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
`
`S
`
`is
`
`is desirable to look for channel designs
`available spectrum, it
`and simulation of a
`Abstract-This paper discusses the analysis
`which provide good performance -for both speech and data
`technique for combating the effects
`of multipath propagation
`and
`transmission, and which are also bandwidth efficient. The
`cochannel interference on a narrow-band digital mobile channel. This
`channel designs presented in this paper could accommodate
`system uses the discrete Fourier transform
`to orthogonally frequency
`speech or data transmission. For the narrow channel assumed,
`multiplex many narrow subchannels, each signaling at a very low rate,
`a low-bit-rate speech coder would be required. For example, a
`into one high-rate channel. When this technique is used with pilot-based
`7.5 kHz channel using
`the system proposed in this paper can
`correction, the effects of flat Rayleigh fading can
`be reduced signifi-
`support 8.6 kbits/s. In what follows,
`the channel will be as-
`cantly. An improvement in signal-to-interference ratio of 6 dB can be
`sumed to be transmitting data symbols.
`In additim, with each
`obtained over the
`bursty Rayleigh channel.
`In a conventional serial data system,
`the symbols are trans-
`a low rate, this technique can provide added
`subchannel signaling at
`mitted sequentially, with
`the frequency spectrum of each data
`protection against delay spread. To enhance the behavior of the technique
`symbol allowed to occupy the entire available bandwidth. Due
`in a heavily frequency-selective environment, interpolated pilots are used.
`to the bursty nature of the Rayleigh channel, several adjacent
`A frequency offset reference scheme is employed for the pilots to improve
`symbols may be completely destroyed during a fade. To
`illu-
`protection against cochannel interference.
`strate the severity of the problem, consider the following ex-
`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 17 dB below the average level
`will bury the desired signal in the interference. At a carrier fre-
`quency of 850 MHz and a vehicle speed of 60 mph, the aver-
`age fade duration for a fade 17 dB below the local mean of the
`desired signal is 0.75 ms [ 11. For a data rate of 10 kbits/s, 7 or
`8 adjacent bits would be destroyed during such a fade.
`the
`In a serial system, higher data rates can be achieved, at
`expense of a degradation in performance, by using higher order
`modulations or, at the expense of increased channel band-
`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 t o a rate much less than the reciprocal of
`the delay spread
`to prevent intersymbol interference.
`De-
`creasing the symbol interval makes the system more susceptible
`t o 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
`for ,hdio Communication of the IEEE
`Paper approved by the Editor
`advantage of spreading out the total signaling interval, thereby
`Communications Society
`for publication without oral presentation. Manu-
`reducing the sensitivity of the system to delay spread.
`script received June 18, 1984; revised January 14, 1985.
`The author is with AT&T Bell Laboratories, Holmdel, NJ 07733.
`Several systems have previously used orthogonal frequency
`0090-6778/85/0700-0665$01.00 0 1985 IEEE
`
`I. INTRODUCTION
`EVERE 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
`[ 1 1. This scattering produces rapid
`channel very challenging
`random amplitude and phase variations in the received
`signal
`as the vehicle moves
`in the multipath
`field. In addition, the
`vehicle motion introduces a Doppler shift, which causes a
`broadening of the signal spectrum. Measurements confirm
`that the short4erm 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-
`quency may be only partially correlated with the received en-
`velope at a different frequency. This decorrelation
`is due to
`the difference in propagation time delays associated with the
`various scattered waves making up the total signal. The spread
`in arrival times, known as delay spread, causes transmitted
`data pulses t o overlap, resulting in intersymbol interference.
`In a typical urban environment, a spread
`of several micro-
`seconds and greater can be occasionally expected.
`There is an additional impairment in a cellular mobile sys-
`tem. The available radio channels are reused at different loca-
`tions within the overall cellular service area in order to use the
`Thus, mobiles simultane-
`assigned spectrum more efficiently.
`ously using
`the same channel in different locations interfere
`with each other. This
`is termed cochannel interference and
`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-
`ing the transmission path. This impairment is alleviated in cel-
`lular systems by using transmitted and received base-station
`[ 11, and will
`signals at two different geographical locations
`not be discussed in this paper.
`Given the harsh mobile environment and the, scarcity of
`
`1
`
`APPLE 1009
`
`

