4.15.2 Viterbi Equalization
`
`
`Section 4.15 Baseband Processing for Channel Estimation and Equalization
`
`231
`
`In practice, the operation of a wireless communication system deviates from this ideal
`setting—hence the need to speak of an “estimate” of the complex impulse response
`h(t} at the output of the matchedfilter. Hereafter, we refer to this estimate as hest(t) .
`Ignoring the effect of channel noise, we now note from Eqs.(4.45) and (4.46) that
`
`(4.47)
`hest(t) = p(t) @h(t+T.)
`where A(t) is the actual value of the complex baseband impulse response of the chan-
`nel. The effect of ignoring w(¢) is justified only when the signal-to-noise ratio is high.
`
`As mentioned previously, a primary objective of the baseband processoris to undo
`the convolution performed on the transmitted signal by the channel, which is
`indeed a task well suited for the Viterbi algorithm functioning as an equalizer. This
`is yet another novel application of the algorithm, building on what wesaid earlier in
`Section 4.9 on convolutional decoding: the Viterbi algorithm is a maximum-likelihood
`sequence estimator.
`Consider, then, a channel with memory [, requiring the use of a Viterbi equalizer
`with a window of length /. (For the application at hand, a value of 4 is considered typi-
`cal for /.) Correspondingly, the equalizer has 2! possible states, with each state consist-
`ing of / symbols. As with convolutional decoding, we need a metric for the design of
`the equalizer, which, in turn, requires the generation of two kinds of waveforms:
`
`1. Estimated received waveforms. This set of waveforms is generated by cycling a
`local modulator and channel model through all the possible bit sequences for
`every bit period. The combination of local modulator and channel model based
`on the channel estimate /est(r) is termed the estimated waveform generator, with
`its output denoted by the complex waveform Zest(t}.
`2. Compensated received waveform. From Eq. (4.45), we note that, except for a
`delay, the compleximpulse response estimate Hest(f) equals the actual complex
`impulse response A(t), convolved with the real autocorrelation function p{r).
`Since the estimated waveform generator embodies the channel model, it follows
`that the actual received signal ¥gata(t} should also be convolved with p(z). Then
`the compensated version of ¥gatq(t) , namely,
`
`Edata(!) = p(t) @ h(t)
`would be on par with the estimated received waveform Eest(t) .
`-
`Note that E data(f) and Eest(t) are both continuous-time signals.
`In order to generate fairly accurate digital representations of Gdata(t) and
`Eest(t) , it is necessary that they be sampled at a rate of m times the incomingbit rate,
`$o as to prevent aliasing. That is, each bit of data (actual as well as estimated) is repre-
`sented by n samples, where » is an integer equal to or greater than two,
`The squared Euclidean distance between the ith sample of the Ath bit in the
`actual received waveform E data(t) and the corresponding ith sample of the estimated
`
`(4.48)
`
`
`
`
`
`
`
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`
`pertaining to a possible state v of the equalizer may be
`received waveform €est(f)
`expressed as the sum of two squared terms, one due to the in-phase components of
`these two waveformsand the other due to their quadrature components:
`is
`=
`2,
`2
`»
`uy, (i) = (Gaata,rh, i) — Gest,2)) + Edata,o(h 1) —Eestot, i)
`With 7 samples per bit, the sample index i ranges from 0 to 7-1. Hence, we may
`define the transition metric for bit k of the actual signal and possible state v of the
`equalizer as
`
`2
`
`yn-l
`2
`as
`Hey = YY be v@
`i=0
`
`(4.49)
`
`where v = 0;1,....2/73
`Putting the ideas discussed here together, we may now formulate the block dia-
`gram of Fig. 4.22 for the baseband processor for channel estimation and equalization,
`leading to data recovery. The processor consists of three subsystems: the estimated
`waveform generator, transition metric computer, and Viterbi equalizer.
