IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 39, NO. 5, MAY 1991
`
`783
`
`OFDM for Data Communication Over
`I:
`Mobile Radio FM Channels-Part
`Analysis and Experimental Results
`
`Eduardo F. Casas, Member, IEEE,
`
`and Cyril L u n g , Member, IEEE
`
`Abstract-This paper describes the performance of OFDM/FM
`modulation for digital communication over Rayleigh-fading mo-
`bile radio channels. The use of orthogonal frequency division
`multiplexing (OFDM) over mobile radio channels was proposed
`by Cimini [l]. OFDM transmits blocks of bits in parallel and
`reduces the bit error rate (BER) by averaging the effects of fading
`over the bits in the block. OFDM/FM is a modulation technique
`in which the OFDM baseband signal is used to modulate an
`FM transmitter. OFDM/FM can be implemented simply and
`inexpensively by retrofitting existing FM communication systems.
`Expressions are derived for the BER and word error rate
`(WER) within a block when each subchannel is QAM-modulated.
`Several numerical methods are developed to evaluate the overall
`BER and WER An experimental OFDM/FM system was imple-
`mented and tested using unmodified VHF FM radio equipment
`and a fading channel simulator. The BER and WER results
`obtained from the hardware measurements agree closely with
`the numerical results.
`
`I. INTRODUCTION
`HE demand for data communication over mobile radio
`
`T channels. has increased steadily over the last few years
`
`and will likely continue to grow [2], [3]. A common ap-
`plication is found in mobile data terminals (MDT’s) used
`for emergency, law and order, public utility, and a host of
`commercial services such as courier, dispatch, and inven-
`tory control. MDT’s allow remote mobile users direct access
`to computerized databases, resulting in greater productivity.
`Another benefit is the more efficient use of the allocated
`(and increasingly scarce) radio spectrum. Features such as the
`transmission of graphical information or the use of encryption
`for secure communication can also be readily implemented.
`The design of a VHF/UHF mobile radio data communica-
`tion system presents a challenging problem [4]. In most areas
`multipath propagation causes a moving receiver to experience
`severe and rapid fluctuations of received signal strength. In a
`commonly used and proven model [4], [5], it is assumed that
`there is no line-of-sight path from the transmitter to the re-
`ceiver; rather, the received signal is made up of a large number
`
`of component waves scattered by buildings and other objects
`near the mobile. Under certain conditions, it can be shown
`that over short distances the amplitude of the received signal
`can be well approximated by a Rayleigh distribution. During
`a deep fade the received signal strength may be reduced to
`an unacceptably low level. If a conventional serial modulation
`scheme is used, the bits “hit” by such a fade will be lost.
`Recently, Cimini [l] proposed the use of an orthogonal
`frequency division multiplexing (OFDM) scheme in which the
`bits in a block (packet) are transmitted in parallel, each at a
`low baud rate. The intent of the scheme is to spread out the
`effect of the fade over many bits. Rather than have a few
`adjacent bits completely destroyed by a fade, the hope is that
`all the bits will only be slightly affected. Another technique
`[6] uses a chirp filter to spread individual signaling pulses
`over time.
`The OFDM signal is generated using digital signal pro-
`cessing (DSP) techniques at baseband and this signal must
`then modulate an RF carrier. In Cimini’s [l] proposal the
`signal is translated directly to the RF frequency, resulting
`in a system that we call OFDM/SSB. Frequency modulation
`(FM) can also be used, resulting in our proposed OFDM/FM
`system. An OFDM/FM system has the advantage that it
`can use existing unmodified FM radio equipment and can
`therefore be implemented more quickly and at lower cost than
`an OFDM/SSB system which requires precise and relatively
`complex coherent reception.
`The following section briefly describes the Rayleigh fading
`channel and OFDM/FM. A simple model for the OFDM
`channel is introduced and used to derive the bit and word
`error rates for OFDM/FM in Section 111. Section IV describes
`several numerical methods that can be used to evaluate the
`performance of OFDM/FM while Section V describes experi-
`mental measurements on an OFDM/FM system and compares
`the experimental and numerical results.
`
`11. PRELIMINARIES
`
`Paper approved by the Editor for Mobile Communications of the IEEE
`Communications Society. Manuscript received October 5, 1989; revised
`April 4, 1990. This work was supported in part by a Natural Sciences and
`Engineering Research Council (NSERC) Post-Graduate Scholarship, Mobile
`Data International, Inc., Communications Fellowship, and NSERC under
`Grant A-1731.
