`
`
`
`
`
`Section 4.15 Baseband Processing for Channel Estimation and Equalization
`
`23‘!
`
`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
`Mt) at the output of the matched filter. Hereafter, we refer to this estimate as hesdt) .
`Ignoring the effect of channel noise, we now note from Eqs. (4.45) and (4.46) that
`
`imam a p(t) e Elm TC)
`
`(4.47)
`
`where Jim is the actual value of the complex baseband impulse response of the chan-
`nel. The effect of ignoring w(r) is justified only when the signal-to-noise ratio is high.
`
`4.15.2 Viterbi Equalization
`
`As mentioned previously, a primary objective of the baseband processor is 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, buiiding on what we said earlier in
`Section 4.9 on convolutional decoding: the Viterbi algorithm is a maximum-likeiihood
`sequence estimator.
`Consider, then, a channel with memory I, requiring the use of a Virerbi equalizer
`with a window of length I. (For the application at hand, a value of 4 is considered typi-
`cal for l.) Correspondingly, the equalizer has 21 possible states, with each state consist-
`ing of 1 symbols. As with convolutionai 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 l—bit sequences for
`every bit period. The combination of local modulator and channel model based
`on the channel estimate hestU) is termed the estimated waveform generator, with
`its output denoted by the complex waveform East“) .
`
`2. Compensated received waveform. From Eq. (4.45), we note that, except for a
`delay, the complexflimpuise response estimate hesfit) equals the actual complex
`impulse response Mt), convolved with the real autocorrelation function p(t).
`Since the estimated waveform generator embodies the channel model, it follows
`that the actual received signai Emma) should also be convolved with p(r) .Then
`the compensated version of idatalf} , namely,
`
`Edatait) = p(r)®fi(r)
`
`(4-48)
`
`would be on par with the estimated received waveform Emu) .
`~
`Note that Edam) and East“) are both continuous-time signals.
`In order to generate fairly accurate digital representations of édataU) and
`565d!) , it is necessary that they be sampled at a rate of n times the incoming bit rate,
`so as to prevent aliasing. That is, each bit of data (actual as well as estimated) is repre~
`sented by rt samples, where n is an integer equal to or greater than two.
`The squared Euclidean distance between the ith sample of the kth bit in the
`actual received waveform Eden-4(3) and the corresponding ith sample of the estimated
`
`
`
`
`
`Page 251 of 474
`
`SAMSUNG EXHIBIT 1010 (Part 3 of 4)
`
`Page 251 of 474
`
`SAMSUNG EXHIBIT 1010 (Part 3 of 4)
`
`

`

`232
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`received waveform 555:0) pertaining to a possible state v of the equalizer may be
`expressed as the sum of two squared terms, one due to the in-phase components of
`these two waveforms and the other due to their quadrature components:
`~
`~
`2
`~
`~
`11:41) = (5.1.1.41. 11—565mm», 1)) +rcdara,Q(k.11—éeagrv,a)
`With 11 samples per bit, the sample index 1' ranges from 0 to n— 1. Hence, we may
`define the transition metric for bit k of the actual signal and possible state v of the
`equalizer as
`
`2
`
`2
`11—1
`= Z pkgvp')
`.:0
`
`(4.49)
`
`where V : 0,1,...2!‘1
`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 performs its
`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 ,uk’v (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:
`
`1. Compute the transition metric #kv for bit k of the actual received signal and
`state V of the equalizer, where v—— 0,1" ”21— 1 and 1 stands for the window length
`of the equalizer.
`
`2. Compute the accumulated transition metric for every possible path in the trellis
`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 node in the trellis
`
`JTaiwamnailt)
`
`4135(0)
`* .1 .1 -.»
`
`Channel
`estimator
`
`Estimated
`waveform WWW“ ~
`_cnerator
`
` igchannelu)
`
`XaaiaU)
`
`Auto-
`correlator
`
`Transition
`metric
`com nuter
`
`“mm-i»
`dam“)
`
`Baseband
`local
`mod ulator
`
`Viterbi
`equalizer
`
`Maximum-
`likelihood
`estimate of
`interleaved
`output
`
`FIGURE 4.22 Block diagram of baseband processor for channel estimation and equalization.
`The lighter arrows indicate complex signals.
`
`
`
`Page 252 of 474
`
`Page 252 of 474
`
`