`Building on the idea of the Viterbi algorithm as a maximum-likelihood sequence
`estimator, we may now describe the way in which the Viterbi equalizer performsits
`computations. The basic difference between the Viterbi equalizer and the Viterbi
`decoder (discussed in Section 4.9) lies in what is used for the transition metric. Specifi-
`cally, we use (ty, (defined in Eq. (4.49)) for equalization and the Hamming distance
`for hard-decision-based convolutional decoding. Accordingly, the steps involved in the
`Viterbi equalization are as follows:
`
`ad
`
`1. Compute the transition metric “4, ,, for bit k of the actual received signal and
`state v of the equalizer, where v = OAscat! ! and / stands for the window length
`of the equalizer.
`Compute the accumulated transition metric for every possible path in thetrellis
`representing the equalizer. The metric for a particular path is defined as the
`squared Euclidean distance between the estimated received waveform repre-
`sented by that path and the actual received waveform. For each nodein thetrellis
`
`
`
`Page 252 of 474
`
`“|
`
`X
`
`t
`
`channel ) 3
`
`Channel
`Gsiinator
`
`Hest!
`
`()
`
`i
`
`pace eal nc agpiaiaaaacaait Beene
`generator
`modulator
`
`‘
`
`
`
` i €channei(t)
`
`Fatal)
`————_-s
`
`Auto-
`correlator
`T
`
`_|
`See
`x
`data(f)
`
`tiaustiian
`metric
`computer
`
`Viterbi
`angles
`4
`
`PameUnMNE
`likelihood
`estimate of
`interleaved
`output
`
`FIGURE 4.22 Block diagram of baseband processor for channel estimation and equalization.
`The lighter arrows indicate complex signals.
`
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`

`
`
`Section 4.16 Time-Division Multiple Access
`
`233
`
`(i.c., each state of the equalizer), the Viterbi algorithm compares the two paths
`entering that node. The path with the lower metric is retained, and the other path
`is discarded.
`
`3. Repeat the computation for every bit of the received signal.
`4, The survivor, or active, path discovered by the algorithm defines the /-bit
`sequence applied to the local modulator in Fig. 4.22 for which the estimated
`received waveform Eesi(t)
`is the closest
`to the actual received waveform
`Gdata(t) in Euclidean distance. With this sequence at hand, the tasks of channel
`estimation and equalization are completed.
`One last commentis in order: The window length / assigned to the equalizer depends
`not only on the memory of the channel, but also on whether the modulator used in
`the transmitter has memory of its own or not (Le., partiai-response modulation). Let
`lmem Genote the memory of the modulator and lyanne denote the memory of the
`channel. Then we may express the window length of the equalizer as
`(4.50)
`f= lmem + channel
`= 2 for GMSK.With /inanne = 4for example, we thus have [= 6.
`
`For example, fom
`
`mem
`
`4.16 TIME-DIVISION MULTIPLE ACCESS
`
`The discussion thus far has focused on specific functional blocks (ie., speech coding,
`channel shaping, coding, and modulation) that are basic to the design of a digital com-
`munication system. With this material at hand, we are now ready to discuss TDMA, a
`widely used form of multiple access for wireless communications.
`The purpose of a time-division multiple-access (TDMA) system is to permit a
`number of users, say, NV, to access a wireless communication channel of bandwidth B
`on a time-shared basis. The immediately apparent features that distinguish TDMA
`from FDMA are twofold:
`
`1. Each user has access te the full bandwidth B of the channel, whereas in FOMA
`each useris assigned a fraction of the channel bandwidth, namely, B/N.
`2, Each user accesses the channel for only a fraction of the time thatit is in use and
`on a periodic and orderly basis, with the transmission rate being N times the
`user’s required rate. By contrast, in FDMA,each user accesses the channel on a
`continuous-time basis.
`
`Both of these features have significant implications for the operation of a TDMA
`wireless communication system. Access to the full bandwidth of the wireless channel
`means that we may now be deahng with wideband data transmission, which makes the
`TDMA system vulnerable to frequency-selective fading. In contrast, FOMA deals
`with narrowband transmission, which meansthat the fading channels are typically fre-
`quency flat. To combat the frequency-selective fading problem requires the use of
`sophisticated signal-processing techniques. Access to the channel on a time-shared
`basis has implications of its own. In particular, the transmission of information-bearing
`data over the channel takes place in the form of bursts, which, in turn, further compli-
`cates the requirement of synchronizing the receiver to the transmitter.
