Frequency Domain Reciprocal Modulation for Channels with Dynamic Multipath

This paper describes a new modulation technique known as frequency domain reciprocal modulation (FDRM) that has a characteristic of high immunity to dynamic multipath distortion. FDRM is a multicarrier transmission technology that is related to orthogonal frequency division multiplexing (OFDM). FDRM uses frequency domain reciprocal harmonic carriers to allow automatic cancellation of all linear distortion, random noise reduction, and improved channel characterization. Holtzman also proposes a dynamic mix of FDRM harmonic carrier pairs with OFDM harmonic carriers to allow the PHY standard to adapt to changing channel conditions. Purpose For Consideration as a physical layer technology for inclusion in the proposed 802.16.4 standard Notice This document has been prepared to assist IEEE 802.16. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). 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The Chair will disclose this notification via the IEEE 802.16 web site . 2001-01-14 IEEE 802.16.4c-01/09 1 Frequency Domain Reciprocal Modulation for Channels with Dynamic Multipath Thomas H. Williams Holtzman Inc. Longmont, CO Introduction Single frequency carrier transmission systems, such as QPSK and 8-VSB, typically perform poorly in channels with severe dynamic multipath distortion for a couple of reasons. First, for single frequency carrier transmission systems to perform without intersymbol interference (ISI) the channels must be accurately equalized or “flattened”. Adaptive equalizers can usually perform the necessary equalization, but the channel’s frequency response must first be accurately characterized to determine the correct coefficients for the adaptive equalizers, and the adaptive equalizers must then be rapidly re-programmed. However, when the multipath is highly dynamic, single frequency carrier transmission systems fail because the channel can not be characterized fast enough to yield an accurate solution for the channel condition. This problem is greatly aggravated by the presence of random noise in the channel. Second, in the case of multipath with deep spectral fades, there may be no practical equalizer solution that results in low ISI. For example, if the channel fades to near zero at some frequency the equalizer must provide a huge gain at that same frequency. If there is random noise present in the channel, the noise at that frequency will also receive a huge amplification, creating ISI. Multicarrier transmission systems, such as OFDM, are block transmission systems that can solve these transmission problems. Multicarrier transmission systems transform blocks of high speed time-domain symbols into blocks of slow-speed frequency-domain harmonically-related carriers (HCs). If a guard interval (or cyclic extension) is formed on the block transmission, and if the guard interval is longer than the longest echo in the channel, all ISI between HCs can be eliminated. If there is a deep fade at some frequency, a few of the HCs may be lost, but forward error correcting codes (FEC) can be used to correct the errors caused by a small number of lost HCs. Although the ISI between HCs is eliminated, each HC must be multiplied by a single magnitude and phase correction coefficient to restore the HC’s magnitude and phase to the correct values. Typically an interleaved subset of HCs are made into static pilots that are incorporated into the transmitted block to assist in the determination of the magnitude and phase correction factors that each HC should use. If the channel’s frequency response changes relatively slowly in frequency between pilot HCs, the pilot’s values can be interpolated for the correction factors. OFDM is an excellent transmission system, but there are a few weaknesses with this system. First, if the channel is noisy, random noise will contaminate each HC as well as the pilot HC. The noise on the pilot HC will result in an incorrect correction coefficient for all of the HCs that rely on the accuracy of its value. Thus, if the pilot is at the same level as the HCs, there is a 3 dB random noise penalty on each HC because the pilot HCs is also affected by random noise. Second, use of a pilot represents lost bandwidth. Third, the guard interval also represents lost bandwidth. Fourth, relative to single frequency carrier systems, OFDM transmissions produce large voltage spikes that clip active devices. OFDM has a peak to average power ratio that is higher than equivalent single frequency carrier systems. Frequency domain reciprocal modulation (FDRM) is a new multicarrier transmission system. FDRM is an OFDMlike technique that offers an advantage in microwave frequency channels afflicted with dynamic multipath. In