IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7, JULY-1985
`
`665
`
`Analysis and Simulation of a Digital Mobile Channel
`Using Orthogonal Frequency Division Multiplexing
`
`LEONARD J. CIMINI, JR., MEMBER, IEEE
`
`Abstract-This paper discusses the analysis and simulation of a
`technique for combating the effects of multipath propagation and
`cochannel interference on a narrow蛐band digital mobile channel. This
`system uses the discrete Fourier transform to orthogonally frequency
`multiplex many narrow subchannels, each signaling at a very low rate,
`into one high-rate channel. When this technique is used with pilot-based
`correction, the effects of flat Rayleigh fading can be reduced signifi(cid:173)
`cantly. An improvement in signal-to-interference ratio of 6 dB can be
`obtained over the bursty Rayleigh channel. In addition, with each
`subchannel signaling at a low rate, this technique can provide added
`protection against delay spr邙d. To enhance the behavior of the technique
`in a heavily frequency-selective environment, interpolated pilots are us乩
`A frequency offset reference scheme is employed for the pilots to improve
`protection against cochannel interference.
`
`I. INTRODUCTION
`SEVERE multipath propagation, arising from multiple scat-
`tering by buildings and other structures in the vicinity of a
`mobile unit, makes the design of a mobile communication
`channel very challenging [ 1]. This scattering produces rapid
`random amplitude and phase variations in the received signal
`as the vehicle moves in the multipath field. In add1tion, the
`vehicle motion introduces a Doppler shift, which causes a
`broadening of the signal spectrum. Measurements confirm
`that the short-term statistics of the resultant signal envelope
`approximate a Rayleigh distribution.
`Multipath fading may also be frequency selective, that is,
`the complex fading envelope of the received signal at one fre(cid:173)
`quency may be only partially correlated with the received en(cid:173)
`velope at a different frequency. This decorrelation is due to
`the difference in propagation time dela·ys associated with the
`various scattered waves making up the total signal. The spread
`in arrival times, known as delay spread, causes transmitted
`data pulses to overlap, resulting in intersymbol interference.
`In a typical urban environment, a spread of several micro(cid:173)
`seconds and greater can be occasionally expected.
`There is an additional impairment in a cellular mobile sys(cid:173)
`tern. The available radio channels are reused at different loca(cid:173)
`tions within the overall cellular service area in order to use the
`assigned spectrum more efficiently. Thus, mobiles simultane(cid:173)
`ously using the same channel in different locations interfere
`with each other. This is termed cochannel interference and is
`often the dominant impairment.
`In addition, there is a long-term variation of the local mean
`of the received signal, called shadow fading. Shadow fading in
`a mobile radio environment is caused by large obstacles block(cid:173)
`ing the transmission path. This impairment is alleviated in eel(cid:173)
`lular systems by using transmitted and received base-station
`signals at two different geographical locations [ 1], and will
`not be discussed in this paper.
`Given the har油 mobile environment and the. scarcity of
`
`Paper approved by the Editor for JQdio Communication of the IEEE
`Communications Society for publication without oral presentation. Manu(cid:173)
`即ript received June 18, 1984; revised January 14, 1985.
`The author is with AT&T Bell Laboratories, Holmdel, NJ 07733.
`
`available spectrum, it is desirable to look for channel designs
`which provide good performance·for both speech and data
`transmission, and which are also bandwidth efficient. The
`channel designs presented in this paper could accommodate
`speech or data transmission. For the narrow channel assumed,
`a low-bit-rate speech coder would be required. For example, a
`7 .5 kHz channel using the system proposed in this paper can
`噩pport 8.6 kbits/s. In what follows, the channel will be as(cid:173)
`sumed to be transmitting data symbols.
`In a conventional serial data system, the symbols are trans(cid:173)
`mitted sequentially, with the frequency spectrum of each data
`symbol allowed to occupy the entire available bandwidth. Due
`to the bursty nature of the Rayleigh channel, several adjacent
`symbols may be completely destroyed during a fade. To illu(cid:173)
`strate the severity of the problem, consider the following ex(cid:173)
`ample. Assume that there is a cochannel interferer with an
`average power level 17 dB below that of the desired signal.