`

`
`
`Section 4.16 Time—Division Multiple Access
`
`233
`
`(i.e., 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 1—bit
`sequence applied to the local modulator in Fig.4.22 for which the estimated
`received waveform 56510)
`is the closest
`to the actual received waveform
`‘g’damm in Euclidean distance. With this sequence at hand, the tasks or" channel
`estimation and equalization are completed.
`
`One last comment is in order: The window length l 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 (i.e., partial-response modulation). Let
`Imam denote the memory of the modulator and [channel denote the memory of the
`channel. Then we may express the window length of the equalizer as
`
`For example, I
`
`mcm
`
`z 2 for GMSK.With lchaunel = 4, for example, we thus have I = 6.
`
`I = [mam + [channel
`
`(4‘50)
`
`4.16 TIME-DIVISION MULTIPLE ACCESS
`
`The discussion thus far has focused on specific functional blocks (i.e., 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, N, 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 to the full bandwidth B of the channel, whereas in FDMA
`each user is assigned a fraction of the channel. bandwidth, namely, B/N.
`
`2. Each user accesses the channel for only a fraction of the time that it 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 dealing with wideband data transmission, which makes the
`TDMA system vulnerable to frequency-selective fading. In contrast, FDMA deals
`with narrowband transmission, which means that the fading channels are typically fre-
`quency flat. To combat the frequency—selective fading problem requires the use of
`sophisticated signalaprocessing 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 complim
`cates the requirement of synchronizing the receiver to the transmitter.
`
`
`
`Page 253 of 474
`
`Page 253 of 474
`
`

`

`234
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`In the context of implementation, unfortunately, there is no TDMA structure
`applicable to all TDMA wireless systems in operation. Nevertheless, they do share a
`common feature: Each frame of the TDMA structure 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 TDMA systems differ from one another.
`Typically, the bits constituting each slot of a TDMA frame are divided into two
`functional groups:
`
`0 Traffic data bits, which represent digitized speech or other forms of information-
`bearing data.
`
`' Overhead bits, whose function is to assist the receiver in performing some auxil-
`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—bnrsr 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 as it is received over a succession of frames.
`Up to now, the discussion of the TDMA framing 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 diplcxer can be avoided at the mobile terminal. A
`diplexcr 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 RF carrier 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 FDMA. 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.
`
`
`
`Page 254 of 474
`
`Page 254 of 474
`
`

`

`
`
`
`4.16.2
`
`Section 4.16 Time-Division Multiple Access
`
`235
`
`4. With FDMA, the base station rnust have a channel unit (transmitterlreceiver pair)
`for each active session.With TDMA, the same channel unit is shared between mul~
`
`tiple sessions; thus, the base station hardware can be significantly 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 technoi-
`ogy in the form of silicon chips for cost-effectiveness. Moreover, this same enabhng
`technology has made it possible to implement other functionai needs of TDMA sys-
`terns efficiently:
`
`0 sophisticated timing and fast acquisition operations for synchronizing the
`receiver to the transmitter, and
`
`0 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
`"FDMA preferable to FDMA. However, a major disadvantage of TDMA is that its
`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 TDMA systems.
`
`TDMA Overlaid on FDMA
`
`From the discussion presented thus far, it may appear that TDMA is implemented in a
`rigorous, pure form. In reality, however, TDMA is 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 gigahcrtz,
`which represents over nine orders of magnitude. By international agreement, this spec—
`trum is shared by allotting certain portions of it to certain applications. For example, in
`North America, the band from 11.8 to 130 MHz is dedicated to aeronautical safety com-
`munications, and the bands from 82M49 to 869-894 MHz are dedicated to public tele—
`phony. In a very high level sense, this is a form of FDMA: sharing the Spectrum on the
`basis offiequency.
`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. In this sense, TDMA
`comes in three basic forms:
`
`1. Widebtmd 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 TDMA service occu~
`pics the full bandwidth of the satellite transponder.
`
`2. Medium-band TDMA. In this form of TDMA, there is a significant number of
`frequency (FDMA) channels, but the bandwidth of each channel is 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
`differenbfrequency channels to different cells and to perform the necessary task
`of interference management.
`
`
`
`Page 255 of 474
`
`Page 255 of 474
`
`