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`Chapter 4 Coding and Time-Division Multiple Access
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`In the context of implementation, unfortunately, there is no TDMAstructure
`applicable to all TDMA wireless systems in operation. Nevertheless, they do share a
`common feature: Each frame of the TDMAstructure contains N time slots of equal
`duration.It is in the detailed structure of each slot and in the way in which the transmit-
`ting and receiving slots are assigned in time that TDMAsystemsdiffer from one another.
`Typically, the bits constituting each slot of a TDMAframeare divided into two
`functional groups:
`
`° Traffic data bits, which represent digitized speech or other forms of information-
`bearing data.
`¢ Overhead bits, whose functionis to assist the receiver in performing someauxil-
`iary functions that are essential for satisfactory TDMA operation.
`
`The auxiliary functions include synchronization and channel estimation. Specifically,
`the synchronization bits in a slot enable the receiver to recover sinusoidal carrier and
`bit-timing information, which are needed for coherent demodulation. The framing bits
`are used to estimate the unknown impulse response of the channel, which is needed
`for estimating the transmitted signal. As already mentioned, in TDMA systems, the
`transmission of information-bearing signals pertaining to any user is not continuous in
`time. Rather, it is discontinuous, requiring the use of a buffer-and-burst strategy. The
`burst form of data transmission over the channel results in an increase in the synchro-
`nization overhead, as each receiver is required to piece the transmitted signal (e.g.,
`speech) together asit is received over a succession of frames.
`Up to now, the discussion of the TDMAframing structure has been of a generic
`nature. Theme Example 1, presented in Section 4.17, describes the frame structure of a
`specific system.
`
`4.16.1
`
`Advantages of TDMA over FDMA
`
`The following are some of the advantages TDMA has over FDMA:
`
`1. With TDMA,the use of a diplexer can be avoided at the mobile terminal. A
`diplexer is a complicated and expensive arrangement of filters that allows the
`mobile terminal to transmit and receive data at the same time without jamming
`its own information-bearing signal. In TDMA,the terminal need not transmit
`and receive at the same time; hence, a diplexer is not needed.
`2. With TDMA, only one RFcarrier at a time is present in the channel.If the chan-
`nel includes a nonlinearity, then the effects of the nonlinearity are much reduced
`on a single carrier than if multiple carriers were present, as in FDOMA. Examples
`of such nonlinearities are the power amplifiers employed in base stations or
`those in satellite transponders.
`3. With voice, a significant portion of the call consists of quiet time, when neither
`party is speaking. With a TDMA strategy, special processing techniques can be
`employed to fill the quiet times with data or other voice calls to improve the
`channel’s efficiency.
`
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`

`4.16.2
`
`Page 255 of 474
`
`
`
`
`Section 4.16 Time-Division Multiple Access
`
`235
`
`4, With FDMA,the base station must have a channelunit (transmitter/receiver pair)
`for each active session. With TDMA,the same channelunit is shared between mul-
`tiple sessions; thus, the base station hardware can besignificantly simplified.
`To achieve some of these advantages requires the use of complicated signal-processing
`techniques, which, in turn, necessitates a reliance on digital signal-processing technol-
`ogy in the form ofsilicon chips for cost-effectiveness. Moreover, this same enabling
`technology has made it possible to implement other functional needs of TDMAsys-
`temsefficiently:
`* sophisticated timing and fast acquisition operations for synchronizing the
`receiver to the transmitter, and
`* source coding and channel coding techniques for the efficient and reliable trans-
`mission of information over the channel.
`
`Putting all these operational advantages and practical realities together has made
`TDMApreferable to FDOMA. However, a major disadvantage of TDMA is thatits
`deployment requires an increased rate of data transmission across the wireless channel,
`which, in turn, may result in increased intersymbol interference (ISI), making channel
`equalization in the receiver a necessary practical requirement in TDMAsystems.