a first implementation, a single block transmission is used. The odd-numbered HCs are unique symbols, and the evennumbered HCs are made into frequency-domain reciprocals of their adjacent odd-numbered HCs. This new modulation technique essentially employs correlated data on adjacent HCs to cancel the effects of all linear distortion. Cancellation of all linear distortion is an intrinsic property of this new modulation technique. The effects of rapid fades are also canceled automatically by FDRM. Additionally, FDRM is useful for transmission of bursty data packets because a demodulation process is simplified by using two blocks of data. In a second two-block transmission implementation, a first block of data is immediately followed by a second block which is a reciprocal of the first block in the frequency domain. The first block may be viewed as simply a special type of OFDM, and the second block may be described as having all HCs that are reciprocals in the frequency domain of the corresponding-frequency HCs in the first block. By sending the blocks sequentially, approximately the same set of echoes are applied to both blocks and the echoes are canceled when the two blocks are processed together. FDRM offers several advantages in point to multipoint wireless services, but its strongest assets are its adaptability to rapidly changing channel conditions, a 3 dB improvement in noise performance over OFDM, and its suitability to infrequent bursty transmissions. References [1]-[4] are other publications on FDRM. 2001-01-14 IEEE 802.16.4c-01/09 2 OFDM Primer Befor e describi ng FDRM it is useful to explai n orthogon al frequen cy divisio n multiple xing (OFDM ) which is a simil ar technol ogy. If y ou are fam iliar with OFDM, you may want to read th is section because i t leads in to to a discu ssion of F DRM. Altho ugh OFDM w as invente d in the l ate 60’ s, it has bee n made a p ractical t ransmissio n method w ith the co ming of th e digital signal pro cessor (DS P) which c an perform a discret e FFT oper ation very quickly. OFDM is a block trans mission me thod that is in wide use for a variety o f services , such as digital te rrestrial television and audio broad casting in Europe, c oaxial cab le telepho ny systems , and high speed tel ephone mod ems. The O FDM signal may be tr ansmitted as a baseb and signal through a baseband channel su ch as tele phone line s. Alter nately, th e OFDM sig nal may be modulated onto a ra dio freque ncy (RF) c arrier usi ng single, double, o r vesti gial sideb and modula tion for t ransmissio n over a R F or micro wave chann el. When using doub le sideban d modul ation, the real comp onents are used to m odulate th e inphase channel an d the imag inary comp onents are used to modulat e the quad rature cha nnel. Thi s allows d ifferent i nformation to be car ried in th e upper an d lower sideb ands. A tra nsmitted d ata block is made up of many h armonic ca rriers (HC s) at diff erent freq uencies th at can be accur ately dist inguished from each other at t he receive site beca use the HC s are orth ogonal to each other . Ortho gonality i s achieved because t he individ ual HCs (w hich are c osine wave s) compris ing the co mposite si gnal are i nteger mul tiples of a fundamen tal freque ncy. Infor mation is conveyed b y assignin g differen t discrete values to th e magnitud es and pha ses of the individua l HCs. Fo r example, if E(t) is an OFDM transmiss ion with o nly four HCs, it may be represente d as: E t A t A t A t A t ( ) cos( ) cos( ) cos( ) cos( ) = ⋅ + + ⋅ + + ⋅ + + ⋅ + 1 1 2 2 3 3 4 4 2 3 4 ω φ ω φ ω φ ω φ (1) The m agnitudes of An may take on va lues such as 1.33 or 0.75 and the phase may take o n values s uch as 45, 135, -45, or -135 de grees. Th e index va riable n i s the HC n umber. The magnit ude and ph ase angle comprise t he coeff icient of a HC. In practice, hundreds o r even tho usands of individual HCs make up an OFDM transmiss ion. Figur e 1 is a t ime domain plot of a 4-HC wave form with each of th e individu al HCs plo tted, as w ell as the sum of the 4 individua l HCs. Th is wavefor m, compris ed of 4 su mmed HCs, is referre d to as a normal (N) data bloc k. Figur e 1 has an other feat ure: a gua rd interva l (GI) has been form ed by copy ing a numb er of micr oseconds f rom the e nd of the transmissi on block a nd attachi ng the sam ples onto the beginn ing. The guard inte rval is al so descr ibed as a ‘ cyclic ex tension’ . If the ti me duratio n of the g uard inter val is sli ghtly long er than th e duration of the l ongest ech o that aff licts the channel, t he echo ca n be compl etely canc eled in a noise-free channel. With conve ntional OF DM, an equ alizer is still need ed to canc el the eff ects of an echo, but it needs only to