`

`236
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`3. Narrowband TDMA. This last form of TDMA is a simple step up from a pure
`FDMA system. The number of users time~sharing a single channel is small, and
`the number of frequency channels is typically large. The bandwidth of a channel
`in narrowband TDMA is relatively small (usually less than 50 kHz), and, as a
`consequence, we can usually assume the multipath phenomenon to be flat fad-
`ing. The North American IS-54 digital telephone system is an example of a nar-
`rowband TDMA system. (See Note 2 of Chapter 3.)
`
`The appropriate choice of granularity for the underlying FDMA systems depends
`upon several factors:
`
`- 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.
`
`0 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.
`
`0 Propagation conditions may favor higher bandwidth systems, but only if appro-
`priate measures are implemented to use this advantage. Frequency-selective fad~
`ing that occurs in medium and wideband TDMA systems can provide a diversity
`advantage, but only if the receiver includes an effective equalizer.
`
`One final comment is in order: TDMA is the not the only choice of multiple access for
`overlaying on an FDMA baseline. 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 FDMA baseline. Moreover, wireless communication is 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 TDMA overlaid on FDMA; rather, it also
`includes a third multiple-access strategy known as frequency hopping (FH); that is,
`GSM is, in reality, an FDMA/TDMAIFH system. Frequency hopping is also discussed
`in Chapter 5.
`
`4.17 THEME EXAMPLE 1: (55M13
`
`The Global Sysrem for Mobile (GSM) communications is a digital wireless communica-
`tion system that is used all over the world. Figure 4.23 displays the basic TDMA frame
`structure of GSM. The structure 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. The 3 mil 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
`time slot is used for channel equalization. Finally, the guard time, occupying 8.25 bits, is
`included at 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.
`
`
`
`Page 256 of 474
`
`Page 256 of 474
`
`

`

`
`
`
`
`%— Frame : 4.6155 ms —%
`
`
`
`T5,
`
`T52
`
`T53
`
`rs4 T55
`
`rs6
`
`Section 4.17 Theme Example 1: GSM
`
`237
`
`rs7
`
`TS: Time slot
`T: Tail (bits)
`F: Flag (bit)
`Train: Training interval for equalizer
`Guard: Guard time interval
`
`Guard
`Data
`Train
`I Data
`3 II-IF-I-
`? Tirne slot = 156.25 bits = 577;“ 4%
`FIGURE 4.23 Frame structure of GSM communications.
`
`The frame efi‘iciency of a TDMA system 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
`
`
`[1 _ 40.25
`
`156.25
`
`)x 100 = 74.24%
`
`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 channel is partitioned in both time and frequency. The channei is parti-
`tioned in time because, with eight slots in a TDMA frame, each carrier frequency
`supports eight physical channels mapped onto the eight slots. A time slot assigned to a
`particular physical channei is naturally used in every TDMA frame for as long as that
`channel is engaged by a mobile user. Consequently, partitioning of the channel in 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 TDMA system to combat the fading problem even more effectively. 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 TDMA frame will 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 one is sufficiently iarge.
`
`For uplink transmission, in Europe, GSM uses the frequency band 890 to 915 MHZ, and
`for downiink transmission, it uses the frequency band 935 to 960 MHZ. In either case,
`the maximum frequency change from one frame to the next is 25 MHZ. Expressed as a
`
`
`
`Page 257 of 474
`
`Page 257 of 474
`
`

