Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems

IEEE Communications Magazine • April 200258 Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems 0163-6804/02/$17.00 © 2002 IEEE ABSTRACT Broadband wireless access systems deployed in residential and business environments are likely to face hostile radio propagation environ- ments, with multipath delay spread extending over tens or hundreds of bit intervals. Orthogo- nal frequency-division multiplex (OFDM) is a recognized multicarrier solution to combat the effects of such multipath conditions. This article surveys frequency domain equalization (FDE) applied to single-carrier (SC) modulation solu- tions. SC radio modems with frequency domain equalization have similar performance, efficien- cy, and low signal processing complexity advan- tages as OFDM, and in addition are less sensitive than OFDM to RF impairments such as power amplifier nonlinearities. We discuss similarities and differences of SC and OFDM systems and coexistence possibilities, and present examples of SC-FDE performance capabilities. INTRODUCTION Broadband wireless access technologies, offering bit rates of tens of megabits per second or more to residential and business subscribers, are attractive and economical alternatives to broad- band wired access technologies. Air interface standards for such broadband wireless metropoli- tan area network (MAN) systems in licensed and unlicensed bands below 11 GHz are being devel- oped by the IEEE 802.16 working group and also by the European Telecommunications Stan- dards Institute (ETSI) Broadband Radio Access Network (BRAN) High-Performance MAN (HiperMAN) group. Such systems, installed with minimal labor costs, may operate over non-line- of-sight (NLOS) links, serving residential and small office/home office (SOHO) subscribers. In such environments multipath can be severe. This raises the question of what types of anti-multi- path measures are necessary, and consistent with low-cost solutions. Several variations of orthogo- nal frequency-division multiplexing (OFDM) have been proposed as effective anti-multipath techniques, primarily because of the favorable trade-off they offer between performance in severe multipath and signal processing complexi- ty [1]. This article discusses an alternative approach based on more traditional single-carrier (SC) modulation methods. We show that when com- bined with frequency domain equalization (FDE), this SC approach delivers performance similar to OFDM, with essentially the same overall com- plexity. In addition, SC modulation uses a single carrier, instead of the many typically used in OFDM, so the peak-to-average transmitted power ratio for SC-modulated signals is smaller. This in turn means that the power amplifier of an SC transmitter requires a smaller linear range to sup- port a given average power (in other words, requires less peak power backoff). As such, this enables the use of a cheaper power amplifier than a comparable OFDM system; and this is a benefit of some importance, since the power amplifier can be one of the more costly components in a consumer broadband wireless transceiver. MULTIPATH CHANNEL CHARACTERISTICS AND ANTI-MULTIPATH APPROACHES Broadband cellular wireless access systems in residential neighborhoods must cope with the dominant propagation impairment of multipath, which causes multiple echoes of the transmitted David Falconer, Carleton University Sirikiat Lek Ariyavisitakul, Radia Communications Anader Benyamin-Seeyar, Harris Corp. Brian Eidson, Conexant Systems, Inc. WIDEBAND WIRELESS ACCESS TECHNOLOGIES TO BROADBAND INTERNET IEEE Communications Magazine • April 2002 59 signal to be received with delay spreads of up to tens of microseconds [2]. For bit rates in the range of tens of megabits per second, this trans- lates to intersymbol interference that can span up to 100 or more data symbols. For example, at a 5 MHz symbol rate, a 20 ms multipath delay profile spans 100 data symbols. For channel responses spanning tens or hun- dreds of symbols, practical modulation and anti- multipath alternatives are: • SC modulation with receiver equalization done in the time domain • OFDM • SC modulation with receiver equalization in the frequency domain A brief description of each of these anti-mul- tipath alternatives follows. SINGLE-CARRIER MODULATION WITH TIME DOMAIN EQUALIZATION AT THE RECEIVER A conventional anti-multipath approach, which was pioneered in voiceband telephone modems and has been applied in many other digital com- munications systems, is to transmit a single carri- er, modulated by data using, for example, quadrature amplitude modulation (QAM), and to use an adaptive equalizer at the receiver to compensate for intersymbol interference (ISI) [3]. Its main components are one or more transversal filters for which the number of adap- tive tap coefficients is on the order of the num- ber of data symbols spanned by the multipath. For the above-mentioned 20 ms delay spread example, this would mean a transversal filter with at least 100 taps, and at least several hun- dred multiplication operations per data symbol. For tens of megasymbols per second and more than about 30–50-symbol ISI, the complexity and required digital processing speed become exorbi- tant, and this time domain equalization approach becomes unattractive. OFDM OFDM transmits