The choice of OFDM as the multiple access technology is based not only on physicallayer consideration, but also on the MAC layer, data link layer, and network layer requirements.. Mostno
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As its name suggests, the system is based on OFDM, however, OFDMA is much more than just
a physical layer solution It is a cross-layer-optimized technology that exploits the unique physicalproperties of OFDM, enabling significant higher layer advantages that contribute to very efficientpacket data transmission in a cellular network
Packet-switched air interface
The telephone network, designed basically for voice, is an example of circuit-switched systems.Circuit-switched systems exist only at the physical layer that uses the channel resource to create anend-to-end bit pipe They are conceptually simple as the bit pipe is a dedicated resource, and the pipedoes not need to be controlled once it is created (some control may be required in setting up or tearingdown the pipe) Circuit-switched systems, however, are very inefficient for burst data traffic Packet-switched systems, on the other hand, are very efficient for data traffic but require that the upper layers
be controlled in addition to the physical layer that creates the bit pipe The MAC layer is required forthe many data users to share the bit pipe The data link layer is needed to take the error-prone pipeand create a reliable link for the network layers to pass packet data flows over The Internet is the bestexample of a packet-switched network Because all conventional cellular wireless systems, including3G, were fundamentally designed for circuit-switched voice, they were designed and optimized pri-marily at the physical layer Some people suggested that the choice of CDMA as the physical layermultiple access technology was also dictated by voice requirements OFDMA, on the other hand, is apacket-switched scheme designed for data and is optimized across the physical, MAC, data link, andnetwork layers The choice of OFDM as the multiple access technology is based not only on physicallayer consideration, but also on the MAC layer, data link layer, and network layer requirements
Physical layer advantages: OFDMA
As discussed earlier, most of the physical layer advantages of OFDM are well understood Mostnotably, OFDM creates a robust multiple access technology to deal with the impairments of thewireless channel, such as multipath fading, delay spread, and Doppler shifts Advanced OFDM-baseddata systems typically divide the available spectrum into a number of equally spaced tones For eachOFDM symbol duration, information carrying symbols (based on modulation such as QPSK, QAM,etc.) are loaded on each tone
The OFDMA can also use fast hopping across all tones in a predetermined pseudorandom pattern,making it an SS technology With fast hopping, a user that is assigned one tone does not transmit everysymbol on the same tone, but uses a hopping pattern to jump to a different tone for every symbol.Different BSs use different hopping patterns, and each uses the entire available spectrum (thus torealize frequency reuse of 1) In cellular deployment, this adds to the advantages of CDMA systems,including frequency diversity and out of cell (intercell) interference averaging spectral efficiencybenefit that narrowband systems such as conventional TDMA do not have
As discussed earlier, different users within the same cell use different resources (tones) and hence
do not interfere with each other This is similar to TDMA, where different users in a cell transmit
at different time slots and do not interfere with one another In contrast, CDMA users in a cell dointerfere with each other, increasing the total interference in the system OFDMA therefore has the
physical layer benefits of both CDMA and TDMA and is at least three times (3times) more efficient
than CDMA In other words, at the physical layer, OFDMA creates the biggest pipe of all cellular
technologies Even though the 3times advantage at the physical layer is a huge advantage, the most
significant advantage of OFDMA for data is at the MAC and link layers
MAC and link layer advantages
OFDMA exploits the granular nature of resources in OFDM to come up with extremely efficientcontrol layers In OFDM, when designed appropriately, it is possible to send a very small amount
Trang 2MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 297(as little as one bit) of information from the transmitter to the receiver with virtually no overhead.Therefore, a transmitter that is previously not transmitting can start transmitting as little as one bit ofinformation, and then stop, without causing any resource overhead This is unlike CDMA or TDMA,
in which the granularity is much coarser, and merely initiating a transmission wastes a significantresource Hence, in TDMA, for example, there is a frame structure, and whenever a transmission
is initiated, a minimum of one frame (a few hundred bits) of information is transmitted The framestructure does not cause any significant inefficiency in user data transmission, as data traffic typicallyconsists of a large number of bits However, for the transmission of control-layer information, theframe structure is extremely inefficient, as the control information typically consists of one or twobits but requires a whole frame Not having a granular technology can therefore be very detrimentalfrom a MAC layer and link layer point of view