`
`TDMA Overlaid on FOMA
`
`From the discussion presented thus far, it may appear that TDMAis implemented in a
`rigorous, pure form. In reality, however, TDMAis implemented in an overlaid fashion
`on FDMA,for practical reasons. To appreciate this point,it is important that we first rec-
`ognize that the usable radio spectrum extends from tens of hertz to tens of gigahertz,
`which represents over nine orders of magnitude. By international agreement, this spec-
`trum is shared byallotting certain portionsof it to certain applications. For example, in
`North America, the band from 118 to 130 MHz is dedicated to aeronautical safety com-
`munications, and the bands from 824-849 to 869-894 MHzare dedicated to public tele-
`phony. In a very high level sense, this is a form of FDMA:sharing the spectrum on the
`basis offrequency.
`Hence, every wireless communication system has an FDMA baseline, and
`multiple-access schemes such as TDMA are overlaid on this baseline. One of the
`issues is the granularity of the underlying FDMA structure. Tn this sense, TOMA
`comes in three basic forms:
`
`1. Wideband TDMA. In this form of TDMA,there is only one or a small number of
`frequency channels, typically several megahertz wide. Wideband TDMA has
`been used in satellite communication systems in which the TDMAservice occu-
`pies the full bandwidth of the satellite transponder.
`2 Medium-band TDMA. In this form of TDMA,thereis a significant number of
`frequency (FDMA)channels, but the bandwidth of each channelis still large
`enough (100 to 500 kHz) that frequency-selective fading can be expected. The
`GSM system discussed as a theme example in Section 4.17 is an example of
`medium-band TDMA,with sufficient FDMA channels being available to assign
`different-frequency channels to different cells and to perform the necessary task
`of interference management,
`
`
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`

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`236
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`3. Narrowband TDMA. This last form of TDMAis a simple step up from a pure
`FDMAsystem. The number of users time-sharing a single channel is small, and
`the numberof frequency channels is typically large. The bandwidth of a channel
`in narrowband TDMAisrelatively small (usually less than 50 kHz), and, as a
`consequence, we can usually assume the multipath phenomenon to beflat fad-
`ing. The North American IS-54 digital telephone system is an example of a nar-
`rowband TDMAsystem. (See Note 2 of Chapter 3.)
`
`The appropriate choice of granularity for the underlying FDMA systems depends
`upon several factors:
`
`e In a cellular system, the granularity has to be sufficient to allow different fre-
`quency assignments in a neighboring cell and perform flexible interference
`management.
`e System complexity increases with the channel bandwidth and data-transmission
`rate, with the increase in complexity occurring in both the synchronization and
`processing aspects of the system. Lower bandwidths tend to imply lower cost
`solutions and lower power requirements.
`e Propagation conditions may favor higher bandwidth systems, but only if appro-
`priate measures are implementedto use this advantage. Frequency-selective fad-
`ing that occurs in medium and wideband TDMAsystemscan provide a diversity
`advantage, but only if the receiver includes an effective equalizer.
`
`Onefinal commentis in order: TDMAis the not the only choice of multiple access for
`overlaying on an FDMAbaseline. In Chapter 5, we will present code-division multiple
`access (CDMA), which can be considered a wideband system,but, in reality, is still
`overlaid on an FDMAbaseline. Moreover, wireless communicationis not limited to a
`single overlay. For example, from the discussion to be presented in Section 4.17, we
`will see that the GSM system is not simply TDMAoverlaid on FDMA;rather,it also
`includes a third multiple-access strategy known as frequency hopping (FH); that is,
`GSMis, in reality, an FDMA/TDMA/FHsystem. Frequency hoppingis also discussed
`in Chapter5.