`The authors are with the Department of Electrical Engineering, University
`of British Columbia, Vancouver, B.C. V6T 1W5, Canada.
`IEEE Log Number 9144542.
`
`A. VHFIUHF Mobile Radio Channel
`The channel model used in this paper is a nonfrequency-
`selective (flat) Rayleigh fading model in which additive white
`Gaussian noise is the major noise source. Field measure-
`ments [7]-[12] have shown that the flat fading assumption is
`reasonable for narrow-band (under 20 kHz bandwidth) signals.
`
`00904778/91/0500-0783$01.00 0 1991 IEEE
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`Fig. 1. An implementation of an OFDM system.
`
`Gaussian
`Noise
`
`W
`
`w
`
`Fig. 2. The equivalent baseband channel model.
`
`complex data values using an FFT, and decodes the complex
`data values back into bits.
`
`B. Orthogonal Frequency Division Multiplexing
`Description: OFDM uses frequency division multiplexing
`with subcarrier frequencies spaced at the symbol (baud) rate.
`111. OFDM BIT ERROR RATE ANALYSIS
`That is, if the block duration is T , the subcarrier frequencies
`In this section, a simple and general model for the mobile
`are at 1/T, 2/T, 3/T, . . .. This frequency spacing makes the
`radio channel, the equivalent baseband channel (EBC) model,
`subcarriers orthogonal over one symbol interval [13]-[ 171.
`is described and then used to obtain an expression for the
`Modulation is done by using several bits (typically two to
`bit error rate (BER) of OFDM. The assumption that errors
`five) to set the amplitude and phase of each subcarrier. occur independently is used to determine the word error rate
`can be
`(WER). The final subsection describes how the EBC model
`An OFDM
`by
`can be applied to the OFDM/FM channel.
`using an inverse discrete Fourier transform (DFT) to convert
`the complex phase/amplitude data for each subcarrier into
`a sampled OFDM signal. Similarly, demodulation can be
`performed with a DFT which extracts the phase and amplitude
`of each subcarrier from the sampled OFDM signal.
`Because OFDM can be used to efficiently multiplex many
`bits into one block (symbol), the baud (symbol) rate can be
`greatly reduced compared to conventional serial modulation
`methods. The symbol rate is typically reduced by hundreds or
`thousands of times.
`Previously, OFDM modems have been used for data trans-
`mission over telephone channels [ 171 -[21]. OFDM-like multi-
`carrier modems have also been used on HF (3 to 30 MHz)
`radio channels [22]-[26].
`The DFT extracts the phase and amplitude information for
`N/2 (complex) subchannels from the N (real) samples in
`the block. Some subchannels may not be usable because the
`signal-to-noise ratio (SNR) at that frequency may be too low.
`If the fraction of subchannels that are usable is p and M
`bits can be transmitted on each subchannel, then the number
`of bits per block is Nb = pMN/2. The block duration is
`T = N / f s where fs is the sampling rate. The bit rate is
`therefore R = Nb/T = fspM/2.
`Implementation: Fig. 1 shows a block diagram of an OFDM
`implementation. The modulator collects a block of bits from
`the data source, encodes them into complex (QAM) data
`values, and converts the data to signal samples using an
`inverse FFT. The digital-to-analog (D/A) converter produces
`the analog baseband OFDM signal.
`This baseband signal modulates an RF transmitter. The mod-
`ulated signal is transmitted over the fading channel. A receiver
`recovers the baseband signal from the received RF signal
`which may have been corrupted by fading and additive noise.
`The demodulator collects a block of samples from the
`analog-to-digital (A/D) converter, converts the samples to
`
`A. The Equivalent Baseband Channel Model
`The model used to predict the performance of OFDM over
`mobile radio channels must include all significant effects and
`yet be kept simple enough for analysis and efficient numerical
`work. Towards this end, the EBC model converts the effects of
`fading at IF (or RF) into equivalent effects at baseband. Two
`effects are considered: time-varying channel gain (fading), and
`additive noise.
`Fig. 2 is a diagram of the EBC model. The received
`samples, y = {yo, y1, . . . , Y N - ~ } , are the sum of the received
`data and noise samples. The received data samples are the
`transmitted data samples 5 scaled by the channel gain vector
`s. The received noise samples are zero-mean Gaussian random
`variables scaled by the channel noise gain vector n.