`

`238
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`percentage of the mean carrier frequency, the maximum frequency hopping for the
`downlink is approximately
`
`0
`_
`25
`W0 x 100 — 2.8 /o
`
`With this percentage of maximum frequency hopping, it turns out that the time spent
`by a rapidly 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 proteCw
`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 was discussed in
`Sections 3.7 and 4.14. For GSM, the timeubandwidth product WT of GMSK is 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 GMSK signals so specified is confined to a bandwidth of 250
`kHz, which means that, 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 ZOO-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
`
`a Power spectrum, dB
`
`|II :
`
`-60r
`
`ll
`
`l
`
`1
`
`l
`
`Carrier
`i
`Carrier
`frequency n,,,,,r frequency
`F200 ah—zooah—mu —>l ——> Frequency, kHz
`
`FIGURE 4.24 Power spectrum of GMSK signal for GSM communications.
`
`
`
`Page 258 of 474
`
`
`
`
`
`7
`
`:i
`l
`1—80
`ll
`Limp
`
`1
`
`l
`
`Page 258 of 474
`
`

`

`1 i
`
`i
`
`i
`
`i
`
`.
`
`E
`
`'
`
`
`
`Section 4.18 Theme Example 2: Joint Equalization and Decoding
`
`239
`
`passband version of the baseband power spectrum of Fig. 3.21 corresponding to
`WTb : 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 amount close to
`40 dB at the carrier frequencies of both adjacent subchannels, which means that the
`
`effect of cochannel interference in GSM is smail.
`
`4.13 THEME EXAMPLE 2: JOINT EQUALEZATEON AND DECODING14
`
`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 be stated as foliows:
`
`The performance of the receiver of a digital communication system, embodying
`the plot of bit error rate (BER) versus transmitted signal energy per bit—to-noise
`spectral density ratio, Eb/NO, may be significantly improved by using
`
`(i) a concatenated encoding strategy at the transmitter and
`
`(ii) an iterative receiver, with all of its components operating in soft-input, soft-
`oatpat (i.e., analog) form.
`
`The iterative receiver is the hallmark of the turbo coding principie.
`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 statisticaliy 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, at first sight, this structure Eooks familiar
`
`Binary
`stream
`
`
`
`Channel encoder:
`Outer encoder l
`
`Interleaver
`
`Wireless channel:
`Inner encoder
`
`Received
`signal
`
`
`
`
`(a)
`
`Additive white
`Gaussian noise
`
`
`
`
`
`qualizer:
`Inner decoder
`
`RECEIVSd
`Signal
`
`Deinterleaver
`
`
`
`
`
`Channel decoder:
`Outer decoder
`
`Hard
`limiter
`
`Estimate
`of original
`binary
`stream
`
`(b)
`
`Joint equalizationvandwdecoding problem.
`FIGURE 4.25
`(a) Turbo encoder of the serial form. with the channei viewed as the inner encoder.
`(b) Iterative Turbo decoder, highlighting the application of feedback around the two decoding
`stages.
`
`
`
`Page 259 of 474
`
`Page 259 of 474
`
`

`

`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 encoder can be justified along the following lines:
`
`0 The channel encoder, introduced into the transmitter chain to improve the reli-
`ability of communication, is viewed as the outer encoder.
`
`- The wireless channel, essential for the communication process, is viewed as the
`inner encoder.
`
`0 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. 425(b), in accordance with the receiver part of the turbo-coding prinr
`ciple. Herein lies the basis of a novel receiver structure made up of the following
`constituents:
`
`0 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 decoder acts as the outer decoder.
`
`0 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.
`
`- An interleaver, 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 interleavet
`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
`performance of the other. The bootstrap action manifests itself as follows:
`
`- The equalizer uses frequency diversity in the channel to improve the decoder
`performance through [SI reduction.
`
`0 The decoder uses time diversity in the code to improve the equalizer perfor—
`mance through improved estimates ofuncoded data symbols.
`
`Page 260 of 474
`
`Page 260 of 474
`
`