OFDMA takes advantage of the granularity of OFDM in its control-layer design, enabling theMAC layer to perform efficient packet switching over the air and at the same time provide all thehooks to handle QoS It also supports a data link layer that uses local (as opposed to end-to-end)feedback to create a very reliable link from an unreliable wireless channel, with very low delays.The network layer’s traffic therefore experiences small delays and no significant delay jitter Hence,interactive applications such as (packet) voice can be supported Moreover, Internet protocols such
as TCP/IP run smoothly and efficiently over an OFDMA air link As discussed in Chapter 3, TCP/IPperformance on 3G networks is very inefficient because the data link layer introduces significant delayjitter so that channel errors are misinterpreted by TCP as network congestion and TCP responds bybacking off to the lowest rate
Packet switching leads to efficient statistical multiplexing of data users and helps the wirelessoperators to support a much greater number of users for a given user experience This desirable feature
in OFDMA, together with QoS support and a three times bigger pipe, allows the operators to profitably
scale their wireless networks to meet the burgeoning data traffic demand in an all-you-can-eat pricingenvironment
As mentioned in Section 2.2.3, the UWB technology can be viewed as a derivative from the spreadingspectrum technology, in particular, the time hopping spread spectrum (THSS) technique, which isalso considered as a multiple access technology, being particularly suited for extreme narrow pulsetransmissions Before discussing the technical details about the UWB technologies, we would like toreview briefly the history as well as the recent research activities carried out in this area
Since the introduction of UWB technology to commercial applications in the early 1990s [674],much of its initial research has been focused on the application of the THSS [675], where sev-eral pulses in each symbol duration are sent with a particular time offset pattern determined by aunique signature code for multiple access The implementation of a THSS-UWB system requires aprecise network-wise synchronization clock This inevitably increases overall hardware complexity
at a transceiver, which used to be a major concern in realizing a feasible UWB system at its earlystage On the other hand, DS techniques can also work jointly with UWB systems to provide multipleaccess among different users within the same wireless personal area network (WPAN) The operation
of a DS-UWB system does not need an accurate synchronization clock and the use of antipodalpulses in DS modulation can boost up effective transmission power, which is very important toimprove the detection efficiency of a UWB receiver, due to the severe emission constraints imposed
on the power spectral mask specified in the FCC Part15.209, in which the maximal transmittingpower for a UWB transmitter should be lower than−41.3 dBm within the bandwidth from 3.1 to10.6 GHz
The UWB technologies have been standardized in IEEE 802.15.3a as a technology for WPANs.Figure 7.18 shows all IEEE 802 standards, including those for WLANs as IEEE 802.11 standards,
Trang 3298 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS
Figure 7.18 Various IEEE 802 standards, in which UWB technologies have been covered in IEEE802.15.3a standard for WPAN applications
wireless metropolitan area networks (WMANs) as IEEE 802.16 standards, WPANs as IEEE 802.15standards, and so on It is noted that IEEE 802.15.4.a is emerging as the standard for low-data-ratetransmission
The FCC issued a notice of inquiry (NOI) in September 1998 and within a year the Time DomainCorporation, US Radar, and Zircon Corporation had received waivers from the FCC to allow limiteddeployment of a small number of UWB devices to support continued development of the technology,and the University of Southern California (USC) UltRa Lab had an experimental licence to studyUWB radio transmissions A notice of proposed rule making (NPRM) was issued in May 2000 InApril 2002, after extensive commentary from the industry, the FCC issued its first report and order
on UWB technology, thereby providing regulations to support deployment of UWB radio systems.This FCC action was a major change in the approach to the regulation of RF emissions, allowing
a significant portion of the RF spectrum, originally allocated in many smaller bands exclusively forspecific uses, to be effectively shared with low-power UWB radios
The FCC regulations classify UWB applications into several categories (see Table 7.5) with ent emission regulations in each case Maximum emissions in the prescribed bands are at an effective
differ-Table 7.5 The application categories specified by FCC UWB regulations
Application Frequency band for operation User limitations
at Part 1 limitCommunications and
measurement systems
3.1 to 10.6 GHz (differentout-of-band emissionlimits for indoor andoutdoor devices)
No
Imaging: ground penetrating
radar, wall, medical
Trang 4MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 299
Part 15 Limit
Figure 7.19 FCC regulated spectral masks regarding the indoor and outdoor UWB communicationsapplications
Figure 7.20 Other communications applications in the vicinity of UWB operating bands
isotropic radiated power (EIRP) of−41.3 dBm per MHz, and the −10 dB level of the emissions mustfall within the prescribed band, as shown in Figure 7.19, which should be compared with Figure 7.20
to know other communication applications in the vicinity of the UWB operating bands
7.6.1 Major UWB Technologies
There are four major UWB technologies that have been proposed in the literature The first type
is Time Hopped (TH) UWB or Time-modulated (TM) UWB,1 which is a traditional UWB scheme
1 The traditional impulse radio technology can be called as either time hopped (TH) UWB or time modulated (TM) UWB It should be noted that both names are used very often.