`Both s and n are functions of T , the IF signal-to-noise
`ratio (SNR) vector. We assume that the IF noise level is
`fixed so that T is proportional to the IF signal level. The
`functions s = f S ( r ) and n = fn(r), define what we call
`the SN curves of the receiver. The SN curves can be obtained
`either from analysis of ideal receiver performance [4] or from
`measurements (Section V).
`The model assumes that the receiver SN curves are mem-
`oryless. This allows the average signal and noise powers to
`be obtained by averaging the instantaneous signal and noise
`powers. Such a quasi-static approximation is valid when the
`Doppler rate is less than the baseband bandwidth [27], [28],
`as is the case with land mobile radio applications.
`
`B. BER Analysis
`An expression for the BER of a given OFDM block trans-
`mitted over the equivalent baseband channel is derived in this
`section. The notation a indicates a vector {ao, al, . , alv-1)
`and (a) denotes the time average of the variable a over N
`
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`CASAS AND LEUNG OFDM FOR DATA COMMUNICATION-PART
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`samples, i.e., (U) = l/N(ao + a1 + . . . + alv-1). The word
`sample is used for quantities in the time domain, while the
`term value is used for quantities in the frequency domain.
`Mean and Variance of the Received Value: In Appendix A,
`the ensemble average of the m-th received data value Y,
`over the set of all possible transmitted data vectors with the
`m-th data value fixed at X , = D(D = f l f j ) and over all
`possible noise vectors w is found conditioned on a given fixed
`signal level vector T (and the corresponding s and n) as
`E[Y,(X, = D , X - , = D*,T] M D(s).
`
`(1)
`
`785
`
`word error rate (WER). The assumption of random bit errors
`would simplify the prediction of the error rate of words
`contained within an OFDM block. Experimental results (see
`Section V) showed that the independent error assumption is a
`good approximation for the system that was studied.
`In order to predict the WER it will be assumed that the
`bit errors are independent. Such an assumption would not
`be valid for a conventional serial modulation scheme on a
`fading channel. With this assumption, the block WER can be
`expressed easily in terms of the block BER, namely,
`
`WERblock = 1 - (1 - BERblock)Nw
`The conditional variance (given the same conditions as for where Nw is the number of bits per word.
`the mean) of a received data value Y,, is found to be
`
`(5)
`
`Bit Error Rate Within a Block: Since the interference
`(between subchannels) on each subchannel is caused by a large
`number of independent subchannels, the central limit theorem
`indicates that the distribution of this interference should be
`approximately Gaussian. This is confirmed by measurements
`of the interference distribution in the experimental OFDM/FM
`system described in Section V. Since the effect of the channel
`noise is also Gaussian (because of the linearity of the DFT)
`and independent of the interchannel interference (because T
`is fixed), the sum of the noise and interference will also be
`Gaussian and their powers will add.
`Using signal-space arguments [29] it is then possible to ob-
`tain the BER within a block for the QAM encoding described
`in Section IV-C as
`
`where a = (s), P = (s2), and y = ( n 2 ) .
`Evaluating the Overall BER: The overall BER can be
`obtained by using the joint distribution of a, P, and y, i.e.,
`
`(4)
`
`To obtain estimates of the overall BER, the joint distribution
`of a, p, and y is required. Unfortunately, no closed-form
`expression is available for this joint distribution, p ( a , P,y). In
`Section IV, a Monte-Carlo numerical integration procedure is
`described that can be used to evaluate this expression.
`
`C. WER Analysis
`In many data communication systems, any error within
`a related group of bits (a word) invalidates all of the bits.
`In such systems the performance measure of interest is the
`
`D. Modeling the OFDMIFM Channel
`Baseband Noise Distribution: Although the probability dis-
`tribution of the FM discriminator output noise depends on the
`SNR [30], the noise values after the DFT demodulator can
`be assumed to be Gaussian because the DFT sum makes any
`noise distribution approximately Gaussian.
`Baseband Noise Spectrum: The spectrum of the discrimina-
`tor noise output also depends on the IF SNR. The distribution
`of the noise power among the subchannels thus depends on
`the IF SNR. The distribution of the noise among the different
`subchannels will vary from block to block because fading
`causes the IF SNR to vary. To simplify the analysis, however,
`it was assumed that the blocks were sufficiently long so that the
`distribution of noise power among the subchannels was almost
`the same for all blocks. It was also assumed that differences in
`subchannel SNR’s due to the uneven spectral distribution of
`the noise were corrected by changing the allocation of power
`among the subchannels in the transmitted baseband signal. The
`noise spectrum was therefore assumed to be independent of
`the IF SNR. The validity of this assumption was later verified
`experimentally.