`

`
`
`i
`l
`
`---l
`
`i
`
`Section 4.18 Theme Example 2: Joint Equalization and Decoding
`
`24‘!
`
`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
`
`the serial concatenated encoder of Fig.4.25(a), with the following
`Consider
`specifications:
`
`1. Channel encoder (outer encoder): convolutional encoder
`Code rate 21/2
`
`Constraint length, K m 3
`Generator polynomials:
`g(1)(D)=1~l-Dz
`543(1)): 1 +1) +02
`2. Interleavcr:
`Type: pseudorandom interieaver
`Block size: 1000 bits
`
`3. Wireless channei: Tapped-delay-iine model with the foliowing tap weights (see
`Fig. 4.26, where T denotes the symbol duration):
`
`wO = 0.93
`
`W1 2 “0.17
`
`W2 = 0.35
`
`Euclidean norm of the tap-weight vector w:
`
`2 1/2
`2
`2
`leIl = (wO-i—wl ~I— W2)
`
`= ((0.93)2+{70.17)2+(0.35)2)
`:1
`
`1/2
`
`4. Modulation (not shown in Fig. 425(3)): Binary phase-shift keying (BPSK). With
`this simple method of modulation, the baseband model of the system assumes a
`real—valued form throughout the system.
`
`
`
`Output
`
`FIGURE 4.26 Tappededelay—line model of wireless channel with three tap—weights; the
`blocks labeied Tact like unit-delay operations
`
`
`
`Page 261 of 474
`
`Page 261 of 474
`
`

`

`242
`
`Chapter 4 Coding and Time-Division Multiple Access
`
`The iterative two—stage receiver of Fig. 4.25(b) was implemented as follows:
`
`1. Equalizer (inner decoder).
`. The channel impulse response, assumed to be known.
`- The decoding trellis, formed on the basis of the channel impulse response (i.e.,
`tap weights of the tapped-delay-line model) and BPSK.
`2. Deinterleaver, designed to deinterleave the soft outputs produced by the
`equalizer.
`3. Channel decoder (outer decoder).
`- The decoding trellis, formed on the basis of the convolutional encoder’s gen-
`erator polynomials g(1)(D) and g(2)(D)
`0 Construction of the decoding trellis, 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 maximum a posterior probability (MAP) algorithm, discussed in
`Section 4.12.
`
`Using computer simulations of the encoderfdecoder system of Fig. 4.25, we plot the
`receiver performance, in terms of BER versus EbI’NO, in Fig. 4.27, on the basis of which
`we may make the following observations:
`
`10“
`
`Iteration 1
`
`Iteration 2
`
`—1
`
`10 E
`
`fi 10'2 E
`m
`1
`
`10’3 I;
`
`
`
`
`
`Iterations 4,5
`Iteration
`
`
`10‘ 4
`—4
`
`I
`—2
`
`I
`0
`
`I
`2
`
`I
`4
`EbeU
`
`I
`6
`
`I
`8
`
`I
`10
`
`12
`
`FIGURE 4.27 Performance receiver curves for the iterative joint equalization-and-decoding
`experiment.
`
`
`
`Page 262 of 474
`
`Page 262 of 474
`
`

`

`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 the first iteration; in effect, iteration 1 represents what is achievable
`with a noniterative (i.e., conventional) receiver.
`2. The receiver converges in about five iterations.
`3. Littie change in receiver performance occurs in going from iteration 4 to
`iteration 5.
`
`Problem 4.5 The baseband model used in the computer experiment on joint equalization
`and decoding is real valued, which is justified for BPSK modulation. To improve spectral effi-
`ciency, QPSK modulation is commonly used. Discuss the modifications that would have to be
`made to the baseband model in order for it to handle QPSK modulation.
`I
`
`The computer experiment just presented assumes that the receiver has perfect knowl-
`edge of the channel state information (CSI). In practice, we have to deai with a wireless
`channel that is typically nonstationary, in which case the equalizer structure has to be
`expanded to include a CSI estimator. (See Problem 4.24.)
`
`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 antim-
`ber of ways:
`
`1. The system could permanently assign one channel to each user.
`
`2. The system could poll each user at regular intervals to see if he or she had any-
`thing to transmit.
`
`3. The system could provide a random-access channel that the users could access at
`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 deiays if there is a large number of users, and if
`the users are mobile, the polling process can become compiicated. In this section, we
`will consider the third approach of assigning a random-access channel.
`
`:
`
` 4.19 THEME EXAMPiE 3: RANDOM-ACCESS TECHNIQUES
`
`4.19.1 Pure Aioha15
`
`Consider