`

`666
`
`IEEE'TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7 , JULY 1985
`
`cos WOt
`
`SERIAL
`
`
`STREAM DATA
`4
`f* =- At
`(SPEECH OR DATA)
`
`b ENCODER L
`
`d ( n ) = a ( n ) + j b ( n )
`
`M u L n u x , D ( t )
`CHANNEL
`
`CHANNEL
`
`sinw,,,,,t
`
`(b)
`Fig. 1. Basic OFDM system. (a) Transmitter.
`
`(b) Receiver.
`
`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 = l/f, where fs is the symbol rate) modulate
`N subcarrier frequencies, which are then frequency
`Chvision
`T has been increased
`multiplexed. The signaling interval
`to
`less susceptible to delay spread
`N A t , which makes the system
`impairments. In addition, the subcarrier frequencies
`are
`separated by multiples of 1/T so that, with no signal dislortion
`in transmission, the coherent detection of a signal element in
`any one subchannel of the parallel system gives no output for
`a received element in any
`other subchannel. Using a twodi-
`d ( n )
`mensional digital modulation format, the data symbols
`a(n)'+ jb(n) (where a(n) and b ( n ) are
`can, be represented as
`real sequences representing the in-phase and quadratur,e com-
`ponents, respectively) and the transmitted waveform can be
`represented as
`
`N - 1
`
`[3]-[8]. In particular, in the
`division multiplexing (OFDM)
`early 1960's, this technique was used in several high-frequency
`[ 9 ] , ANDEFT
`military systems (for example, KINEPLEX
`[ 101, KATHRYN [ 1 11, [ 121 ), where fast fading was not a
`problem. Similar modems have found applications in voice
`bandwidth data communications (for example, [ 131 ) to allevi-
`ate the degradations caused by an impulsive noise environment.
`In this paper, a parallel system which uses the OFDM tech-
`nique is described. In Section 11 an analysis and simulation of
`the'basic system, using pilot-based correction,
`is presented. In
`Section 111 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-
`ence-thermal noise
`is assumed negligible. Man-made environ-
`mental noise, such as that caused by automotive ignitions or
`neon lights,
`is also ignored. However, these impairments are
`basically impulsive and
`their effect should be greatly reduced
`by this technique.
`11. BASIC PRINCIPLES OF OPERATION
`following analyses can be easily extended to include pulse
`A, Orthogonal Frequency Division Multiplexing (OFDM)
`shaping other than the assumed rectangular shape.
`Theoretically, M-ary
`digital modulation scheme:: using
`When an efficient use of bandwidth is not required, the most
`'bit rate
`OFDM can achieve a bandwidth efficiency, defined as
`effective parallel system uses conventional frequency division
`per unit bandwidth, of logz M bits/s/Hz. This is easily shown
`multiplexing where the spectra of the different subchannels do
`as follows. Given that the symbol rate of the serial data stream
`not overlap. In such a system, there
`is sufficient guard space
`is l/At, the bit rate for a corresponding M-ary syljtem
`is
`between adjacent subchannels to isolate them at the receiver
`log2 M/At. Each subchannel, however, transmits at
`z! much
`using conventional filters. A much more efficient use
`of band-
`lower rate, log2 M/(NAt>. The total bandwidth of the 'OFDM
`if the spectra of
`width can be obtained with a parallel system
`system is
`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-
`
`where f n = fo + n A f and A f = 1/NAt. This expression ;tnd the
`
`where fn is the nth subcarrier and 6 is the one-sided bandwidth
`of the subchannel (where the bandwidth
`is considerec: as
`the
`
`2
`
`