pe rform a singl e complex multiplica tion on ea ch receive d HC’s coe fficient t o correct the effect of the li near disto rtion. Figure 1 A Normal (N) Waveform Comprised of 4 Harmonics in the Time Domain 2001-01-14 IEEE 802.16.4c-01/09 3 Figur e 2 is a f requency d omain (spe ctral) plo t showing the 4 HCs of Figure 1 as 4 ver tical spec tral lines . The HC’s magnitudes can be se en, and th e HC’s pha ses are pr inted abov e the HCs spectral l ines. Figure 2 The Four Harmonics of Figure 2 Viewed in the Frequency Domain As mentioned above, each HC needs to be multiplied by a single complex coefficient to cancel any echoes. To assist in determining each correct coefficient, a set of pilot HCs with predetermined magnitude and phase values is typically used. An estimate of the linear distortion on each HC can be computed by measuring linear distortion on the pilot HCs and interpolating for the data HC frequencies. A set of pilot HCs may be viewed as a training or reference signal for OFDM. Frequency Domain Reciprocal Modulation As mentioned in the introduction section, there are two implementations of FDRM: a single block with interleaved reciprocals HCs, and two block implementation with the reciprocal HCs all located in the second block. For clarity, the following explanation first describes the two-block implementation. The discussion of the single block implementation, with its advantages and disadvantages follows later. Two-Block FDRM Holtzman’s new FDRM modulation is based on two consecutive blocks of data that contain the same information but use different encoding. The first block is similar to normal (N) OFDM with the restriction that low-valued magnitudes are not used for HCs. The second block is a “reciprocal” (R) in the frequency domain to the first block. A reciprocal block is formed by a complex division of the magnitude and phase of each HC in a normal OFDM block into 1.0 at an angle of 0 degrees. The computed reciprocal coefficients are used for the corresponding same-frequency HCs in the reciprocal block. The two blocks are sent out in adjacent time slots so that approximately the same echo is applied to both blocks. At the receive site each HC from a reciprocal block is divided into the corresponding HC in the normal block, and a square root is performed on the quotient. This process yields the transmitted data without linear distortion, as will be explained. Thus, echo cancellation is an inherent property of FDRM. A Reciprocal Example Assume a 127th HC in a first normal block with a frequency of 127,000 Hz is sent with a magnitude of 2.0 at a phase of +60 degrees. A corresponding 127th HC, also with a frequency of 127, 000 Hz, in the reciprocal block will have a magnitude of 0.5 at a phase of -60 degrees. In general a reciprocal block has a similar noise-like appearance to the normal block from which it is derived. In a special case, when all HCs have the same amplitude, the reciprocal block appears to be the normal block played backwards in time. De-gh osting wit h Two Data Blocks Figur e 3 featur es a recip rocal (R) data block to the OF DM transmi ssion illu strated in Figure 1. Each HC compr ising the reciprocal sum signa l is the r eciprocal of the HC with the s ame freque ncy in Fig ure 2. Re member that the recipr ocal of a complex nu mber is co mputed by dividing t he magnitu de compone nt into 1. 0 and chang ing the si gn on the phase angl e componen t. Note t hat if the magnitude was large r in Figur e 1 for a given HC, i t is small er in Figu re 3. Lik ewise, if the phase angle of a HC is pos itive in F igure 1, i t is negat ive in Fig ure 3, and v ice-versa. Figure 4 is a freq uency resp onse plot of the rec iprocal da ta block. Note that to av oid a divi sion by ze ro probl em, it is necessary that the c oefficient s in the n ormal bloc k not have zero or near-ze ro magnitu des. If a signal su ch as a bu rst transm ission of convention al single carrier fr equency 16 QAM w ere examin ed in the frequency domain, so me of the coefficien ts would l ikely have very low valued magni tudes. Th us, some o f its reci procal coe fficients would be h uge, makin g an impra ctical sig nal for trans mitting ov er physica l channels . OFDM ha s the nece ssary prop erty of co ntrolled m agnitudes in the fre quency domai n. 2001-01-14 IEEE 802.16.4c-01/09 4 Figure 3 A Reciprocal (R) Waveform Comprised of Four Harmonics. The Harmonics are the Reciprocals of the Harmonics at the Same Frequency Illustrated in Figure 2 Figure 4 The Reciprocals of the Four Harmonics of Figure 3, Viewed in the Frequency Domain. Operation Assume a transmitted signal block is S( f ) in the frequency domain and a channel’s frequency response is H( f ). The variable f represents discrete frequency steps. The