`This condition occurs approximately 10 percent of the time in
`a cellular mobile system. A fade 1 7 dB below the average level
`will bury the desired signal in the interference. At a carrier fre(cid:173)
`quency of 850 MHz and a vehicle speed of 60 mph, the aver(cid:173)
`age fade duration for a fade 17 dB below the local mean of the
`desired signal is 0. 75 ms [ 1]. For a data rate of 10 kbits/s, 7 or
`8 adjacent bits would be destroyed during such a fade.
`In a serial system, higher data rates can be achieved, at the
`expense of a degradation in performance, by using higher order
`modulations or, at the expense of increased channel band(cid:173)
`width, by decreasing the symbol interval. However, delay
`spread imposes a waiting period that determines when the next
`pulse can be transmitted. This waiting period requires that the
`signaling be reduced to a rate much less than the reciprocal of
`the delay spread to prevent intersymbol interference. De(cid:173)
`creasing the symbol interval makes the system more susceptible
`to delay spread impairments.
`A parallel or multiplexed data system offers possibilities
`for alleviating many of the problems encountered with serial
`systems. A parallel system is one in which several sequential
`streams of data are transmitted simultaneously, so that at any
`instant many data elements are being transmitted. In such a
`system, the spectrum of an individual data element normally
`occupies only a small part of the available bandwidth. In a
`classical parallel data system, the total signal frequency band is
`divided into N nonoverlapping frequency subchannels. Each
`subchannel is modulated with a separate symbol and, then, the
`N subchannels are frequency multiplexed. A more efficient use
`of bandwidth can be obtained with a parallel system if the
`spectra of the individual subchannels are permitted to overlap,
`with specific orthogonality constraints imposed to facilitate
`separation of the subchannels at the receiver.
`A parallel approach has the advantage of spreading out a
`fade over many symbols. This effectively randomizes the burst
`errors caused by the Rayleigh fading, so that instead of several
`adjacent symbols being completely destroyed, many symbols
`are only slightly distorted. This allows precise reconstruction
`of a majority of them. A parallel approach has the additional
`advantage of spreading out the total signaling interval, thereby
`reducing the sensitivity of the system to delay spread.
`Several systems have previously used orthogonal frequency
`
`0090-6778/85/0700-0665$01.00©1985 IEEE
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on July 04,2022 at 19:06:47 UTC from IEEE Xplore. Restrictions apply.
`
`VWGoA EX1018
`U.S. Patent No. 8,467,366
`
`

`

`666
`
`IEEE"TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7, JULY 1985
`
`SERIAL
`
`STREAM —
`
`, • = .!.
`l:,.t.
`(SPEECH OR DATA)
`
`CHANNEL
`
`COS Wot.
`
`sinw,.._1t.
`fn =f0+n l::.f, l::,,f,. 上N!it.
`
`C心NNEL
`
`d{n)= o(n)+ j b(n)
`
`cos "'ot.
`
`(a)
`
`,.
`Q (0)
`
`^
`b (0)
`
`^ a(N-1)
`t (N-1)
`
`sinw N-1 t.
`(b)
`Fig. l. Basic OFDM system. (a) Trans面tter. (b) Receiver.
`
`division multiplexing (OFDM) [3] 一[ 8]. In particular, i1,1 the
`early 1960's, this technique was used in several 扣gh-frequency
`militazy systems (for example, KINEPLEX [9], ANDEFT
`[101, KATHRYN [11), [12]), where fast fadmg was not a
`problem. Similar modems have found applications in voice
`bandwidth data communications (for example, [ 13]) to allevi(cid:173)
`ate the degradations caused by an 面pulsive noise environ1,11ent.
`In this paper, a parallel system which uses the OFDM tech靄
`nique is described. In Section II an analysis and simulation of
`the basic system, using pilot砸based correction, is presented. In
`Section III a practical 7.5 kHz channel design is presented,
`along with a discussion of several of the problems encountered
`in reliably retrieving the pilots used. in the data correction
`process. Several solutions to these problems are also presented.
`This investigation is simplified by the assumption that the
`sole source of additive signal degradation is cochannel interfer(cid:173)
`ence-thermal noise is as~umed negligible. Man-made environ霾
`mental noise, such as that caused by automotive ignitions or
`neon 迤hts, is also ignored. f[owever, these inlpairments are
`basically 血pulsive and their effect should be greatly reduced
`by this technique.