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and is often called impulse radio (IR) UWB The TH-UWB is by far the earliest version of UWB
technology and remains an important solution even today The TH-UWB can be further divided intotwo subcategories, that is, analog impulse radio multiple access (AIRMA) and digital impulse radiomultiple access (DIRMA), which were suggested and studied in [613, 624, 637] The second UWB
technology is called direct-sequence CDMA-based UWB and can be implemented with a multi-carrier
CDMA architecture The DS-CDMA UWB scheme will be discussed in detail in Subsections 7.6.1,7.6.2, 7.6.3, 7.6.4, and 7.6.5 Another UWB scheme that has gained much popularity is based onOFDM technology, namely, OFDM-UWB, which can be implemented on a multiband (MB) OFDMscheme The MB-OFDM UWB technology is particularly useful when cognitive radio technology isused, as discussed in Chapter 9 In addition, some people also proposed frequency-modulation (FM)based UWB systems, which can be implemented by swept frequency technology Figure 7.21 shows
a family tree for all possible UWB technologies that have been proposed so far Because of limitedspace, we will only focus on the discussions on TH-UWB (or TM-UWB) and DS-CDMA UWB inthis subsection
TH-UWB technology
The basic concept of a TH-UWB system is shown in Figure 7.22, where the system consists offour major parts, namely, modulator2, delay unit, transmission time controller, and a pseudorandomsequences generator Obviously, in such a TH-UWB system, the data is sent in bursts and transmissiontime is controlled by the pseudorandom sequences generator
Understandably, the bandwidth of such a TM-UWB system is determined by the width and shape
of impulses, which usually takes some special waveforms, such as “monocycle.” The design of themonocycles suitable for IR applications is a very interesting research topic in that the shape of themonocycles should provide a very good time ACF for a better detection efficiency and fit FCC spectralmask as illustrated in Figure 7.19 There are many pulse waveforms that have been proposed, such asGaussian pulse and its derivative functions, Hermite pulse and its modified versions, prolate spheroidalwaveforms, Laplacian monocycle, cubic monocycle, wavelets, and so on For more information onthese popular impulses suitable for UWB applications, please refer to the large number of referencesgiven at the end of this book [604–691]
Figure 7.21 Family tree for various UWB technologies proposed so far
2 The most commonly used modulator scheme in an IR (or time hopping UWB) is pulse position modulation (PPM), although many other modulation schemes can also be used, such as pulse amplitude modulation (PAM), on-off-keying (OOK), pulse shape modulation (PSM), and so on.
Trang 6MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 301
Figure 7.22 Block diagram for a TH-UWB IR transmitter
The data signal should be sent out from an IR system, as shown in Figure 7.22, using less transmission The base band signal can be converted directly from the received signal and nointermediate frequency unit is required, thus reducing the implementation complexity The TM-UWBscheme can provide a relatively large PG due to the fact that it has a very narrow impulse (whosewidth is of the order of a nanosecond) This large PG also entails several other operational advantages,which are explained as follows First of all, it offers an excellent multipath immunity because of itsvery high so time resolution that almost all multipath components can be separated and combinedcoherently at a receiver If the time between two pulses is longer than the channel delay spread,there will be no ISI between two consecutive pulses, nor between two symbols.3 Second, it gives agood resistance to external interference based on the same reasons as any SS system The big PGalso ensures a relatively low-power spectral density, which helps in not causing interference to otherexisting wireless applications, as shown in Figure 7.20
carrier-It is to be noted that the data-carrying modulation in an IR-UWB system is usually PPM, whichcontrols the appearance position of a pulse in a certain duration to represent different data-information
On the other hand, the multiple access capability of an IR-UWB system is implemented through timehopping schemes, as briefly discussed in Subsection 2.2.3 Different users in a pico-cell can beassigned different PN sequences that control the timing of pulses, as shown in Figure 7.23, whereonly three users are present for simplicity of illustration and 13 hopping slots are shown in onesymbol duration In this case, there is no overlapping in the hopping slots among the three users,implying that there will be no MAI
A TH-UWB can offer a very good time diversity gain if multiple hopping patterns can be assigned
to a single user Therefore, it is intuitively true that it can be made very robust against time-selectivefading, especially suitable for the applications where fast mobility is present.4
DS-CDMA UWB technology
The direct-sequence CDMA UWB scheme is the focus of discussion in this subsection The analysis
of a DS-CDMA UWB system is given in the following subsections A DS-CDMA UWB schemeworks like a conventional DS-CDMA system The pulse trains are used to perform DS modulation
to spread the signal A PN code is assigned to a particular user and will be used to spread its data bitinto multiple chips In the same way as in IR, various data modulation schemes, such as PAM, OOK,PSM, and so on, can also be used in the DS-CDMA UWB system Figure 7.24 shows an example
of the PAM-modulated DS-CDMA UWB scheme
3 This is particularly true if a UWB system is operating in an indoor environment where the delay spread is relatively small.