`Experimental measurements of the noise powers in the
`different subchannels in the presence of fading showed that
`subchannels at lower frequencies had more noise. This caused
`subchannels at lower frequencies to have higher error rates.
`Measurements of the error rates in the different subchannels
`showed that the error rates could be made approximately equal
`by using a -10 dB per decade preemphasis at the transmit-
`ter in addition to the built-in +20 dB per decade standard
`pre-emphasis.
`Random FM Noise: The spectrum of the “random FM’ noise
`at the discriminator output is independent of the SNR and
`decreases as (l/f) for frequencies above the Doppler rate
`[27]. The effect of random FM at a given Doppler rate can be
`included in the model by modifying the ‘N’ portion of the SN
`curves. However, this was not necessary since the level of the
`random FM noise was not significant at any of the Doppler
`rates measured as shown by the measurements described in
`Section V-F.
`Clipping Noise: Clipping in the FM transmitter was modeled
`as an additional source of additive white Gaussian noise.
`Although the clipping is not independent of the signal level,
`it should normally form a relatively small portion of the total
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`Fig. 4. The numerical integration method.
`
`When the block is very long, each block will have the same
`statistics and therefore each block will have the same BER.
`The overall BER will be the block BER for the average block
`statistics. That is, if
`"
`
`P = 1 s2(?-)p(r) d7-1
`
`-
`
`00
`
`S ( T ) P ( T ) dr1
`
`-20
`
`-10
`
`IF SNR (de)
`Fig. 3. Theoretical and measured SN curves.
`
`10
`
`al
`
`T i =
`
`30
`
`then
`
`noise power. For example, in the experimental measurements
`the modulating signal level was set so that clipping distortion
`had no measurable effect on the BER.
`Squelch: Squelch can be incorporated into the SN curves
`by setting the values of s and n to zero when the IF SNR
`level falls below the squelch threshold. This assumes an ideal
`squelch circuit that has no hysteresis or delay.
`FM Receiver SN Curves: Fig. 3 shows typical measured and
`theoretical FM receiver SN curves. This example shows the
`nonlinear SN curves of an FM discriminator. The measured
`curves show the effect of baseband SNR limiting due to
`clipping. The maximum baseband SNR ("limiting baseband
`S N R ) is about 18 dB. A similar effect would be produced
`by random FM.
`
`Iv. EVALUATION OF ERROR RATES
`This section describes three methods to evaluate the BER
`and WER performance of OFDM. These are 1) a computation
`for very short or very long block lengths, 2) a Monte-Carlo
`integration, and 3) a baseband signal processing simulation.
`The results obtained using these methods will be compared to
`experimental results in Section V.
`
`A. BER for Very Short and Very Long Blocks
`When the block duration is very short relative to the average
`fade duration, the received signal level will be constant during
`the block. Thus, (s) = s, (s2) = s2, and (n2) = n2. The
`bit error rate for each block, BERblock, as a function of
`the IF SNR can be averaged over the Rayleigh signal level
`distribution to obtain the average overall BER. That is,
`
`BEkhort block =
`
`BERblock (s(r), s2(r)1 n2(r))p(r) dr.
`
`(6)
`Note that since the signal level is constant over the block
`( s ) ~ = (s2) and (3) simplifies to
`
`I"
`
`and 7 =
`
`03
`
`n2(r)p(r) dr,
`
`(8)
`
`(9)
`
`B. Monte-Carlo Integration
`The second method uses a Monte-Carlo numerical
`integration technique to evaluate the BER given by (4). The
`method involves generating random fading waveforms and
`then using their a, p, and y statistics to compute the expected
`overall BER.
`Fig. 4 shows the steps in this procedure. A Monte-Carlo
`procedure is used in which signal level vectors r are chosen at
`random from a waveform which is Rayleigh distributed with
`the appropriate Doppler rate. From each T the values of a, p,
`and 7 and the resulting BERblock are calculated. The arith-
`metic mean of these BERblock values gives the overall BER.
`This method can be used to evaluate the BER for any
`channel that can be accurately described by the EBC model.