`
`II. BASIC PRINCIPLES OF OPERATION
`A. Orthogonal Frequency Di泅ion Multiplexing (OFDM}
`When an efficient use of bandwidtp. is not required, the most
`effective parallel system uses conventional frequency division
`multiplexing where; the spectra of the different subchannels do
`not overlap. In such a system, there is sufficient guard space
`between adjacent subchannels to isolate them at the receiver
`using conventio:qal filters. A much more efficient use of band(cid:173)
`width can be obtained with a parallel system if the spectra of
`the individual subchannels are permitted to overlap. With the
`addition of coherent detection and the use of subcarrier tones
`separated by the reciprocal of the signaling element duration
`(orthogonal tones), independent separation of the multiplexed
`tones is possible.
`Consider the system shown in Fig. 1. The transmitted spec-
`
`tral shape is chosen so that interchannel interference does not
`occur; that is, the spectra of the individual subchannels are zero
`at the other subcarrier frequencies. The N serial data elements
`(spaced by At = I/八 where fs is the symbol rate) modulate
`N subcarrier frequencies, which are then frequency c.ivision
`multiplexed. The signaling interval T has been incrensed to
`Nil.t, which rriakes the s泝tern les·s susceptible to delay spread
`the subcarrier frequencies are
`In addition,
`impairments.
`separated l:Jy multiples of 1 /Tso that, with no signal dis~ortion
`in transmission, the coherent detection of a signal eler;ient in
`any one subchannel of the parallel system gives no output for
`a receiveq element in any other subchannel. Using a two-di(cid:173)
`mensional digital modulatipn format, the data symbols d(n)
`can. be represented as a(n)'+ jb(n) (where a(n) and b(n) are
`real seqll~nces representing the in-phase and quadrature com(cid:173)
`ponents, respectively) and the transmitted waveform can be
`represented as
`
`D(t) = L {a(n) cos (w11t) + b(n) sin (wnt)}·.
`
`N-1
`
`·n=o
`
`(1)
`
`where 九= fo + nAf and 11[= l/N/1t. This expression and the
`following analyses can be easily extended to include pulse
`shaping other than the assumed rectangular shape.
`Theoretically, M-ary digital modulation schemei: using
`OFDM can achieve a bandwidth efficiency, defined as bit rate
`per U!].it bandwidth, of log2 M bits 困 Hz. This is easily shown
`as follows. Given that the symbol rate of the serial data stream
`is 1/At, the bit rate for a corresponding M-ary sy1,tem is
`log2 叩.:lt. Each subchannel, however, transmits at a much
`lower rate, lo距 M/(Ni:::.t). The total bandwidth of the OFDM
`system is
`B = f N - l -
`
`f o + 26
`
`(2)
`
`where 几 is the nth sub carrier and 6 is the one-sided bandwidth
`of the subchannel (where the bandwidth is co函dereC as the
`
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`
`

`

`CIMINI: ANALYSIS AND SIMULATION OF DIGITAL MOBILE CHANNEL
`
`667
`
`COCHANNEL
`INTERFERER
`
`Fig. 2. OFDM system implemented with an FFT.
`
`distance to the first null). The subcarriers are uniformly spaced
`sothatfN-1 -fo=(N- 璘 f. Since 幻= I/NL\t due to the
`J;。= (1 —(1/N))(l/l::,.t).
`orthogonality constraint, IN_ 1 -
`Therefore, the bandwidth efficiency~becomes
`
`Further reductions i.11 complexity are possible by using the
`fast Fourier transform (FFT) algorithm to implement the
`DFT when N is large.
`
`Iog2 M
`
`13 = (1 -~) + 28.6t
`
`(3)
`
`For orthogonal frequency spacing and strictly band-limited
`spectra (bandwidth -6!) with 8 = l. .6f = l/2N.6t, 13 = log2 M
`2
`bits困 Hz. In reality, however, the spectra overflow this min-
`imum bandwidth by some factor Cl'so that 8 = (1 + 0')(1/
`2N.6t) and the efficiency (3) becomes
`
`log2 M
`(3 =一 <log2 M.
`Q'.
`I+--:-(cid:173)N
`To obtain the highest bandwidth efficiency in an OFDM sys(cid:173)
`tern, N must be large and a must be small.