4 Because of the fact that most UWB systems are operated in an indoor environment, this advantage may not
be well exploited.
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U
U
U
Figure 7.23 Multiple access capability provided by a TH-UWB IR system
Figure 7.24 Conceptual diagram of a DS-CDMA UWB system with PAM
Many results have been reported on the performance of the DS-CDMA-based UWB systems, asshown in [594–673] Srinivasa [677] presents a comparison between a TH-PPM UWB and a TH
DS spreading with antipodal signaling (TH/DS-BPSK) in terms of their multiple access performance,where the study was limited to an AWGN channel only Foester [678] characterized the performance
of a direct sequence UWB system in the presence of multipath and narrowband interferences It wasshown that the code design that tries to minimize sequence autocorrelation sidelobes as well as crosscorrelation among spreading codes is critical for a good performance under multipath, multiuser, andnarrowband interferences at the same time
A comprehensive review on almost all possible multiple access techniques suitable for based WPANs or piconet was given in [679] It was suggested that, among all multiple access schemes(i.e FDMA, TDMA, and CDMA), CDMA is the most suitable for UWB applications The use ofCDMA allows multiple piconets to be relatively independent, and it is able to produce the highestaggregate data rate It was also pointed out that CDMA is completely compatible with high QoS,
Trang 8UWB-MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 303video streaming capable MAC layer protocols, such as the TDMA-based IEEE 802.15.3 On theimplementation side, to map to high-speed low-voltage low-power IC technologies, UWB systemsmust use low peak-to-average pulse trains with a relatively high chip rate These high chip rates areperfectly suited for building UWB CDMA systems.
Qinghua Li and Rusch [680, 681] studied the effectiveness of an adaptive MMSE multiuserdetection for a DS-CDMA-based UWB system, particularly under the interference of an IEEE 802.11aOFDM transmitter, as shown in Figure 7.20 Extensive simulations were performed using channelsounding techniques in the 2- to 8-GHz band in a residential environment, which was characterized
by a high level of multipath fragmentation It was demonstrated that the adaptive MMSE is able toreject intersymbol and interchip interference for those channels much more effectively than by using
a RAKE receiver with four to eight fingers It was also shown that the same receiver setting canreject a narrowband interferer generated from an adjacent IEEE 802.11a transmitter The majority ofthe work was carried out on the basis of computer simulations
Sadler and Swami [682] investigated a DS-UWB system with so-called episodic transmission,
that is, the system should sendn pulses per information bit and allow for off time separation between
pulses Several issues on the design of a DS-UWB system, such as PG, jamming margin, coding gain,and multiple access interference, power control, and so on, were investigated The BER performance
was studied using a Chernoff bound and considering a single-user matched-filter receiver in an AWGN
channel scenario
The comparison between two UWB techniques for implementing multiple access communications,
specifically TH-PPM and DS-BPSK schemes, was made by Canadeo et al [683] They carried out a
spreading-code-dependent study on both UWB schemes A generic channel model based on a verysimple delay tapped line was used The coefficients in this multipath channel model were constants,implying that no fading was considered
Boudaker and Letaief [684] outlined the attractive features of DS-UWB multiple access systemsemploying antipodal signaling and compared it with the TH scheme An appropriate DS-UWB trans-mitter and receiver were designed, and the system signal processing formulation was investigated.The performance of such communication systems in an AWGN channel in terms of multiple accesscapability, error rate performance, and achievable transmission rate were evaluated without MI Only
a single matched-filter detector was considered