`It is faster than the more detailed simulation described in
`the following section because it does not involve generating
`random data or noise or computing DIT'S.
`
`C. Software Simulation of the Equivalent Baseband Channel
`The OFDM system can be studied in more detail by
`generating a sampled baseband OFDM waveform and pass-
`ing it through an equivalent baseband channel. This method
`involves performing most of the baseband signal processing
`for an OFDM system. It allows testing of signal processing
`procedures that cannot be included in the EBC model or whose
`effect is too complex to analyze. However, this approach
`is considerably slower' than the Monte-Carlo
`integration
`method.
`Fig. 5 shows the steps involved in the baseband simulation.
`A block of bits from a pseudo-random bit sequence (PRBS)
`generator is QAM-encoded into a block of complex values.
`The inverse FIT generates the baseband OFDM signal by
`converting each block of N / 2 complex values into N samples.
`The Rayleigh-fading generator produces the signal envelope.
`The SN lookup table and the channel simulator implement the
`
`A typical simulation (about 3 million samples for each of four SNR's and
`three block sizes) required about 8.5 h CPU time on a Sun 3/50 compared to
`about 1.5 h for the numerical integration procedure.
`
`

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`CASAS AND LEUNG: OFDM FOR DATA COMMUNICATION-PART
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`Fig. 7. Fading channel simulator.
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`Fig. 5. Simulation using the equivalent baseband channel.
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`FM
`TlXtlSlWiUW
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`Fading Channel
`Simuhtor
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`FM
`F@ceiUw
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`low-pass
`filer
`Fig. 6. Block diagram of experimental setup.
`
`equivalent baseband channel (shown in Fig. 2) and combine
`the baseband signal and Gaussian noise. The FIT demodulates
`the OFDM signal and the QAM decoder recovers the binary
`data. The final step in the simulation is to compare the
`transmitted and received bit sequences and to compute the
`BER and WER.
`The QAM data encoding is done by using two bits per sub-
`channel: one bit for the imaginary (quadrature) component and
`one bit for the real (in-phase) component. A 0 b is converted
`to a value of -1, and a 1 b to a + l . Unused subchannels are
`set to zero. The decoding is done by comparing the received
`values to a threshold of zero.
`A more detailed simulation that includes the IF stages of
`the receiver could be used to study other effects but would
`require significantly more computation.
`
`V. EXPERIMENT
`This section describes a laboratory experiment used to
`demonstrate the feasibility of OFDM/FM using unmodified
`commercial VHF FM radio equipment. The performance of
`this experimental system is compared to results obtained using
`the methods of Section IV.
`
`A. Experimental Hardware
`Fig. 6 shows a block diagram of the experimental setup. The
`various components used are described below. The transmitter
`and receiver were placed in cast aluminum boxes and their
`power supply leads were passed through EM1 filters to provide
`RF shielding. An 11 dB 50 ohm attenuator was mounted inside
`the transmitter shielding box to reduce the RF output level
`to 12.5 dBm.
`Transmitter: The transmitter was an Icom model IC-2AT
`narrow-band FM transceiver designed for operation in the
`144 to 148 MHz amateur band. Its specifications are similar
`to those of commercial land mobile radio equipment [31].
`The audio processing circuitry contains a +20 dB per decade
`preemphasis network, a limiter (peak clipping) circuit and
`
`a low-pass filter. The frequency deviation was measured to
`be 5 kHz.
`Channel Simulator: Fig. 7 shows the channel simulator. The
`simulator consists of a Rayleigh-fading simulator [32], an RF
`attenuator, a noise source, and a combiner/splitter.
`The signal and noise levels were measured at RF. To ensure
`that the IF SNR and the RF SNR were equal, the receiver’s
`internal noise was masked by adding noise to the RF signal.
`The level of noise added ensured that the noise added by the
`receiver had a small (<0.5 dB) effect on the IF SNR.
`Receiver: The FM receiver was another Icom model IC-
`2AT transceiver. The receiver IF filter bandwidth specification
`is 67.5 kHz at -6 dB and f 1 5 kHz at -60 dB. The receiver
`uses a Motorola MC3357 ‘‘Low Power Narrow-Band FM I F
`IC for most of the IF and AF signal processing functions. The
`FM detector is a quadrature-type discriminator [33], [34]. The
`squelch level was set to minimum so that the receiver audio
`output was always on.