`
`(4)
`
`B. Implementation of OFDM Using the Discrete Fourier
`Transform
`The principal objections to the use of parallel systems are
`the complexity of the equipment required to implement the
`system, and the possib 山ty of severe mutual interference among
`subchannels when the transmission me1ium distorts the sig(cid:173)
`nal. The equipment complexity (filters, modulators, etc.) can
`be greatly reduced by eliminating any pulse shaping, and by
`using the discrete Fourier transform (DFT) to implement the
`modulation processes, as shown in [7], [8]. There it is shown
`that a multitone data signal is effectively the Fourier trans(cid:173)
`form of the original data stream, and that a bank of coherent
`demodulators is effectively an inverse Fourier transform. This
`can be seen by writing (1) as
`
`C Pilot-Based Correction
`If the transmission channel is distortionless, the orthogo(cid:173)
`nality of the subcarriers allows the transmitted signals to be
`received without error at the receiver. Consider the system in
`Fig. 2 with the block of data represented by the sequence of
`N complex numbers { d(O), d(l), …, d(N- 囯 These complex
`numbers are generated by·the data encoder from a binary data
`sequence. A DFT is performed on this block of data, giving
`the transmitted symbols2
`
`(6)
`
`N-I
`D(m) = DFT{d(n)} =~d(n)e-i(2rr/N)nm.
`n=O
`Notice that this is a sampled version of (5) where the complex
`notation has been retained. All future analyses will be done in
`the complex domain. Under the assumption of a distortionless
`channel, the received data sequence (the output of the inverse
`DFT) will be exactly the transmitted sequence due to the
`orthogonality of the sub carrier tones (exponentials).
`If the transmission channel distorts the signal, this orthog(cid:173)
`onality is impaired. In a flat Rayleigh fading environment (i.e.,
`the environment is not frequency selective), the effects of the
`Rayleigh channel can be represented as a multiplicative noise
`process on the transmitted signal. This multiplicative process
`is characterized by a complex fading envelope with samples
`Z(m) = A(m)e頂 (m) where the A(m) are samples from a Ray(cid:173)
`leigh distribution and the 0(m) are samples from a uniform
`distribution [ 1). These samples multiply the sequence of (6)
`to give
`
`R(m) = Z(m)D(m).
`
`(7)
`
`The output data sequence d(k) is the inverse DFT of (7),
`
`D(t) = Re 図 d(n)e-jwnt]
`
`(5)
`
`N-1
`1
`蛔= -~Z(m)D(m)ei(21T/N)km
`N m=O
`
`Letting t = mAt, the resulting sampled sequence D(m) is seen
`as the real part of the DFT of the sequence d(n).1 The act of
`truncating the signal to the interval (0, NAt) imposes a sin x/x
`frequency response on each subchannel with zeros at multiples
`of I 兀 This spectral shape has large sidelobes, and gives rise to
`significant interchannel interference in the presence of multi(cid:173)
`path. This point will be discussed in more detail in Section III.
`
`N-1
`1 N 刁
`=~d(n{N n~O Z(m)ei(2rr/N)m(k-n)]
`
`N-I
`=~d(n)z(k - n)
`n=o
`
`(8)
`
`1 It is convenient in this paper to think of d(n) as being in the frequency
`domain and D(m) as being in the time domain, contrary to the, usual
`engineering interpretation [8].
`
`2 Throughout this paper, all indexes will be assumed to belong to the set {O,
`I, 2, , .. , N _ 1}.
`
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`
`

`

`668
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7, JULY 1985
`
`where z(n) is the inverse DFT of Z(m). It can be seen from
`(8) that there is a complex-weighted averaging of the samples
`of the complex fading envelope. Jf Z(m) = 1 for all m (the
`distortionless channel), z(k - n) is simply the Kronecker delta
`function -okn and d(k) = d(k). In the presence of fading,
`z(k - n) =I= o kn and
`.
`d(k) = d(k)z(O) + L d(n)z(k - n).
`
`N-1
`
`n=O
`n*k
`
`(9)
`
`The second term on the right represents the interchannel (in·
`tersymbol) interference caused by the loss of orthogonality.
`Without correction for the fading, the output sequence is cor(cid:173)
`rupted by intersymbol interference even if there is no cochan(cid:173)
`nel interferer.