`

`CIMINI: ANALYSIS AND SIMULATION OF DIGITAL MOBILE CHANNEL
`
`667
`
`PILOT
`
`/STREAM\
`/
`
`I
`
`'
`
`PHASE
`
`R (m)
`
`6h1)
`GAIN
`FFT-,
`*CORRECTION CORRECTION
`-
`-
`Fig. 2. OFDM system implemented with an FFT.
`
`hL PARALLEL
`. t CONVERTER
`
`TO SERIAL
`
`COCHANNEL
`INTERFERER
`
`7-
`
`a ( n ) ,
`
`DECODER
`
`distance to the first null). The subcarriers are uniformly spaced
`so that f N - - fo = (N - 1)Af. Since A f = l/NAt due to the
`f N - 1 - fo = (1 - (l/N))(l/&).
`orthogonality constraint,
`Therefore, the bandwidth efficiency P becomes
`
`(3)
`
`spectra (bandwidth Af) with 6 = 4 Af = 1/2NAt, = log2 M
`For orthogonal frequency spacing and strictly band-limited
`the spectra overflow this min-
`bits/s/Hz. In reality, however,
`CY so that 6 = ( I + a ) ( l /
`imum bandwidth by some factor
`2NA[) and the efficienc,y (3) becomes
`< log2 M.
`
`Further reductions in complexity are possible by using the
`to implement the
`fast Fourier transform (FFT) algorithm
`DFT when N is large.
`
`C. Pilot-Based Correction
`is distortionless, the orthogo-
`If the transmission channel
`nality of the subcarriers allows the transmitted
`signals to be
`received without error at the receiver. Consider the system in
`the block of data represented by the sequence of
`Fig. 2 with
`N complex numbers {d(O), d(l), .-, d(N - 1)). These complex
`numbers are generated byethe data encoder from a binary data
`sequence. A DFT is performed on this block
`of data, giving
`the transmitted symbols2
`N - 1
`
`sys-
`
`p=- log'
`1 +-
`CY
`Notice that this is a sampled version of ( 5 ) where the complex
`N
`notation has been retained. All future analyses will be done in
`the complex domain. Under the assumption of a distortionless
`To obtain the highest bandwidth efficiency in an OFDM
`channel, the received data sequence (the output of the inverse
`tem,N must be large and CY must be small.
`DFT) will be exactly the transmitted sequence due to the
`B. Implementation of OFDM Using the Discrete Fourier
`orthogonality of the subcarrier tones (exponentials).
`Transform
`If the transmission channel distorts the
`signal, this orthog-
`onality is impaired. In a flat Rayleigh fading environment (i.e.,
`The principal objections to the use of parallel systems are
`the environment is not frequency selective), the effects of the
`the complexity of the equipment required to implement the
`Rayleigh channel can be represented as a multiplicative noise
`system, and the possibility of severe mutual interference among
`process on the transmitted
`signal. This multiplicative process
`subchannels when the transmission medium distorts the
`sig-
`is characterized by a complex fading envelope with samples
`nal. The equipment complexity (filters, modulators, etc.) can
`Z ( m ) = A ( m ) e l e ( m ) where the A ( m ) are samples from a Ray-
`be greatly reduced by eliminating any pulse shaping, and by
`B(m) are samples from a uniform
`leigh distribution and the
`using the discrete Fourier transform (DFT)
`t o implement the
`modulation processes, as shown in [71, 181 . There it is shown
`distribution [ 11. These samples multiply the sequence of
`to give
`that a multitone data signal is effectively
`the Fourier
`trans-
`form of the original data stream, and that a bank of coherent
`R(m) = Z(m)D(m).
`demodulators is effectively an inverse Fourier transform. This
`can be seen by writing (1) as
`
`The output data sequence i ( k ) is the inverse DFT of (7),
`
`(6)
`
`(7)
`
`n =0
`Letting t = mAt, the resulting sampled sequence D ( m ) is seen
`as the real part of the DFT of the sequence d(n).l 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 1/T. This spectral shape has large sidelobes, and gives rise t o
`significant interchannel interference in
`the presence of multi-
`path. This point will be discussed in more detail in Section 111.
`' 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].
`
`d(n)z(k - n )
`
`N - 1
`=
`n =o
`* Throughout this paper, all indexes will be assumed to belong to the set (0,
`1, 2, ..., N - 1 ) .
`
`3
`
`