An interesting method for implementing a DS-UWB system based on a new multi-carrier pulsewaveform was proposed in [685] A unique frequency domain processing technique was used at thereceiver side to exploit diversity in the frequency domain and provide resistance against intersymbolinterference and multiple access interference The performance of such a frequency domain processingDS-UWB scheme was compared with a DS-UWB system using traditional time-domain processingtechniques
An UWB system with PPM for data modulation and DS spreading for multiple access in anindoor fading environment was considered in [686] A RAKE receiver was used to combine a subset
of the resolvable multipath components using MRC technique In the following subsections, we willconsider a multipath environment, modeled by a discrete-time linear filter with an impulse responsewhose coefficients are lognormally distributed random variables
Runkle et al [688] compared a multi-carrier UWB with a DS-CDMA UWB The results illustrated
that a significant advantage can be obtained if a UWB system is implemented by DS-CDMA niques The multi-carrier UWB was implemented by a MB OFDM architecture The authors explainedhow the DS-CDMA UWB architecture could support robust and flexible multiuser capabilities, pro-tect against in-band interference, and provide high resolution ranging capability for safety-of-lifeapplications
tech-A comparison of the average BER and outage probability performance of the three UWB multipleaccess and modulation combinations for a single-user UWB radio was reported by [689] The threeschemes are TH with bit flipping modulation, TH-PPM, and DS with bit flipping modulation Theauthors used the channel models recommended for use in the IEEE 802.15.3a evaluation The results
Trang 9304 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESSshowed that direct sequence multiple access coding was more likely to achieve the lowest BER for
a fixed channel
Unfortunately, most of the currently reported researches on UWB have separated the issues
on pulse waveform design from system-level performance, such as bit error probability, and so
on In other words, the previous system-level analysis on BER performance seldom considered thecharacteristic features of UWB pulses used in the system, as seen from all the papers referred in thepreceding text [675–689] On the other hand, most of the current research on UWB pulse waveformswas focused on the requirements concerning their spectral shapes and has little to do with the overallsystem BER performance In the following subsections, we demonstrate a BER performance analysisthat is associated with the characteristic feature of UWB pulse waveforms We give a unified approach
to derive a closed form BER expression by taking into account major factors of a UWB system, such asnoninteger chip asynchronous transmission of the signals, multiple access interference, MI, and so on,
as well as their impact on the BER performance In particular, we introduce a merit parameter, namely,
normalized mean squared autocorrelation function (NMSACF) of the pulse waveform denoted by
7.6.2 DS-CDMA UWB System Model
Let us consider a DS-CDMA UWB radio system withK users An ultranarrow pulse waveform g(t)
defined over (0, T c ) is used to directly modulate the binary data stream {b (k)
antipodal pulses Presumably, a pulse covers just a chip durationT c, and a signature code hasN
chips such thatT b = NT c, whereN is the PG.
The block diagram of this generic DS-CDMA UWB transceiver is shown in Figure 7.25, whereeach transmitted signal will experience fading in the channel with its impulse response beingh k (t) for
thek-th user The receiver model is tuned to the first user’s transmitted signal with its signature code
being{a (1)
n }N−1
n=0 The received signal will be processed by signature code matched filtering as well
as pulse waveform–correlation before making a decision for thej -th bit, or at time t = (j + 1)T b.The transmitted signal from thek-th user can be written as
α is a fading coefficient, which may obey any distribution dependent on a particular environment,
andδ(t − τ k ) is an impulse function being unit at t = τ kand zero elsewhere The received signal can
k=1is the delay of thek-th user, n(t) obeys
Gaussian Distribution N(0, σ2) or can simply be denoted as n(t) ∼ N(0, σ2), which specifies a
Trang 10MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 305
Figure 7.25 A block diagram of a DS-CDMA UWB transceiver (a) Transmitter model; (b) Receivermodel, where the receiver is intended for userk and a flat fading channel is used.