`Pilot-based correction provides an amplitude and phase
`reference which can be used to counteract the unwanted ef(cid:173)
`fects of multipath propagation. Similar considerations have
`been analyzed for single-sideband mobile .radio systems [ 14] ,
`[ I 5]. Coherent detection, by definition, requires a phase
`reference; however, gain correction is also needed in an OFDM
`system in a fading environment to remove intersymbol inter(cid:173)
`ference. If phase and gain correction is employeq in the absence
`of cochannel interference, it is easily 油 own, in (9), that
`d(k) = d(k).
`In a cellular mobile system, the dominant transmission
`impairment often comes from other users using the same
`carrier frequency. It is assumed here that the desired signal
`and a single undesired cochannel interferer are received si(cid:173)
`rnultaneously, and that both are digital signals modulated by
`different data sequences with identical signaling rates. It is
`also assumed that they are subject to mutually independent
`Rayleigh fading.
`When a cochannel interferer is present in the received sig(cid:173)
`nal, it is not advantageous to do unlimited gain correction,
`due to the possibility of enhancing the energy of the interferer
`during deep fades of the desired signal. The detrimental effects
`of unlimited gain correction in the presence of a cochannel
`interferer can be seen as follows. Let D(m) be the desired
`transmitted signal sequence and let J(m) be the correspondin
`cochannel interferer sequence. With Zd(m) = Aa(m)ei囧(mJ
`and Z;(m) = A;(m)ei91(m) the desired and interferer com(cid:173)
`plex fading sequences, respectively, the sequence present at
`the receiver can be represented as
`
`R(m) = Zd(m)D(m) + V'訖 (m)J(m)
`
`(10)
`
`where'Y is the interference-to-signal power ratio (SIR-1).
`R(m) is corrected by a complex correction sequenceZc(m) =
`Zp(m), the complex pilot fading envelope, giving
`
`D(m)=- = - D(m)+~-—J(m).
`
`R(m)
`
`Zd(m)
`
`Zc(m) Zp(m)
`
`Zi(m)
`
`Zp(m)
`
`(11)
`
`Taking the inverse DFT of (11), the received data sequence
`becomes
`
`N-1
`N-1 1
`d(k) =~d(n)z(k - n) + .Ji~.,..
`m"'O N Zp(m)
`n=O
`,
`·I(m)ej(2 可N)mk
`
`(12)
`
`where
`
`1 N-1 Zd(m)
`L
`z(k - n) =—
`N m=O 今 (m)
`
`ei<2 可N)m (k- n).
`
`If unlimited gain and phase correction is used [i.e., Zpim) =
`Zd(m)J, z(k - n) = okn, there is no intersymbol interference,
`and (12) becomes
`
`N-1
`1
`Zi(m)
`a(k) = a(k) +..;:; - L 曰－一 ej(21t/N)mk_
`Nm=。
`Zd(m)
`
`(13)
`
`The only distortion is caused by the cochannel intel'ferer.
`However,·since Z;(m) and Zd(m) are statistically independent,
`the desired s珺nal may be in a fade when the interferer is not,
`and unlimited gain correction may boost the interferer a,rerage
`energy above that of the desired 呣nal.
`One alternative to unlimited gain and phase correction is to
`have a limit on the gain correction, so as not to follow foe de(cid:173)
`噩ed signal into deep fades [ 1]. This 邸 done at the expense of
`increased intersymbol interference, due to imperfect correc(cid:173)
`tion of the desired signal. In this situation, the correction sig(cid:173)
`nal is of the form
`Zc(m)=I 心(m)ei回(m)
`eei8a(m)
`
`when Ad(m) > e
`whenAd(m).,;;;e
`
`(14)
`
`is the gain limit and is defined relative to the average
`where€
`value of the local field strength. Therefore, in (12), z(k -- n) =I=
`o kn, resulting in intersymbol interference. Consequently, there
`is a tradeoff between increasing the intersymbol interference
`and boosting the cochannel interference energy.
`Another alternative is to develop an optimum gain c:orrec(cid:173)
`tion factor which takes both distortion effects into account.
`An optimum gain correction factor F(m) has been deri·red by
`minimizing the mean-square distortion betweenD(m) andD(m).
`The derivation of F(m) has been omitted for the sake of brevity.
`The correction sequence then becomes
`
`為(m) = Zp(m)F(m)
`
`=Za(m) [1 十笠訂］
`
`(15)
`
`This correction procedure would be more difficult to imple(cid:173)
`ment than the gain limiting procedure described.above ....