transmitted signal block may be a burst of OFDM (orthogonal frequency division multiplex) modulation which is comprised of multiple harmonically-related carriers (HCs). The normal received signal is: X f S f H f ( ) ( ) ( ) = ⋅ (2) If a reciprocal signal block is created: R f S f ( ) ( ) = 1 (3) and sent through the same channel the received reciprocal signal will be: Y f R f H f H f S f ( ) ( ) ( ) ( ) ( ) = ⋅ = (4) The undistorted signal can be found by dividing the received reciprocal block into the normal block and performing a square root on the quotient: S f X f Y f S f H f H f S f S f ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = ⋅ = 2 (5) 2001-01-14 IEEE 802.16.4c-01/09 5 Figure 5 A Carrier, Its Reciprocal, and an Echo Distorting Both A Pro cessing Ex ample Refer to Figure 5 for a v ector diag ram of ill ustrating how an ech o is cance led using two HCs. Assu me a N h armonic ca rrier at s ome freque ncy is tra nsmitted w ith a magn itude of 1 .333 at an angle of +45 degre es. S t t N ( ) . cos( ) = + 1333 45 ω [lab eled as ‘N ’ ] (6) There fore, the R harmonic carrier a t that sam e frequenc y will hav e a magnit ude of 0.7 5 at an an gle of -45 degrees. R= S t t R ( ) . cos( ) = − 0 75 45 ω [lab eled as ‘R ’ ] (7) Assum e an echo with ampli tude 0.5 a t an angle of 115 de grees iden tically co ntaminates both the N and R harmo nic carrie rs. H = + 10 0 0 5 115 . @ deg . @ deg. or (8) H = 0 909 29 88 . @ . deg. (9) After reception , the rece ived N har monic carr ier will b e the vect or sum of the SN(t) a nd its ech o signal ( labeled as N-ECH O). N-ECH O is the p roduct of SN(t) a nd the ech o. Theref ore the re ceived N h armonic ca rrier’ s co efficient is: XN=1.21 [email protected] de g. [labele d as ‘N-SU M’] (10) The r eceived R harmonic c arrier wil l be the v ector sum of the SR(t) a nd its ech o signal ( labeled as R-ECHO). RECHO is the pro duct of SR(t) a nd the sam e echo. T herefore, the receiv ed R harmo nic carrie r’ s coeffi cient is: YR=0.68 2 @-15.12 deg. [label ed as ‘R-S UM’] (11) The r eceived N harmonic c arrier’ s c oefficient divided b y the rece ived R har monic carr ier’ s coef ficient is : X Y S N R N ⋅ = = 1 1777 90 2 . @ deg. (12) The o riginally transmitte d harmonic carrier’ s coefficie nt was the refore 1.3 3 (square root of 1. 769) at 45 degrees (half of 90), w hich is th e correct answer. 2001-01-14 IEEE 802.16.4c-01/09 6 SN = 1333 45 . @ deg. (13) Likewise, the channel’s frequency response can be determined by multiplying X(f) by Y(f): X f Y f S f H f H f S f H f ( ) ( ) ( ) ( ) ( ) ( ) ( ) ⋅ = ⋅ ⋅ = 2 (14) so the channel’s frequency response is: H f H f ( ) ( ) = 2 (15) Continuing with the earlier example, H f U f U f N R ( ) ( ) ( ) . @ . deg = ⋅ = 0 909 29 88 (16) which is the frequency response when contaminated with an echo. If the channel has slowly moving echoes, reciprocal blocks can be sent infrequently, or sent sparsely in the time domain. The channel’s frequency response data, H(f), may be used to provide echo correction for normal blocks that do not have reciprocal blocks accompanying them. Echo cancellation is accomplished by dividing each normal block HC by H(f). Likewise, if neighboring HCs have nearly the same echo, reciprocals HCs can be used sparsely in the frequency domain. The frequency response data can also be used to compute an impulse response of the channel by performing the inverse fast Fourier transform (IFFT) on the set of coefficients, H(f). The impulse response then may be used to program a conventional adaptive equalizer. If the channel’s frequency response is slowly changing and the level of random noise is high, time averaging of coefficients can be used to improve the accuracy of the characterization of the channel. Single Block FDRM Another way to use FDRM is to interleave normal and reciprocal harmonic carriers within the same block. Thus the reciprocal value to a harmonic carrier can be located at the next adjacent harmonic carrier frequency. With this technique odd numbered HCs could use normal coefficients and the even numbered HCs could use reciprocal coefficients. In ot her words, instead o f transmit t ing a N d ata block followed b y a R data block, a single dat a block compr ised of al ternating N and R ha rmonic car riers is t ransmitted . For exa mple, the spectral o rder of th e first 10 HCs i n a single block tra nsmission may be: N1, R 1, N2, R2, N3, R3, N 4, R4, N5, R5 ..... . where N1 is the first N H C and R1 i s the firs t R HC, N2 is the se cond N HC and R2 is the second R HC etc . This variant o f the basi c idea can be succes sfully use d if appro ximately t he same ec ho is appl ied by the signal pa th to tw o HCs that are at ad jacent fre quencies. This comm only occur s in pract ical chann