`Computer: An IBM PC/AT-compatible computer was used
`for all of the digital signal processing tasks as well as test data
`generation and BER and WER measurement. All of the signal
`processing computations were done using IEEE-standard 32 b
`floating point numbers.
`AID and D / A Board: The analog interface circuit was
`designed and built for this project. It contains a 10 b A/D
`converter, a 12 b D/A converter, a sample-and-hold amplifier,
`buffer amplifiers, and a timing circuit.
`Reconstruction and Antialiasing Filters: A Krohn-Hite
`model 3342 filter was used to reconstruct the analog waveform
`from the D/A output samples. The reconstruction filter used
`one eighth-order Butterworth low-pass section with a -3 dB
`frequency of 4 kHz and a one eighth-order Butterworth high-
`pass section with a -3 dB frequency of 100 Hz. The high-pass
`section was used to provide AC coupling to the transmitter.
`A second Krohn-Hite model 3342 filter was used to low-
`pass filter the receiver AF output signal to avoid aliasing. This
`anti-aliasing filter used two cascaded eighth-order Butterworth
`low-pass sections with -3 dB frequencies of 4 kHz.
`Audio Attenuator: An audio attenuator was used to reduce
`the D/A output (approximately 140 mV rms) to a level
`suitable for modulating the transmitter (approximately 6 mV
`rms). The attenuator circuit included a low-pass filter to reduce
`RF leakage and a switch to turn the transmitter on and off.
`
`B. Experimental Software
`The simulation program used in Section IV was modified
`to make BER and WER measurements over the experimental
`channel. Instead of using a subroutine that simulates the
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`..I.
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`Fig. 8. Signal processing for experimental measurements.
`
`channel, the OFDM signal samples are written to the D/A
`and read from the A/D. Two additional processing steps were
`added for use on the hardware channel as follows [35]:
`periodic extension to provide guard times around each
`block, and
`correction for phase and amplitude (linear) channel dis-
`tortion.
`Fig. 8 shows the signal processing steps for the experi-
`mental measurements. A block of pseudorandom bits is QAM-
`encoded and modulated into a block of OFDM samples. The
`block of samples is extended to add guard times before and
`after the block. The samples are sent to the D/A and the
`resulting analog audio signal modulates the FM transmitter.
`The recovered baseband (audio) output of the FM receiver
`is sampled and A/D converted. The received samples are
`demodulated and the complex data values corrected for the
`linear distortion effects of the channel. The received complex
`data values are then decoded into bits which are compared
`to the transmitted data to compute the BER and WER. The
`program can also compare the transmitted and received data
`values on each subchannel to measure the signal and noise
`powers. This was used to measure the SN curves.
`
`C. Measuring the Baseband SN Characteristics
`In order to predict the performance ‘of OFDM over a fading
`channel, knowledge of the channel’s SN curves is required.
`This section describes the measurement of the SN curves.
`The level of the modulating signal will affect the amount
`of clipping and therefore the SN curves. A reasonable strategy
`is to set the modulating signal level as high as possible but
`not so high that distortion due to clipping prevents the system
`from meeting its BER performance objectives. The modulating
`signal level was set to give a limiting baseband SNR of
`17.5 dB, a level for which the BER was very small’ (< lob6).
`Clipping distortion thus limits the total power of the OFDM
`modulating signal. This power must be divided among all
`the subchannels. For the transceivers used in the experiment,
`the subchannels with the highest SNR’s are located around
`the middle of the baseband frequency range. Determining
`which subchannels to use involves a compromise between
`using only the best subchannels to reduce the BER and using
`more subchannels to increase the bit rate. Brief measurements
`of BER as a function of &/No using various subchannel
`frequency ranges showed that a reasonable choice was to use
`
`*The effect of clipping is different from block to block since the data (and
`thus the modulating signal) varies.
`
`frequencies between 1 and 3 kHz and to divide the power
`equally among the subchannels. An approach that was not
`tested but is often used [17], [20], [21], [36] is to encode
`more bits on subchannels with higher SNR’s.
`SN Curves Measurement Method: The SN curves were
`measured by transmitting an OFDM signal over the channel
`and measuring the received baseband signal power and noise
`power. An OFDM test signal was used for several reasons.