`In addition to the impairments caused by intersymbol and
`cochannel interference, frequency-selective fading may also be
`present. This phenomenon causes a decorrelation of :the re(cid:173)
`ceived signal envelopes at different freque_ncies, lessening the
`effectiveness of the pilot-correction procedure, since a data
`point which is being corrected may be decorrelated from the
`corresponding pilot complex fading envelope.
`Finally, one of the major advantages of the OFDM tech(cid:173)
`nique is its ability to "average" out impairments, making ,the
`bursty Rayleigh channel appear much less bursty. The extent
`to which this averaging approaches a Gaussian channel de(cid:173)
`pends on the correlation between samples of the complex
`fading envelope. It can be seen that as N increases, more inde(cid:173)
`pendent fades are averaged. This enables burst errors to be
`randomized and thereby aids in bit error correctio11. This
`property will be more evident in the simulation results, which
`indicate that the curves for the bit error rate fall between the
`linear Rayleigh channel curves and the exponential Gaussian
`channel curves. For large N and high vehicle speeds, the bit
`error curve approaches that for a Gaussian channel.
`
`D. Distortion Analyses
`Several mechanisms contribute to the over詛 distortion of
`the desired signal. In th認 section, emphasis 誌 on the contribu(cid:173)
`tions due to gain limiting, evident in increased inter::ymbol
`interference, and due to cochannel interference. The distor-
`
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`
`

`

`CIMINI: ANALYSIS AND SIMULATION OF DIGITAL MOBILE CHANNEL
`
`669
`
`tion resulting from decorrelation of the pilot due to frequency(cid:173)
`selective fading or due to interference on the pilot is considered
`in Section II-F.
`First, consider the case of gain-limited correction, where
`the amplitude correction is bounded to follow fades only as
`deep as€. Assume that the random processes which produce
`the random sequences are ergodic, thereby permitting the
`equivalence of time and ensemble averages. The pilot complex
`fading envelope at a particular instant in time is Zp(m) =
`Zd(m) and the correction sequence is
`
`Zc(m) = max (心 (m),e)ei 位 (m)_
`
`(16)
`
`30
`
`20
`-0p)
`
`l:lGS
`
`10
`
`The corrected output samples become
`
`Zi(m)
`Zd(m)
`R(m)
`D(m)=- =D(m) 一十壹(m) 一＿
`Zc(m)
`Zc(m)
`Zc(m)
`
`SIR•15dB,
`SIR=10dB
`
`= D(m)Ad(m) min (A二二）
`
`+ Yrf(m)Ai(m)ei(0;(m)-0d(m))
`
`1
`
`min(心(m)'-;)
`
`1
`
`-30
`
`-20
`
`一10
`~(dB)
`Signal-to-distortion ratio for a flat Rayleigh fading environment
`when gain-limited correction is used.
`
`。
`
`10
`
`Fig. 3.
`
`(I 7)
`
`30
`
`。2
`
`
`(8P)
`
`ijOS
`
`10
`
`The signal-to-distortion ratio (SDR) can be defined as in [ 14],
`
`SDR =
`
`ID(m)l2
`
`ID(m)- D(m) 12
`
`(18)
`
`where X denotes a time average of X. Assuming I D(m) 12 =
`丨 /(m) 12 = 1, the denominator in (18) reduces to
`
`lb(m) - D(m) 12
`
`04
`0.
`
`10
`
`20
`SIR (dB)
`Signal-to-distortion ratio for a flat Rayleigh fading environment
`when the optimum gain correction factor is used.
`
`30
`
`40
`
`g .l F
`
`(19)
`
`）二
`」f
`、,＇（m
`
`(A 2r
`?