els, and d epends on the durat ion of the echoes re lative to the freque ncy separa tion betwe en adjacen t HCs. On e advantag e of the s ingle block FDRM over two block FDRM is t hat rapidl y changing multipath will chan ge less ov er a one b lock durat ion than over a two block dur ation, mak ing the as sumption t hat the ec ho did not change ov er the rel evant capt ure perio d twice as valid. A nother adv antage of single blo ck FDRM is that tota l guard in terval t im e is halve d. Test Results from Hardware: Figure 6 is a hardware block diagram of prototype hardware that has been used for demonstrations and tests in the past. The bandwidth is lower than for the present proposal, but the number of HC is roughly similar. The hardware illustrates the principle of operation. A normal burst signal interleaved with a reciprocal burst signal were created using random data and stored in a programmable read-only memory (PROM) as 300 discrete harmonic carriers (HC) situated between 1 and 4 MHz. To create a transmitted burst, data are clocked through a digital-to-analog converter (D-A converter) and up-converted to 51-54 MHz. RF frequency. After passing through a dynamic multipath impaired channel with 500 deep fades/sec, the bursts were down converted back to the 1-4 MHz band. The samples were converted back into digital format by a data acquisition unit (A-D converter) and processed according to equation number (5) in a personal computer. Table 1 lists the parameters used for the demonstration hardware. 2001-01-14 IEEE 802.16.4c-01/09 7 Figure 6 Hardware Block Diagram Table 1 Details of Demonstration Hardware Parameter Value Sample Rate 10.0 M Samples/sec. Each Block’s Duration 204.8 microseconds +GI Guard Interval (GI) 10.24 microseconds Total Burst Duration 215 microseconds HC spacing 4.883 kHz. Occupied Bandwidth 2.93 MHz. Size of Fourier Transform 2048 points Number of HCs 300 Figure 7 A Processed 10 Point Constellation FDRM Burst with Linear Distortion and Noise 2001-01-14 IEEE 802.16.4c-01/09 8 Figure 7 is a screen plot showing the hardware results of an analysis of a burst transmission of a FDRM burst using a 10 point constellation. The second row down illustrates the interleaved transmitted normal and reciprocal signals as a time-domain trace. The bottom trace is a spectral plot showing the effects of noise and a channel tilt. The higher magnitude HCs can be distinguished in the spectral plot. The processed upper and lower sidebands are separated for illustration. The NUSB points (upper sideband normal constellation points) and the RUSB points (upper sideband reciprocal constellation points) are processed together to produce the USB plot. Likewise, the NLSB points (lower sideband normal constellation points) and the RLSB points (lower sideband reciprocal constellation points) are processed together to produce a LSB plot. Each point in a N constellation is divided by the same frequency point in the R constellation to produce the corrected constellation. Note that point spread in the constellation due to noise is higher when the amplitude of the HC is lower. Changing Echoes Two models of fading that are most applicable are typically Ricean fading and Raleigh fading. FDRM works well for both. For a channel with rapid fading, FDRM works very well because the fade affects both the normal and reciprocal HCs. Hence the affect of the fade is canceled automatically. Thus an automatic gain control circuit does not have to have a fast response or an accurately set level. A good practice for AGC circuits receiving FDRM bursts is to allow a change in gain in steps that coincide with the end of a block sequence. The function of the AGC is to use as much of the dynamic range of the analog to digital converter without overloading it. Deep Fades It is possible for the combination of echoes in a channel to produce a deep fade over some portion of the frequency band. The HCs that are unfortunate enough to be located in the portion of the spectrum that is deeply faded will be hopelessly contaminated by any noise in the channel, and must be discarded. In this case, the use of well-known forward error correction techniques will allow the transmitted data to be received without error. What constitutes a “deep fade” depends on the level of the noise floor in the channel. Antenna diversity is another excellent solution because it is improbable that a particular frequency will be deeply faded on the same frequency on two antennas that are physically separated by an appreciable distance. Performance Near Threshold: One might think that sending the HC twice in a different form would reduce the channel capacity by one-half. However the information in both HC’s data is the same, and when the two blocks are processed together