`

`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
`If Z ( m ) = 1 for all m (the
`of the complex fading envelope.
`distortionless channtl), z(k - n ) is simply the Kronecker delta
`presence of fading,
`function 6 k n and d ( k ) = d(k). In the
`z ( k - n ) # 6kn and
`
`is used [i.e., Z p ( , m ) =
`If unlimited gain and phase correction
`Z d ( m ) ] , Z(k - n ) = 6 k n , there is no intersymbol interference,
`and ( 12) becomes
`
`N - 1
`
`n=O
`n # k
`
`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-
`rupted by intersymbol interference even if there is no cochan-
`ne1 interferer.
`Pilot-based correction provides an amplitude and phase
`be used to counteract the unwanted ef-
`reference which can
`fects of multipath propagation. Similar considerations have
`been analyzed for single-sideband mobile-radio systems [ 141,
`[ 151. 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-
`ference. If phase and gain correction is employed in the absence
`pf cochannel interference,
`(9), that
`it is easily shown, in
`d ( k ) = d(k).
`the dominant transmission
`In a cellular mobile system,
`impairment often comes from other users using the same
`carrier frequency. It
`is assumed here that the desired signal
`and a
`si-
`single undesired cochannel interferer are received
`multaneously, 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.
`is present in the received
`When a cochannel interferer
`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 a cochannel
`of unlimited gain correction in the presence
`D(m) be the desired
`interferer can be seen as follows. Let
`transmitted signal sequence and let I ( m ) be the correspondin
`cochannel interferer sequence. With Z d ( m ) = Ad (m)ejed(my
`and Z i ( m ) = A j ( m ) e l e l ( m ) the desired and interferer com-
`plex fading sequences, respectively, the sequence present at
`the receiver can be represented as
`R(m) = zd(nz>D(m> + f i z i ( W ( m >
`(SIR-l).
`where y is the interference-to-signal power ratio
`R ( m ) is corrected by a complex correction sequence Zc(rn) =
`Z,(m), the complex pilot fading envelope, giving
`
`(10)
`
`sig-
`
`Taking the inverse DFT of (1 l), the received data sequence
`becomes
`
`N - l
`=
`
`n=o
`
`d(n)z(k - n ) + fi X - -
`
`N--l 1 z j ( m )
`m=o N Z p ( m )
`
`i
`
`the cochannel inte~ferer.
`is caused by
`The only distortion
`However,. since Zi(rn) and Z d ( m ) are statistically independent,
`the interferer is not,
`the desired signal may be in a fade when
`and unlimited gain correction may boost the interferer alrerage
`energy above that of the desired signal.
`One alternative t o unlimited gain and phase correctio!l is t o
`have a limit on the gain correction, so as not to follow t:he de-
`sired signal into deep fades [ l ] . This is done at the expense of
`increased intersymbol interference, due to imperfect correc-
`tion of the desired signal. In
`this situation, the correction sig-
`nal is of the form
`
`where E is the gain limit and is defined relative to the average
`value of the local field strength. Therefore, in (1 2), z(k -- n ) #
`6,,,
`resulting in intersymbol interference. Consequently, there
`is a tradeoff between increasing
`the intersymbol interference
`and boosting the cochannel interference energy.
`is to develop an optimum gain coset-
`Another alternative
`tion factor which takes both distortion effects into account.
`An optimum gain correction factor F ( m ) has been deri’rfd 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
`Zc(m = z, (m )F(m)
`
`.(3)>’].
`
`=Z,(m) [1+
`
`This correction procedure would be more difficult to imple-
`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-
`ceived signal envelopes at different frequencies, 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-
`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-
`pends on the correlation between
`samples of
`the complex
`fading envelope. It can be seen that as N increases, more inde-
`pendent fades are averaged. This enables burst errors
`to be
`randomized and thereby aids in bit error correctiorl. This
`property will be more evident in the simulation results, which
`indicate that the curves for the bit error rate fall betwcen the
`linear Rayleigh channel curves and the exponential Glmssian
`channel curves. For large N and high vehicle speeds, the bit
`error curve approaches that for a Gaussian channel.
`D. Distortion Analyses
`to the overall distortion of
`Several mechanisms contribute
`the desired signal. In this section, emphasis is on the contribu-
`in increased inter!;ymbol
`to gain limiting, evident
`tions due
`interference, and due to cochannel interference. The distor-
`
`4
`
`

