (M’00–SM’10) received the M.S. and Ph.D.degrees from Xidian University, Xi’an, China, in2002 and 2004, respectively. He graduated in 2007with great honors of Excellent Postdoctoral ResearchFellow from Tsinghua University.

He is currently a Professor and an Advisor ofPh.D. candidates with Beijing Jiaotong University.He is also a Deputy Director of the State KeyLaboratory of Rail Traffic Control and Safety. Hehas authored/co-authored 6 books, 140 scientific re-search papers, and 26 invention patents in his re-

search area. His current interests are the research and applications of OFDMtechniques, HPA linearization techniques, radio propagation and channel mod-eling, GSM for railway systems, and LTE for railway systems. He has re-ceived many awards including the Qiushi Outstanding Youth Award from theHong Kong Qiushi Foundation, the New Century Talents Award from theChinese Ministry of Education, the Zhan Tianyou Railway Science and Tech-nology Award from the Chinese Ministry of Railways, and the Science andTechnology New Star Award from the Beijing Municipal Science and Tech-nology Commission. He is an Associate Editor of IEEE TRANSACTIONS ONCONSUMER ELECTRONICS and an Editorial Committee Member of the journalWireless Personal Communications. He is the Co-Chair or the Session/Trackchair of many international conferences such as the 9th International HeavyHaul Conference in 2009, IEEE ICIRT 2011, HSRCom2011, IEEE ISCE 2012,ICWMMN 2013, IEEE Green HetNet 2013, and IEEE 78th VTC 2014. He isan IET Fellow.

Raed Mesleh (S’00–M’08–SM’13) received thePh.D. degree in electrical engineering from JacobsUniversity Bremen, Bremen, Germany, and has sev-eral years of post-doctoral wireless communicationand optical wireless communication research expe-rience in Germany. In October 2010, he joined theUniversity of Tabuk, Tabuk, Saudi Arabia, wherehe is now an Assistant Professor in the ElectricalEngineering Department and the Director of researchexcellence and intellectual properties units. He in-vented spatial modulation, trellis coded spatial mod-

ulation and the use of OFDM for visible light communication. His mainresearch interests are in spatial modulation, MIMO cooperative wireless com-munication techniques and optical wireless communication. His publicationshave received more than 1400 citations since 2007. He has published more than70 journal and conference papers and holds 7 patents. In 2012, he received theIEEE COMMUNICATION LETTER Exemplary Reviewer Certificate.

Adaptive Generative Models for Digital Wireless Channels...Adaptive Generative Models for Digital...

Documents

Transcript of Adaptive Generative Models for Digital Wireless Channels...Adaptive Generative Models for Digital...