the signals add on a voltage basis (20 log10) while the noise contaminating each block of data is uncorrelated and adds on a power basis (10 log10). Thus the signal to noise ratio of the processed signal should be 3 dB better that either the signals in the N block or R block. Furthermore, since the two HCs form a virtual pilot per equation (6), the energy of the pilot signal is doubled, resulting is a 3 dB more accurate channel characterization relative to a static pilot signal without the energy doubling feature. A received processed signal in the presence of noise is: S f S f H f N f H f S f N f n d ( ) ( ) ( ) ( ) ( ) ( ) ( ) = ⋅ + + (8) where Nn is the random noise disturbing the first block and Nd is the uncorrelated random noise disturbing the second block. Near threshold one might expect that the performance of FDRM may be poor because the Nd term could cancel the signal from the second reciprocal block. Simulation shows that the ‘division by almost zero problem’ at low carrier to noise ratios is not a severe problem. This characteristic is common with other transmission systems using pilots: when noise gets on the pilot, the adaptive equalizer receives inaccurate programming. Phase Ambiguity One of the problems associated with performing the square root function at the receiver is ambiguity about the correct phase, since a square root has two possible solutions. Equation (5) employs the square root function. The phase may be incorrect because of an inexact start of sampling time, or because of transmitter’s frequency or phase being unlocked relative to the receiver’s, or because of group delay (which is a linear distortion). For example, a harmonic carrier received at -135 with a reciprocal at +135 is ambiguous: it could have also been transmitted as a carrier at +45 with a reciprocal at -45 and suffered a 180 O rotation. One solution is to transmit a single pilot frequency and track HC phase change versus frequency. This works for channels with Ricean fading. Another solution is to employ a constellation without 180 rotational symmetry. This works for channels with Raleigh fading. Differential encoding between adjacent HC pairs may also be used. 2001-01-14 IEEE 802.16.4c-01/09 9 Patents granted and pending. See [7] Repla cing Pilot s with Rec iprocals FDRM can be use d to impro ve the dem odulation of convent ional OFDM by conver ting OFDM pilots int o recip rocal Hcs o f adjacent carriers. This mea ns that on ly a fract ion of the total num ber of HCs will have recip rocals. T he FDRM si gnal proce ssing tech nique redu ces the no ise on the adjacent carrier by 3 dB and also reduc es the noi se on the channel ch aracteriza tion by 3 dB. The n oise-reduc ed pilot c an be used to deghos t the other HCs that do not hav e an accom panying re ciprocal Echoes Echoes on a signal present a severe problem to the transmission of digital information. The challenge from a technical standpoint is to determine how much energy must be expended to have accurate current information about the channel’s response. Fortunately, the amount of energy that must be expended in many stationary wireless applications is a relatively small percentage of the total transmitted power because the echo is slowly-moving in time and/or because the echo changes relatively slowly with frequency. That is, neighboring frequency samples have nearly identical echo distortion. One may speak of the information rate that is associated with the channel’s dynamic frequency response, although it is unlikely that anyone would understand what they were talking about. Two factors complicate this idyllic slow-moving situation for wireless signal paths: wind, which makes foliage reflectors/diffusers into sources of dynamic multipath, and infrequent or bursty transmissions, which allow slowly moving echoes to produce large relative changes in the frequency response during the long times between bursts. If pilots or training signals are employed, and insufficient energy is used for pilots, the noise on the pilots will result both in a poor channel model, which gives noise enhancement in the corrected signal. That is, a perfect channel characterization can never improve the receiver’s carrier to noise ratio, but it a poor characterization can hurt it. As mentioned above, FDRM is an adaptable technology that allows HCs with accompanying reciprocal HCs to be spread thickly or thinly through the channel’s passband. Reciprocal HCs can also be spread thickly or thinly through time. The thick use of reciprocals would be a reciprocal accompanying every normal HC in every block. A thin or sparse use of reciprocals would be a reciprocal in every 20th harmonic carrier in frequency and every 10th block in time. Holtzman is proposing the adaptive use of