multiple modulated subcarriers in parallel [1]. Each occupies only a very narrow bandwidth. Since the channel affects only the amplitude and phase of each subcarrier, equaliz- ing each subcarrier’s gain and phase does com- pensation for frequency selective fading. Generation of the multiple subcarriers is done by performing inverse fast Fourier transform (IFFT) processing at the transmitter on blocks of M data symbols; extraction of the subcarriers at the receiver is done by performing the fast Fourier transform (FFT) operation on blocks of M received samples. Typically, the FFT block length M is at least 4–10 times longer than the maximum impulse response span. One reason for this is to minimize the fraction of overhead due to the insertion of a cyclic prefix at the beginning of each block. The cyclic prefix is a repetition of the last data symbols in a block. Its length in data symbols exceeds the maximum expected delay spread. The cyclic prefix is dis- carded at the receiver. Its purpose is to: • Prevent contamination of a block by ISI from the previous block • Make the received block appear to be peri- odic with period M This produces the appearance of circular convo- lution, which is essential to the proper function- ing of the FFT operation. Time domain equalization typically requires a number of multiplications per symbol that is pro- portional to the maximum channel impulse response length. OFDM processing requires on the order of log2 M multiplications per data sym- bol, counting both transmitter and receiver opera- tions. Since M is proportional to the maximum expected channel response length, OFDM appears to offer a better performance/complexity trade-off than conventional SC modulation with time domain equalization for large (> about 20 taps) multipath spread [4]. A variation is adaptive � Figure 1. a) Power amplifier output power spectra [5] for a QPSK 256-point OFDM system: (a) spectrum with ideal power amplifier (infinite power backoff); (b) spectrum with typical power amplifier with 10 dB power backoff; (c) FCC MMDS spectral mask; b) power amplifier output power spectra [5] for a QPSK SC system: (a) spectrum with ideal power amplifier (infinite power backoff); (b) spec- trum with typical power amplifier with 10 dB power backoff; (c) FCC MMDS spectral mask. Frequency (MHz) 200 –80 0 Po w er ( dB ) –20 –10 –30 –40 –50 –60 –70 15105 Frequency (MHz) (b) ba (a) (c) (a) (c) 200 –80 –70 Po w er ( dB ) –60 –50 –40 –30 –20 –10 0 15105 (b) IEEE Communications Magazine • April 200260 OFDM, where the signal constellation on each subchannel depends on channel response at that frequency. It requires feedback from the receiver to the transmitter, and is not commonly employed in radio systems due to complexity and channel time variations. Because of the fixed power and bit rate on each subchannel, some of which might be severely faded by frequency-selective channels, nonadaptive OFDM must be coded. Because the transmitted OFDM signal is a sum of a large number (M) of slowly modulated subcarriers, OFDM has a high peak-to-average power ratio, even if low-level modulation such as quaternary phase shift keying (QPSK) is used on each subcarrier. While there are signal process- ing methods to reduce this ratio, the transmitter power amplifier in an OFDM system generally must be backed off by several dB more than for an SC system to remain linear over the range of signal envelope peaks that must be faithfully reproduced. Figures 1a and 1b (from [5]) illus- trate the spectral regrowth that occurs with 10 dB power backoff at the output of a typical power amplifier for a QPSK OFDM system with 256-point FFT, with 25 percent of the subcarri- ers not used (Fig. 1a), and for a QPSK SC sys- tem with 25 percent excess bandwidth (Fig. 1b). Also shown in these figures is the output power spectrum for an ideal (infinite backoff) power amplifier, and also (with straight lines), the FCC spectral mask for multichannel microwave distri- bution systems (MMDSs) with 6 MHz band- width. Clearly the OFDM system’s output power must be backed off more than 10 dB in this example, in order to comply with the FCC mask. This power backoff penalty is especially impor- tant for subscribers near the edge of a cell, with large path loss, where lower-level modulation such as binary PSK (BPSK) or QPSK modula- tion must be used. The increased power backoff required in this situation for OFDM would increase the cost of the power amplifier required for such sites to “reach” the base station. OFDM systems can also exhibit sensitivity to carrier fre- quency offset and phase noise. Pilot (known) data is also often incorporated into these data blocks for channel tracking and estimation purposes. What’s more, in burst applications, one or more blocks of this size are used for initial receiver training purposes. One other problem associated with OFDM systems involves data packet granularity: the minimum data packet size in an OFDM system is the FFT block length. This problem, which affects the spectral efficiency of short packet transmissions, can be circumvented by using orthogonal fre- quency-division multiple access (OFDMA), in which the FFT block is shared by multiple users, each using a subset of the subcarriers that con- stitute an FFT block. The granularity problem is solved in SC systems by simply transmitting short-duration