`
`4.17 THEME EXAMPLE 1: GSM'3
`
`The Global System for Mobile (GSM) communicationsis a digital wireless communica-
`tion system that is used all over the world. Figure 4.23 displays the basicTDMA frame
`structure of GSM. Thestructure is composed of eight 577-us slots, which makes the
`total frame duration equal to 4.616 ms. The 1-bit flag adjacent to each data burst of 57
`bits is used to identify whether the data bits are digitized speech or some other infor-
`mation-bearing signal. The3 tail bits, all logical zeros, are used in convolutional decod-
`ing of the channel-encoded data bits. The 26-bit training sequence in the middle of the
`timeslot is used for channel equalization. Finally, the guard time, occupying 8.25 bits,is
`includedat the end of each slot to prevent data bursts received at the base station from
`mobile users from overlapping with each other; this is achieved by transmitting no sig-
`nal at all during the guard time.
`
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`

`

`Section 4.17 Theme Example 1: GSM
`
`237
`
`
`
`— Frame=4.6155ms——>|
`
`
`
`
`
`
`TS,|TS;|TS;|TS,|T8s|F8s|TS,
`TS: Timeslot
`T: Tail (bits)
`F: Flag (bit)
`Traim: Training interval for equalizer
`Guard: Guard timeinterval
`
`3 spots|1| aon[i]at[3]S|
`Guard
`Data
`Train
`H Data
`<— Tume slot = 156.25 bits = 577s >
`
`FIGURE 4.23
`
`Framestructure of GSM communications.
`
`The frame efficiency of a TDMAsystem is defined as the number of bits repre-
`senting information-bearing signals (e.g., digitized speech), expressed as a percentage
`of the total number of bits (including the overhead) that are transmitted in a frame.
`With each slot consisting of 156.25 bits, of which 40.25 bits are overhead (ignoring the
`2 flag bits), the frame efficiency of GSM is
`
`
`
`a _ 40.25 \x 100 = 74.24%
`
`156.25
`It is important to note, however, that (as remarked in Section 4.16.2) GSM is not a
`pure TDMA system. Rather, it combines TDMA with frequency hopping. Accord-
`ingly, a physical channelis partitioned in both time and frequency. The channelis parti-
`tioned in time because, with eight slots in a TDMA frame, each carrier frequency
`supports eight physical channels mapped onto theeightslots. A time slot assigned to a
`particular physical channel is naturally used in every TDMAframefor as long as that
`channel is engaged by a mobile user. Consequently, partitioning of the channelin fre-
`quency arises because the carrier assigned to such a slot changes its frequency from
`one frame to the next in accordance with a frequency-hopping algorithm.
`In Section 4.10, we introduced the idea of interleaving as a way of combatting
`the Rayleigh fading problem. Frequency hopping combined with interleaving enables
`a TDMAsystem to combat the fading problem even moreeffectively. In the context
`of a TDMA system, the principle of frequency hopping embodies the following two
`considerations:
`
`1. The carrier used to modulate a TDMA frame changes its frequency from one
`frame to the next.
`
`2. If a particular TDMA frame happens to be in a deep fade, then it is highly
`unlikely that the next TDMAframewill also be in a deep fade, provided that the
`change in carrier frequency applied by the frequency-hopping algorithm from
`the particular frame in question to the next oneis sufficiently large.
`Por uplink transmission, in Europe, GSM uses the frequency band 890 to 915 MHz, and
`for downlink transmission, it uses the frequency band 935 to 960 MHz.In either case,
`the maximum frequency change from one frameto the next is 25 MHz. Expressed as a
`
`
`
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`238
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`percentage of the mean carrier frequency, the maximum frequency hopping for the
`downlink is approximately
`
`25 —500 x 100 = 2.8%
`With this percentage of maximum frequency hopping, it turns out that the time spent
`by arapidly moving mobile user in a deep fade is reduced to about 4.6 ms, which is
`essentially the frame duration. In the case of slowly moving mobile users (e.g.,
`pedestrians), the frequency-hopping algorithm built into the design of GSM pro-
`duces substantial gains against fades.