`

`CIMINI: ANALYSIS AND SIMULATION OF DIGITAL MOBILE CHANNEL
`
`669
`
`tion resulting from decorrelation of the pilot due to frequency-
`
`selective fading or due to interference on the pilot is considered
`in Section 11-F.
`First, consider the case of gain-limited correction, where
`the amplitude correction
`is bounded to follow fades only as
`deep as E. Assume that the random processes which produce
`the random sequences are ergodic, thereby permitting the
`equivalence of time and ensemble averages. The pilot complex
`in time is Z,(m) =
`fading envelope at a particular instant
`z d ( m ) and the correction sequence is
`
`c !s
`8 a
`10
`
`Z,(m> = max (Ad(m), e)eied(m).
`
`(16)
`
`The corrected output samples become
`
`The signal-to-distortion ratio (SDR) can be defined as in [ 141,
`
`where x denotes a time average of
`X . Assuming I D(m) Iz =
`]l(m)' = 1 , the denominator in ( 1 8) reduces to
`I b ( m ) - D(m> l2
`
`-
`
`dB
`=I5 dB
`=io dB
`
`I
`-30
`
`I
`-20
`
`I
`-10
`€(dB)
`a flat Rayleigh fading environment
`Fig. 3. Signal-to-distortion ratio for
`when gain-limited correction is used.
`
`I
`0
`
`I
`10
`
`0
`
`I
`10
`
`I
`20
`SIR (dB)
`Fig. 4. Signal-to-distortion ratio for a flat Rayleigh fading environment
`when the optimum gain correction factor is used.
`
`I
`30
`
`40
`
`S
`
`where E,(x) = -[@ + In (x) +
`(-l)"x"/nn!)J and \k
`is Euler's constant (=0.57721566 .-). The SDRin (20) is plot-
`ted in Fig. 3 for several values of SIR. Obviously,
`if SIR =
`(no cochannel interference), the results reduce to that in
`[ 141
`and no gain limit should be used. However, for SIR < 00 the
`curves dearly indicate the tradeoff between intersymbol
`in-
`terference, caused by gain limiting, and boosting of the co-
`channel interference average energy, caused by unlimited gain
`correction. If unlimited gain correction is used, SDR = -00, in-
`dicating that the interferer completely distorts the desired sig-
`
`-
`
`I]-'
`[ & In (SIR) - 1
`
`(21)
`
`SDR = [( &)
`
`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.
`
`by expected values
`Assuming time averages can be replaced
`is fairly flat.
`is a definite maximum which
`nal. Notice, there
`and assumingdd(m) andAi(m) are statistically independent and
`Although SDR as defined here
`is an analog transmission qual-
`Rayleigh distributed, ( 1 8) becomes, after some manipulations,
`ity measure, it does indicate the degree to which intersymbol
`interference, caused by imperfect gain correction, and cochan-
`ne1 interference are problems. These factors are critically
`im-
`digital transmission. The SDR also clearly shows
`portant in
`the tradeoffs which must be made when choosing the appro-
`priate gain limit. This, in turn, 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
`
`+
`
`SIR
`T
`
`1
`
`
`
`5
`
`