relationship between n(t) and a Gaussian distribution with zero mean and variance σ2 Here, thereceiver intends to detect the first user’s transmission Without loss of generality, letτ1= 0 and τ k
be the relative delay between the first and k-th users’ transmissions Inserting s k (t) and h k (t) into
N −1
n=0
a (1)
n g(t − jT b − nT c ) dt = S + I + η (7.10)
Trang 11306 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESSwhere decision variabley
(j + 1) T b
has been decomposed into three components, useful signalS,
multiple access interferenceI , and noise η The useful signal component is written as
7.6.3 Flat Fading Channel
In this subsection, we will proceed to determine the MAI term in a flat fading channel In general,the calculation of the variance of multiple access interference componentI involves ACF of pulse
waveforms on a chip-by-chip basis, which is to be explained in the sequel
Trang 12MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 307
Chip-wise pulse autocorrelation function
Assume that the signal of interest is the first user’s transmission Let us first consider the interferencecomponent caused by thek-th transmission, which can be written as
The relative delay between the first andk-th users is τ k ∈ (0, T b ), and two consecutive interfering
bits with respect tob j (1)areb (k) j−1andb j (k) We obtain
T b τ
+ b (k) j
C k,1 (i k )
T c
γ k T c g(t)g(t − γ k T c ) dt
andC k,1 (i) is the discrete aperiodic partial cross-correlation between signature codes of the first and k-th users, which is defined as
Trang 13308 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS
Figure 7.26 Calculation of asynchronous cross-correlation function with fractional-chip delay, that
is,τ k = (j + γ k )T c, between transmitting signals from the first andk-th users, where γ ktakes a realvalue such that 0≤ γ k≤ 1
Trang 14MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 309
Figure 7.27 This figure illustrates how to calculate chip-wise pulse autocorrelation functionsR p (γ k T c )
andR p ( −(1 − γ k )T c ).
MAI statistics in a flat fading channel
IfK is sufficiently large, we can approximate the multiple access interference term, that is, I , as a
Gaussian random variable Therefore, the decision variabley
(j + 1)T b
defined in Equation (7.10)will also be Gaussian It is assumed that the appearance frequency of two consecutive bits for the
k-th user is independently equiprobable; that is, P (b (k) j = 1) = P (b (k)
j = −1) =1
2 Besides, we alsohave
Trang 15310 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESSTherefore, the conditional variance ofI kbecomes
k=2I k, we have the conditional mean ofI as
Trang 16MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 311from which we observe that the variance of the combined interference component is closely related
to three parameters; one being the square of the fading coefficientα, the other being the partial CCF
of the signature codes of the first andk-th users, and the last being the ACF of UWB pulse waveform
R p (γ k T c ) and R p
− (1 − γ k ) T c
In fact, both partial cross-correlation function of the signaturecodes and ACF of the pulse waveform can be calculated explicitly if we have the knowledge of usersignature codes and pulse waveforms, and thus the variance of MAI can also be determined
Random sequences
In this subsection, purely random sequences will be used as spreading sequences, whose chips
{a (k)
n }k =1, ,K
n =0, ,N−1will take “−1” and “+1” equally likely In addition, a(k)
i anda j (k)should be dent ifi = j The integer-chip relative delay between the first and k-th users’ transmissions, {i k}K
indepen-k=1,
is uniformly distributed over(0, N − 1); and the fractional-chip relative delay between the first and
k-th users’ transmissions, {γ k}K
k=1, is uniformly distributed over(0, 1) On the basis of these
assump-tions, we can calculate the unconditional expectation of discrete partial cross-correlation functions ofthe first andk-th spreading sequences as follows:
Trang 17312 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS
Trang 18MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 313
we can proceed to derive the BER expression as
7.6.4 Frequency-Selective Fading Channels
In this subsection, we analyze pulse waveform–dependent BER performance of a DS-CDMA UWBradio under a frequency-selective fading environment The multipath fading channel is modeled by amodified Saleh–Valenzuela (S–V) indoor channel model, which was initially proposed by A Salehand R Valenzuela [690] and was modified by J Foerster and Q Li [691]
Modified S–V channel model
The basic idea of the modified S–V channel model can be summarized as follows [691]
• The signal arrivals from an indoor channel can be decomposed into several clusters, each ofwhich consists of several multipath rays Different clusters are formed because of the building’sstructure, such as different storeys; while different rays in the same cluster are formed owing