`GSM employs a moderately complicated, 13-kilobits/s regular pulse-excited
`speech codec (coder/decoder) with a long-term predictor. To provide error protec-
`tion for the speech-encoded bits, concatenated convolutional codes and multilayer
`interleaving are employed. An overall speech delay of 57.5 ms occurs in the system.
`Turning next to the type of digital modulation used in GSM, we find that the
`method of choice is Gaussian minimum-shift keying (GMSK), which wasdiscussed in
`Sections 3.7 and 4.14. For GSM, the time—bandwidth product WT of GMSKis stan-
`dardized at 0.3, which provides the best compromise between increased bandwidth
`occupancy and resistance to cochannel interference. Ninety-nine percent of the radio
`frequency (RF) power of GMSKsignals so specified is confined to a bandwidth of 250
`kHz, which meansthat, for all practical purposes, the sidelobes of the GMSK signal
`are insignificant, for all practical purposes, outside this frequency band.
`The available spectrum is divided into 200-kHz-wide subchannels, each of which
`is assigned to a GSM system transmitting data at 271 kb/s. Figure 4.24 depicts the
`power spectrum of a channel in relation to its two adjacent channels; this plot is the
`
`Ii| H
`
`O
`
`i|
`
`||
`
`1-80
`||
`Legg E
`
`ES
`
`|
`
`|
`
`
`
`()|Power spectrum, dB
`
`
`
`|
`
`|
`
`Carrier
`Carrier
`frequency ---+-——-! frequency
`}<— 200 —>—200 +—200 —>| ——» Frequency, kHz
`
`FIGURE 4.24 Power spectrum of GMSK signal for GSM communications.
`
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` :i
`
`iEz
`
`i£
`
`
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`Page 259 of 474
`
`Section 4.18 Theme Example 2: Joint Equalization and Decoding
`
`239
`
`passband version of the baseband power spectrum of Fig.3.21 corresponding to
`WT, = 0.3. From Fig. 4.24, we may make the following important observation: The
`RF power spectrum of the subchannel shown shaded is down by an amountclose to
`40 dB at the carrier frequencies of both adjacent subchannels, which meansthat the
`effect of cochannel interference in GSM is small.
`
`4.18 THEME EXAMPLE2: JOINT EQUALIZATION AND DECODING"
`
`The material presented in Section 4.12 has taught us an important principle in digital
`communication theory, hereafter referred to as the turbo coding principle. The princi-
`ple may bestated as follows:
`
`The performance of the receiver of a digital communication system, embodying
`the plot ofbit error rate (BER) versus transmitted signal energy per bit-to-noise
`spectral density ratio, E,/Ng, may be significantly improved by using
`
`() aconcatenated encoding strategy at the transmitter and
`(i) an iterative receiver, with all ofits components operating in soft-input, soft-
`output (1.e., analog) form.
`
`Theiterative receiveris the halimark of the turbo coding principle.
`In Fig. 4.15, the concatenated encoding strategy is implemented in parallel form,
`so called because encoder 1 and encoder 2 operate in parallel on their respective
`inputs. Moreover, the two encoder inputs are essentially statistically independent by
`virtue of the turbo interleaver that separates them.
`Alternatively, we can implement the concatenated encoding strategy in serial
`form, as illustrated in Fig. 4.25{a). Although, atfirst sight, this structure looks familiar
`
`Binary
`stream
`
`Channel! encoder:
`Outer encoder i
`
`Interleaver
`
`Wireless channel:
`Inner encoder
`
`Received
`signal
`
`(a)
`
`Additive white
`Gaussian noise
`
`
`
`
` Interleaver
` Received
`
`signal
`
`Equalizer:
`Inner decoder
`
`Deinterleaver
`
`Channel decoder:
`Outer decoder
`
`Estimate
`of original
`binary
`stream
`
`(b)
`
`Joint equalization-and-decoding problem.
`FIGURE 4.25
`(a) Turbo encoder oftheserial form, with the channel viewed as the inner encoder.
`(b) Iterative Turbo decoder, highlighting the application of feedback around the two decoding
`stages.