`

`670
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-33, NO. 7 , JULr‘ 1985
`
`E. Simulation Results
`assuming flat Rayleigh
`Initial simulations were performed
`fading. In these simulations, it
`was also assumed
`that the
`pilots could be recovered perfectly; that
`is, there is no inter-
`ference or distortion on the pilots.
`A symbol rate and chan-
`nel bandwidth of 7.5 kHz3 were used and
`the BER was deter-
`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 vaned in this initial investiga-
`tion, the most important being N , the number of subchannels,
`and u, 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.
`850 MHz, independent
`In particular, at a carrier frequency of
`60
`fades are about 7 in apart,
`giving a fade every 6.6 ms at
`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-
`the total signaling interval
`if N is large,
`is also
`hicle speed,
`large and more fades are again used in the averaging process.
`The results shown in
`Fig. 5, where quadrature phase shift
`keying (QPSK) has been employed, indicate the improvement
`possible if OFDM is used with gain correction under the
`as-
`sumptions of ideal pilot recovery and a flat Rayleigh fading
`environment. Results for both optimum gain correction, as in
`(1 5), and gain-limited correction, as in (14), are given. These
`results clearly indicate
`the effects of vehicle speed and the
`carrier frequency of 850 MHz
`number of subchannels. At a
`60 mph, with gain-limited correc-
`and with a vehicle speed of
`tion, improvements in SIR of
`6-7 dB4 have been obtained
`using 5 12 subchannels ( T = 6 8 ms). This is in comparison to a
`(N = 1) with
`flat Rayleigh channel using coherent detection
`QPSK. A reduction in speed t o 30 mph results
`in a loss
`in
`performance of less than 1 dB. A reduction of N to 128 sub-
`channels-(T = 17 ms) results in an additional 2 dB loss, be-
`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-
`tivity of the BER on the gain limit, shown in Fig. 6, indicates
`that adaptive gain limiting, or some “intelligent” guess at the
`gain limit based on the distortion curves, may be required.
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`1
`
`
`
`- N= 512 v.60 MPH, OPTIMUM GAIN
`--- N= 512, v 560 MPH, GAIN-LIM~TED CORRECTION
`CORRECTION
`***.. N.512,~ =30 MPH, GAIN-LIMITED CORRECTIIW
`N.128, v = ~ O MPH, GAIN-LIMITED CORRECTION
`
`.-e-
`
`10 0
`
`lo-’
`
`40-2
`
`E
`W m
`
`10-3
`
`I 0-4
`
`10-5
`0 2 4 6 8 10 12 44 16 18 2 0 22 24
`SIR (dB)
`Fig. 5. Simulation results assuming perfect pilot recovery in a flat kayleigh
`fading environment (QPSK, = 7.5 Hz).
`
`26
`
`I
`
`-
`
`S I R = I b d B
`
`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
`on
`11-E were obtained under the assumption that the fading
`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-
`quency is high for small frequency separation, and falls essen-
`tially to zero as the separation substantially exceeds the correla-
`tion bandwidth [ 1 ] . The gain correction process, as will be seen,
`1
`requires a high degree of correlation between the phase and
`
`1 0 ’ ~
`SIR
`
`I d4
`
`/
`/
`
`of 4 improvement in spectral efficiency
`Such a channel allows a factor
`over the current 30 kHz cellular mobile telephone service channel.
`All comparisons in this paper will be made at a BER level of
`
`Fig. 6. Sensitivity of BER to variations in gain limit (N = 512, u = 60
`mph,f, = 7.5 kHz).
`
`~
`6
`I
`-24 -22 -20-18 -16 -14-12 -10 - 0 -6 - 4 - 2
`
`6
`
`

`

`
`
`
`
`
`
` CIMINI: ANALYSIS SIMULATION AND
`
`
`
`
`
`
`
`
`
`
`
`
`
`OF DIGITAL MOBILE CHANNEL
`
`loo r -NO
`
`67 1
`
`DELAY SPREAD
`---DELAY SPREAD (A'5OpdI 500 HZ SEPARATIOI
`,o-~ -.-. DELAY SPREAD
`( A e 5 0 p ) , j kHz SEPARATION
`
`io-2
`
`a
`m w
`
`l o m 3
`
` IO-^
`
`\
`
`GAUSSIAN
`CHANNEL
`
`of the phase and
`
`amplitude variations of the pilot and that
`amplitude variations imposed on the data.
`A simple'way to estimate the effects of a delay spread en-
`vironment is to compute the equivalent decorrelation