to different reflecting objects in the propagation path of the cluster
• The amplitude of the rays attenuates according to a Lognormal distribution (instead of aRayleigh Distribution as suggested in the original S–V model [690]) In addition, the vari-ance of amplitude attenuation decays exponentially with the delays of different clusters as well
as different rays in the same cluster
• The arrival processes of both clusters and rays obey Poisson distributions and thus their rival times are exponentially (instead of uniform, as specified in the original S–V model [690])distributed
interar-The modified S–V channel model can be expressed mathematically by
Trang 19314 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESSwhereq ∈ (1, Q) and l ∈ (1, L) stand for cluster and ray indices, respectively; {w q,l}q =1, ,Q
l =1, ,L takes
either+1 or −1 to denote either positive or negative path return; {T q}Q
q=1is the delay of the first ray
E
α2q,l
= 1e −T q / e −τ q,l /γ (7.49)where and γ are the attenuation coefficients for the clusters and rays, respectively; 1is the meanpower of the first ray in the first cluster Therefore, the mean ofα q,lin Equation (7.48) can be writtenas
µ q= 10 ln(1) − 10T q / − 10τ q.l /γ
ln(10) −σ2ln(10)
Received signal in modified S–V channel
The transmitter block diagram for a DS-CDMA UWB radio under frequency-selective fading nels is almost exactly the same as Figure 7.25(a) The only difference is that the channel impulseresponses {h k (t)}K
chan-k=1 in Figure 7.25(a) should be replaced by the modified S–V model defined in
Trang 20MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 315
Figure 7.28 The RAKE receiver for reception of the signal from the first user using the modifiedS–V channel model, where there are totallyL1fingers, the combining coefficients are{β p}L1
is the spreading sequence for the k-th user with its length being N , T c is the chip duration with
T b = NT c, andg(t) denotes the pulse waveform, which was defined in Equation (7.7).
The received signal can be written as
where⊗ denotes convolution operation; n(t) is the AWGN component added in the channel with its
mean and variance being zero andσ2, respectively, or simply represented byn(t) ∼ N(0, σ2) After
the convolution, the received signal can be rewritten as
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It is assumed that anL1-finger RAKE receiver will capture theL1rays in the first cluster multipathreturns The output from thep-th finger is
whereS p, I L,p, I K,p, andη p are the useful signal, MI, MAI, and noise terms generated from the
p-th finger, respectively The useful signal component can be written as
0 g2(t) dt denotes the energy of a single pulse The weighted sum of the useful
signal component yields
Trang 22MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 317Letq (t) = β1
MI statistics in modified S–V channel
From Equation (7.57) we have the MI component in the decision variablev(j ) as I L= L1
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+ b (1) j
Similarly, we can derive the conditional mean and variance for the signal captured from thel-th
ray in theq-th cluster of the first user as
Trang 24MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 319Therefore, the conditional mean and variance of the MI term from the first finger become
is shown in Appendix B that the conditional mean and variance of the MI component seen from theoutput of the first finger can be written as
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mp is defined in Equation (7.37) It is to be noted that parameterσ2
mpis used here to acterize pulse waveforms used in a DS-CDMA UWB radio system and it plays an important role indetermining overall BER performance of the UWB system Finally, the conditional variance of the
char-MI term generated by the RAKE receiver is
MAI statistics in modified S–V channel
From Equation (7.57), the MAI component from the first finger of the RAKE receiver, as shown inFigure 7.28, can be written as
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The relation between the relative delay of clusters and rays can be expressed byT k,q + τ k,q,l+
τ k = i k,q,l,1 T c + γ k,q,l,1 T c Similarly, we can calculate the conditional mean and variance of the MAIterm generated from the first finger due to thel-th ray in the q-th cluster for the k-th user as
thek-th and first users, {τ k}K
k=1, is a uniformly distributed random variable, defined asτ k ∼ U(0, NT c ).
Using the same approach as suggested in Appendix A, we can obtain
σ mp2
... B3G WIRELESS 309Figure 7. 27 This figure illustrates how to calculate chip-wise pulse autocorrelation functionsR p (γ k T c )
and< i>R... class="page_container" data-page="19">
314 MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESSwhereq ∈ (1, Q) and l ∈ (1, L) stand for cluster and ray indices, respectively; {w q,l}q... data-page="22">
MULTIPLE ACCESS TECHNOLOGIES FOR B3G WIRELESS 317Letq (t) = β1
MI statistics in modified S–V channel
From Equation (7. 57) we have the MI component in the