`
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`

`240
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`in the context of a fast-fading wireless communication system, the viewpoint embod-
`ied in its description as a two-stage encodercan bejustified along the following lines:
`
`e The channel encoder, introduced into the transmitter chain to improvethereli-
`ability of communication, is viewed as the outer encoder.
`e The wireless channel, essential for the communication process, is viewed as the
`inner encoder.
`
`¢ The channel interleaver, introduced to disperse the burst of errors produced by
`the possible presence of the fast-fading phenomenon in the wireless channel,
`separates the two encoders in accordance with the transmit part of the turbo-
`coding principle.
`
`Correspondingly, the two-stage decoder is configured as an iterative receiver, as
`shown in Fig. 4.25(b), in accordance with the receiver part of the turbo-coding prin-
`ciple. Herein lies the basis of a novel receiver structure made up of the following
`constituents:
`
`® A soft-input, soft-output channel equalizer, designed to mitigate the effect of
`intersymbol interference (ISI) produced by the transmission of the encoded-
`interleaved signal across the channel; the equalizer acts as the inner decoder.
`° A soft-input, soft-output channel decoder, designed to improve the estimates of
`encoded data symbols; the channel decoderacts as the outer decoder.
`© A channel deinterleaver, designed to undo the permutation that is present in soft
`outputs produced by the equalizer, so as to facilitate proper channel decoding.
`e Aninterleaver, designed to repermute the soft outputs produced by in the chan-
`nel decoder, so that the feedback signal applied to the equalizer assumes a form
`consistent with the received signal.
`
`Now,if we were to open the feedback loop in Fig. 4.25(b) by removing the interleaver
`in the feedback path, we would be left with a conventional receiver defined by the for-
`ward path made up of the channel-equalizer, channel-deinterleaver, channel-decoder
`chain. The practical advantage of the iterative receiver is that it performs joint equal-
`ization and decoding, thereby offering the potential for improving the performance of
`the receiver by virtue of the feedback around the two stages of processing: channel
`equalization and channel decoding.
`In particular, the reduction in bit error rate through joint equalization and
`decoding performed iteratively can be explained by observing that each compo-
`nent in the receiver, namely, the equalizer and the decoder, helps to bootstrap the
`performanceof the other. The bootstrap action manifestsitself as follows:
`
`e The equalizer uses frequency diversity in the channel to improve the decoder
`performance through /SI reduction.
`e The decoder uses time diversity in the code to improve the equalizer perfor-
`mance through improved estimates of uncoded data symbols.
`
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`

`
`
`Section 4.18 Theme Example 2: Joint Equalization and Decoding
`
`241
`
`The net result of this bootstrap action is that, in the course of three to five iterations, a
`significant reduction in the bit error rate is accomplished, as is illustrated in a simple,
`yet insightful, computer experiment described next.
`
`Computer Experiment
`Consider
`the serial concatenated encoder of Fig.4.25(a), with the following
`specifications:
`1. Channel encoder (outer encoder): convolutional encoder
`Code rate = 1/2
`Constraint length, K = 3
`Generator polynomials:
`gD) =1+D?
`g?)(D)=1+D+D°
`2. Interleaver:
`Type: pseudorandom interleaver
`Block size: 1000 bits
`
`3. Wireless channel: Tapped-delay-line model with the following tap weights (see
`Fig. 4.26, where 7 denotes the symbol duration):
`Wo = 0.93
`we ~O17
`wy = 0.35
`
`Euclidean norm of the tap-weight vector w:
`
`a 1/2
`2
`2
`lhw|| = (wg + W] + W)
`= ((0.93)° + (—0.17)* + (0.35)")
`zs |
`4, Modulation (not shown in Fig. 4.25(a)): Binary phase-shift keying (BPSK). With
`this simple method of modulation, the baseband modei of the system assumes a
`real-valued form throughout the system.
`
`1/2
`
`
`
`Output
`
`FIGURE 4.26 Tapped-delay-line model of wireiess channel! with three tap-weights; the
`blocks labeled T act like unit-delay operations.