reciprocals depending on the dynamics of an individual subscriber’s signal path. The Application of FDRM to Microwave Point to Multipoint for IEEE 802.16.4 and Physical Layer Problems in the 5 GHz Frequency Band Holtzman’s Proposal Holtzman proposes the incorporation of FDRM into the PHY layer of 802.16.4. If the problem of longer and dynamic echoes is attacked by adding more and more pilot carriers to a conventional OFDM transmission, additional capacity will be lost. Furthermore, if an OFDM harmonic carrier with a pilot at the same power is replaced with FDRM normal and a reciprocal carrier pair, the FDRM pair would have a 6 dB advantage with a random noise impairment. A three dB advantage would be achieved because of the FDRM voltage addition of the normal and reciprocal carriers, and another 3 dB advantage would be realized from the FDRM noise reduction in the channel characterization. Specifically: 1. Holtzman recommends a mixed system where some of the HCs use OFDM modulation and some of the HCs are paired up to use FDRM modulation. Channel conditions determine a mix. 2. Holtzman recommends that the duration of the block be increased from 3.2 plus a 0.8 microsecond guard interval to 25.6 microseconds plus a 2.4 microsecond guard interval, as shown in Table 2. The longer guard interval should allow for outdoor operation up to several kilometers. The closer spacing of harmonic carriers is necessary to improve performance with longer echoes (which produce closer ripples in the frequency response). 3. Holtzman also recommends the use of adaptive transmissions on both the upstream and downstream paths. Adaptive transmissions mean that the number of points in a constellation, the number and amplitude of reciprocal HCs, the FEC code strength, possibly the duration of the guard interval all be made adjustable by the MAC layer. (COFDM allows the broadcaster to adjust many of the same parameters.) On days with high attenuation due to wet foliage, the transmissions will continue at a lower speed. On windy days with more dynamic multipath, FDRM pairs can be used until an OFDM transmission is completely converted into a FDRM transmission. 2001-01-14 IEEE 802.16.4c-01/09 10 4. When channel fade is extremely severe, the total number of HCs can be reduced to allow more power to be transmitted in the remaining HCs. Table 2 Details of Holtzman Inc. Proposal Parameter Value Sample Rate 20.0 M Samples/sec. Useful Block Duration 25.6 microseconds +GI Guard Interval (GI) 2.4 microseconds Total Block Duration 28 microseconds HC spacing 39.0625 kHz. Spacing Between Two Outermost HCs 16.25 MHz. Size of Fourier Transform 512 points Number of HCs 208 USB + 208 LSB Figure 8 Temporal Plot of Single Block Interleaved FDRM Transmission Figure 8 is a temporal plot of single block FDRM burst that may be used for transmissions. The normal and reciprocal harmonic carriers are interleaved with each other whereby each harmonic carrier has its reciprocal at an adjacent frequency. The burst is shown in outline form, but the actual waveform will have a noisy appearance similar to the temporal plot in Figure 7. A guard interval of 2.4 microseconds represents less than a 10% overhead. The transmission time of 28 microseconds is the duration over which a dynamic multipath will change very little. Figure 9 Spectral Plot of FDRM Figure 9 is a spectral diagram of the Figure 8 burst with a 20 MHz channelization plan. The separation between harmonic carriers is 39.06 kHz and 208 N HCs reside between 208 R HCs in 16.25 MHz. The harmonic carrier at Fc (DC) is not used. 2001-01-14 IEEE 802.16.4c-01/09 11 Figure 11 is a set of constellation plots that exhibits desirable properties with FDRM. Note that as the number of points in a constellation decreases, immunity to random noise increases. The reciprocal constellation plots corresponding to these normal constellations is not illustrated, but can be easily created. These plots have two characteristics that should be pointed out. The first is that there are no constellation points near to the origin. This would create a high value point in the reciprocal constellation, which requires high dynamic range to transmit as mentioned earlier. The second feature is that 180 degrees opposite each point is a vacant area. This feature was employed to allow an easy resolution to the problem of two possible solutions to a square root function as discussed above. Figure 11 Four Normal Constellations for Use with FDRM. Note that Constellations do not have 180 Degree Rotational Symmetry Number of points in constellation N Number of Bits / Symbol = log2(N) Number of Symbols grouped for a binary conversion Number of Bits per Conversion 3 1.58 2 3 5 2.32 4 9 10 3.32 4 13 33 5.04 1 5 2001-01-14 IEEE 802.16.4c-01/09