`First, the IF filter does not have constant gain across
`its passband. The power at the input of the discriminator
`will thus depend on the IF (or RF) spectrum of the FM
`signal. Therefore, to make SN curve measurements that will
`apply to OFDM modulation, a signal with same IF spectrum
`as an OFDM signal is required. Second, the effect of the
`transmitter’s preemphasis filter and the receiver’s deemphasis
`filter will depend on the baseband spectrum of the modulating
`signal. Third, the effect of the clipping at the transmitter will
`depend on the probability distribution of the modulating signal.
`The signal used to measure the SN curves must have the
`same probability distribution as the OFDM signal in order
`to properly measure the amount of distortion due to clipping.
`There is no crosstalk between subchannels when there is
`no fading. In this case, the noise received on each subchannel
`is due solely to additive noise and to distortion effects such
`as clipping and it is possible to measure the “N” portion of
`the SN curves.
`The simulation program was modified to make SN curve
`measurements. The signal power (S) was computed as the
`square of the mean of the received data values. The noise
`power was computed as the variance (second central moment)
`of the received data values. The signal and noise powers
`were measured as an average over the subchannels that were
`used (1-3 kHz).
`SN Curve Results: The measured SN curves are given in
`Fig. 3 along with those of an ideal discriminator [4]. Each
`point is an average of 64 1024-sample measurements. The
`measurements are normalized to give a maximum signal (S)
`level of 0 dB.
`
`D. BER and WER Measurements
`The BER and WER performance of the experimental
`OFDM/FM system over the nonfrequency-selective Rayleigh-
`fading channel were measured and compared against results
`obtained using the numerical techniques.
`BER Results: The Doppler rate used in the experimental
`work and the simulations reported here was 20 Hz, corre-
`sponding to a vehicle speed of 25 km/h at a carrier frequency
`of 850 MHz. The nominal baseband bandwidth was 4 MIZ
`( fs = 8 kHz) and subchannels between 1 and 3 Wz were used
`( p = 0.5) with 4 QAM modulation (M = 2) giving a bit rate
`(R) of 4000 bps. The spectrum of the transmitted OFDM/FM
`RF signal was measured. It was found that the bandwidth is
`f 4 kHz at -30 dB, f 6 kHz at -40 dB, f 7 . 5 kHz at -50 dB,
`and 5 9 kHz at -60 dB.
`Blocks of N = 256, 1024, and 4096 samples were used
`corresponding to Nb = 128,512, and 2048 b/block and block
`128, and 512 ms, respectiveb. IF SNR’s
`durations
`Of 327
`of 10, 15, 20, and 25 dB were used. The IF bandwidth is
`
`

`
`CASAS AND LEUNG: OFDM FOR DATA COMMUNICATION-PART
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`Fig. 9. BER results for fd = 20 Hz and for short and long blocks. The error
`bars show the 95% confidence intervals. The error bars offset to the right are
`for the Monte-Carlo (M.C.) integration results, those to the left are for the
`simulation results, and those that are centered are for the measured results.
`
`14.9 kHz, so that the corresponding values of &/No were
`16, 21, 26, and 31 dB.
`Fig. 9 compares the BER results obtained using 1) the
`Monte-Carlo integration (Section IV-B), 2) the baseband sig-
`nal processing simulation (Section IV-C), and 3) the experi-
`mental OFDM/FM system. The Monte-Carlo integration and
`the baseband signal processing simulation used the measured
`SN curves (Section V-C) shown in Fig. 3. The SN values were
`interpolated from the measured values over the range from
`-60 to +50 dB in 0.1 dB steps.
`The measurements were organized as 12 trials of 60 blocks/
`trial with 4096 samples/block. For the simulation and the
`experiment, this represents about 1.5 million bits. For the
`Monte-Carlo integration this represents a fading waveform
`duration of about 6 min. As shown by the 95% confidence
`interval error bars [37], [38], there are large uncertainties at
`low BER's. The three different BER evaluation methods give
`results that are within about 1 dB. The BER curves for short
`and long block lengths (Section IV-A) are shown in Fig. 9.
`WER Results: Fig. 10 compares the experimental WER
`measurements to the predicted WER. The predicted WER
`was obtained by finding the arithmetic mean of the block
`WER's computed using (5). The block BER's used in (5)
`were obtained from the Monte-Carlo integration program. A
`word length (N,) of 128 b was used. The two curves agree
`to within about 1 dB. This indicates that the independent error
`assumption can be useful in predicting the WER.
`The reason why the WER curves for different block lengths
`inte