`=
`inm mm
`d A+
`
``~
`
`Assuming time averages can be replaced by expected values
`and assuming A d(m) and A ;(m) are statistically independent and
`Rayleigh distributed, (18) becomes, after some manipulations,
`
`SOR= I(三尸 [1 - e-E2] + 1 立 erf (1:)
`
`SIR
`
`1:2
`
`c
`
`十 ~1-1
`SIR
`
`(20)
`
`where E1(x) =-['¥+In (x) + (~;;'可仁 l)Mx叨nn [)J and'¥
`is Euler's constant (=0.57721566 …) . The SDR in (20) is plot(cid:173)
`ted in Fig. 3 for several values of SIR. Obviously, if SIR = oo
`(no co channel interference), the results reduce to that in [ 14]
`and no gain limit should be used. However, for SIR < 00 the
`curves dearly indicate the tradeoff between intersymbol in(cid:173)
`terference, caused by gain limiting, and boosting of the co(cid:173)
`channel interference average energy, caused by unlimited gain
`correction. If unlimited gain correction is used, SDR = -00, in(cid:173)
`dicating that the interferer completely distorts the desired sig-
`
`nal. Notice, there is a definite maximum which is fairly flat.
`Although SDR as defined here is an analog transmission qual(cid:173)
`ity measure, it does indicate the degree to which intersymbol
`interference, caused by imperfect gain correction, and cochan(cid:173)
`nel interference are problems. These factors are critically im(cid:173)
`portant in digital transmission. The SDR also clearly shows
`the tradeoffs which must be made when choosing the appro(cid:173)
`priate gain limit. This, in tum, directly affects the bit error
`rate (BER), as shown in the next section.
`Similar results can be derived for optimum gain correction,
`as in (IS), and the SDR can be shown to be
`
`SDR = [ (s1/ _ l) [ s1:1~l ln (SIR) - 1 ]]-t
`
`(21)
`
`which is plotted versus SIR in Fig. 4. This curve indicates the
`best performance for a given SIR. Notice, by comparing Figs.
`3 and 4, that using gain-limited correction does not sacrifice
`much if the gain limit is in the vicinity of the maximum. Both
`of these results could be used as an aid in determining the
`appropriate level for gain limiting for a given SIR.
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on July 04,2022 at 19:06:47 UTC from IEEE Xplore. Restrictions apply.
`
`

`

`670
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7, JULY 1985
`
`i ..... ~
`
`一 N= 512 v =60 MPH, OPTIMUM GAIN
`CORRECTION
`.
`一一 ·N= 512, v =60 MPH, GAIN-LIMITED CORRECTION
`"… N=512,v :30 MPH, GAIN-LIMITED CORRECTl1:)N
`·一•• N=128, v='30 MPH, GAIN-LIMITED CORRECTION
`
`N:01
`
`10 o
`
`10-1
`
`10·2
`
`U30
`
`10·3
`
`10-4
`
`10·5
`0
`
`2
`
`4
`
`6
`
`..J.........J
`8 10 12 14 16 18 20 22 24 26
`SIR (dBi
`Fig. 5. Simulation results assuming perfect pilot recovery in a flat IR.ayleigh
`fading environment (QPSK,f, = 7.5 kHz).
`
`I
`
`1
`
`10 一4
`
`-2
`10
`
`ij38
`1
`
`io
`3
`
`10 一4
`
`SIR=15dB
`
`SIR•20 dB
`
`、、_____.,
`- - - - - - -
`SIR=17d8
`丶.,...,.
`、,:
`、,----
`,.
`丶，，、，膚.......
`、、＇',,
`' 丶'丶
`'
`
`/ /
`
`丶
`
`_,,.
`
`一－
`
`E. Simulation Results
`Initial simulations were performed assuming flat Rayle珺h
`fading. In these simulations, it was also assumed that the
`pilots could be recovered perfectly; that is, there is no inter(cid:173)
`ference or distortion on the pilots. A symbol rate and chan(cid:173)
`nel bandwidth of 7.5 kHz3 were used and the BER was deter(cid:173)
`mined for several values of SIR (100 000 bits were used in the
`simulation to provide statistical significance). Based on this
`choice for the bandwidth, the maximum bit rate is 7.5 log2 M
`kbits/s. Several parameters were varied in this initial investiga(cid:173)
`tion, the most important being N, the number of subchannels,
`and v, the vehicle speed. Both quantities are very important
`factors in determining the ability of this system to effectively
`randomize the burst errors created by the Rayleigh fading.
`The fading rate is directly proportional to the vehicle speed.
`In particular, at a carrier frequency of 850 MHz, independent
`fades are about 7 in apart, giving a fade every 6.6 ms at 60
`mph. Therefore, for a given value of N, higher vehicle speeds
`should result in better performance because more fades are
`included in the averaging process. Similarly, for a given ve(cid:173)
`hicle speed, if N is large, the total s珺naling interval is also
`large and more fades are again used in the averaging process.