`
`
`
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`

`Chapter 4 Coding and Time-Division Multiple Access
`
`Theiterative two-stage receiver of Fig. 4.25(b) was implementedas follows:
`1. Equalizer (inner decoder).
`e The channel impulse response, assumed to be known.
`° The decodingtrellis, formed on thebasis of the channel impulse response(.e.,
`tap weights of the tapped-delay-line model) and BPSK.
`2. Deinterleaver, designed to deinterleave the soft outputs produced by the
`equalizer.
`Channel decoder (outer decoder).
`° The decodingtrellis, formed on the basis of the convolutional encoder’s gen-
`erator polynomials g)(D) and g?(D)
`¢ Construction of the decodingtrellis, discussed in Section 4.7
`4. Interleaver, designed to interleave the soft outputs produced by the channel
`decoder.
`5, Decoding algorithm for both the equalizer and channel decoder: The logarith-
`mic form of the maximumaposterior probability (MAP) algorithm,discussed in
`Section 4.12.
`Using computer simulations of the encoder/decoder system of Fig. 4.25, we plot the
`receiver performance, in terms of BER versus E,/No, in Fig. 4.27, on the basis of which
`we may makethe following observations:
`
`we
`
`242
`
`Page 262 of 474
`
`10°
`
`[a
`fm 107
`a
`
`to
`
`Iteration 2
`
`Iterations 4, 5
`
`107+
`TTT 10-4
`
`
`
`
`|
`6
`
`8
`
`10
`
`12
`
`-4
`
`l
`-2
`
`|
`0
`
`|
`2
`
`|
`4
`ExNo
`
`FIGURE 4.27.
`experiment.
`
`Performancereceiver curvesfor the iterative joint equalization-and-decoding
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`

` 4.19.1
`
`:
`
`
`
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`Section 4.19 Theme Example 3: Random-Access Techniques
`
`243
`
`1. Iterative detection, performed in accordance with the turbo coding principle,
`provides a significant improvement in receiver performance measured with
`respect to thefirst iteration; in effect, iteration 1 represents what is achievable
`with a noniterative (i-e., conventional) receiver.
`2. The receiver converges in aboutfive iterations.
`3. Little change in receiver performance occurs in going from iteration 4 to
`iteration 5.
`
`Problem 4.5 The baseband modelused in the computer experiment on joint equalization
`and decoding is real valued, which is justified for BPSK modulation. To improve spectral effi-
`ciency, OPSK modulation is commonly used. Discuss the modifications that would have to be
`made to the baseband model in orderfor it to handle OPSK modulation.
`a
`
`The computer experimentjust presented assumes that the receiver has perfect knowi-
`edge of the channel state information (CSI). In practice, we have to deal with a wireless
`channelthat is typically nonstationary, in which case the equalizer structure has to be
`expandedto include a CSI estimator. (See Problem 4.24.)
`
`4.19 THEME EXAMPLE 3: RANDOM-ACCESS TECHNIQUES
`
`There are many instances in multiaccess communications in which a user terminal is
`required to send a packet of information to the base station at a random instant in
`time. Such instances occur, for example, when the terminal wishes to log onto the sys-
`tem or when the user wishes to make a telephone call. The system must provide a
`means by which these random requests can be serviced. This could be done in a num-
`ber of ways:
`
`1. The system could permanently assign one channel to each user.
`2. The system could pol/ each user at regular intervals to see if he or she had any-
`thing to transmit.
`3. The system could provide a random-access channelthat the users could accessat
`any time.
`
`Since a typical user has a low duty cycle, the first approach is wasteful of spectrum. The
`second approach could result in long delaysif there is a large number of users, and if
`the users are mobile, the polling process can become complicated. In this section, we
`will consider the third approach of assigning a random-access channel.
`
`Pure Aloha’?
`
`Consider the following modelof the random-access channel: Let us assumethatthereis
`a large population of user terminals that operate independently of each other and that
`each terminal has no knowledge of when the other terminals will transmit. Ea