`The results shown in Fig. 5, where quadrature phase shift
`keying (QPSK) has bee.n employed, indicate the improvement
`possible if OFDM is used with gain correction under the as(cid:173)
`sumptions of ideal pilot recovery and a flat Rayleigh fading
`environment. Results for both optimum gain correction, as in
`(15), and gain-limited correction, as in (l 4), are given, These
`results clearly indicate the effects of vehicle speed and the
`number of subchannels. At a carrier frequency of 850 MHz
`and with a vehicle speed of 60 mph, with gain-limited correc(cid:173)
`tion, improvements in SIR of 6刁 dB4 have been obtained
`using 512 sub channels (T = 68 ms). This is in comparison to a
`flat Rayleigh channel using coherent detection (N = 1) with
`QPSK. A reduction in speed to 30 mph results in a loss in
`performance of less than 1 dB. A reduction of N to 128 sub(cid:173)
`channels (T = 17 ms) results in an additional 2 dB loss, be(cid:173)
`cause fewer independent fades are included in the averaging
`process. For the cases where gain-limited correction is used,
`the BER curves shown are for the "best" absolute gain limit.
`If the optimum gain correction factor can be determined, an
`additional improvement of 1 dB can be obtained. The sensi(cid:173)
`tivity of the BER on the gain limit, sh0wn in Fig. 6, indicates
`that adaptive gain limiting, or some "intelligent" guess at the
`gain limit based on the distortion curves, may be required.
`
`F Effects of Frequency-Selective Fading
`When good correlation exists between the fading statistics
`of the pilot tone and those of the fading information signal,
`almo'st total suppression of the unwanted amplitude and phase
`fluctuations is possible. The simulation results given in Section
`ll-E were obtained under the assumption that the fading on
`the pilot and the desired signal were totally correlated. This is
`a valid consideration when there is no interference on the pilot
`and when the fading is not frequency selective.
`In general, however, the mobile environment is frequency
`selective, due to the existence of a spread in arrival times of
`the various multipath components. In this. case, the correlation
`in phase and amplitude between two pilots separated in fre(cid:173)
`quency is 扣gh for small frequency separation, and falls essen(cid:173)
`tially to zero as the separation substantially exceeds the correla(cid:173)
`tion band width [ l] . The gain correction process, as will be seen,
`requires a high degree of correlation between the phase and
`
`3 Such a channel allows a factor of 4 improvement in spectral efficiency
`over the current 30 kHz cellular mobile telephone service channel.
`4 All comparisons in this paper will be made at a BER level of 10-2.
`
`10 ` I,,,,
`
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`一 24 -22 -20-18 -16 -14-12-10 -8 -6 -4 -2 0
`
`E (dB)
`Fig. 6. Sensitivity of BER to variations in gain limit (N = 512" v = 60
`mph, fs = 1 .5 kHz).
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on July 04,2022 at 19:06:47 UTC from IEEE Xplore. Restrictions apply.
`
`

`

`CIMINI: ANALYSIS AND SIMULATION OF DIGITAL MOBILE CHANNEL
`
`671
`
`NO 01::LAY SPREAD
`-
`一一一 DELAY SPREAD (l:1=50µs), 500 Hz SEPARATION
`一·一. DELAY SPREAD (l:1=50µ11), 1 kHz SEPARATION
`
`o
`10
`
`10-1
`
`10-2
`
`a: w
`CD
`
`10 -3
`
`10 -4
`
`amplitude variations of the pilot and that of the phase and
`amplitude variations imposed on the data.
`A simple way to estimate the effects of a delay spread en(cid:173)
`vironment is to compute the equivalent decorrelation between
`the pilot and the data caused by the frequency-selective fac!ing
`(for example, see [ 12]). These calculations depend on the
`model used to describe the dispersive channel. In the simula-
`tions, the delay spread channel is simply modeled as a two-im-
`pulse channel response with equal-amplitude signal and echo
`separated by some time .6. As in [ 2, sect. 9 .8] , an approxima-
`tion model will be assumed for the delay distribution. In this
`model, the probability density function of the delay is repre-
`sented as two equal-amplitude, equally likely impulses sep 年
`rate