blocks when necessary. SINGLE-CARRIER MODULATION WITH FREQUENCY DOMAIN ADAPTIVE EQUALIZER PROCESSING AT THE RECEIVER An SC system transmits a single carrier, modu- lated, for example, with QAM, at a high symbol rate. Frequency domain linear equalization in an SC system is simply the frequency domain analog of what is done by a conventional linear time domain equalizer. For channels with severe delay spread, frequency domain equal- ization is computationally simpler than corre- sponding time domain equalization for the same reason OFDM is simpler: because equal- ization is performed on a block of data at a time, and the operations on this block involve an efficient FFT operation and a simple chan- nel inversion operation. Sari et al. [6, 7] pointed out that when combined with FFT processing and the use of a cyclic prefix, an SC system with FDE (SC-FDE) has essentially the same performance and low complexity as an OFDM system. Also notable is that a frequency domain receiver processing SC modulated data shares a number of common signal processing functions with an OFDM receiver. In fact, as we point out in the next section, SC and OFDM modems can easily be configured to coexist, and signifi- cant advantages may be obtained through such coexistence. Figure 2 shows conventional linear equaliza- tion, using a transversal filter with M tap coeffi- cients, but with filtering done in the frequency domain. The block length M, suitable for MMDS systems with 6 MHz bandwidths, would be cho- sen in the range of 64–2048 for both OFDM and SC-FDE systems. There are approximately log2 M multiplications per symbol, as in OFDM. The use of SC modulation and FDE by pro- cessing the FFT of the received signal has sever- al attractive features: • SC modulation has reduced peak-to-average ratio requirements from OFDM, thereby allowing the use of less costly power ampli- fiers. � Figure 2. SC-FDE with linear equalization. From channel Data out To channel Transmitter: Receiver: Data in Code and cyclic prefix over M symbols FFT Multiply by M equalizer coeffcients Inverse FFT Detect and decode � Figure 3. Block processing in frequency domain equalization. Cyclic prefix Last P symbols repeated P symbols Block of M data symbols IEEE Communications Magazine • April 2002 61 • Its performance with FDE is similar to that of OFDM, even for very long channel delay spread. • Frequency domain receiver processing has a similar complexity reduction advantage to that of OFDM: complexity is proportional to log of multipath spread. • Coding, while desirable, is not necessary for combating frequency selectivity, as it is in nonadaptive OFDM. • SC modulation is a well-proven technology in many existing wireless and wireline appli- cations, and its RF system linearity require- ments are well known. A cyclic prefix is appended to each block of M symbols, exactly as in OFDM, as shown in Fig. 3. As an additional function, the cyclic prefix can be combined with a training sequence for equalizer adaptation. For either OFDM or SC-FDE broadband wireless systems operating in severe outdoor multipath environments, typical values of M could be 256–1024, and typical values of P could be 64 or 128. Overlap-save or overlap-add signal processing techniques could also be used to avoid the extra overhead of the cyclic prefix. An inverse FFT returns the equalized signal to the time domain prior to the detection of data symbols. Adaptation of the FDE equaliz- er’s transfer function can be done with least mean square (LMS), root least square (RLS), or least squares minimization (LS) techniques, analogous to adaptation of time domain equal- izers [8, 9]. Figure 4 shows a comparison of the complexi- ties of time domain and frequency domain pro- cessing (SC or OFDM linear equalizers) as a function of the length of the channel impulse response, measured in symbol intervals. Com- plexity here is gauged by the number of complex multiplications per transmitted data symbol, including both the filtering operations and LMS adaptation operations (see [9] for a description of the latter). The frequency domain equalizer is assumed to use an FFT block length equal to eight times the channel length. Decision feedback equalization (DFE) gives better performance for frequency-selective radio channels than linear equalization [3]. In conven- tional DFE equalizers, symbol-by-symbol data symbol decisions are made, filtered, and immedi- ately fed back to remove their interference effect from subsequently detected symbols. Because of the delay inherent in the block FFT signal pro- cessing, this immediate filtered decision feed- back cannot be done in a frequency domain DFE, which uses frequency domain filtering of the fed-back signal. A hybrid time-frequency domain DFE approach, which avoids the above- mentioned feedback delay problem, would be to use frequency domain filtering only for the for- ward filter part of the DFE, and conventional transversal filtering for the feedback part. The transversal feedback filter is relatively simple in any case, since it performs multiplications only on data symbols, and it could be made as short or long as required for adequate performance. Figure 5 illustrates such a hybrid time-frequency domain DFE topology. Once per block, the M FFT output coefficients, {Rl}, are multiplied by the complex-valued M forward equalizer coeffi- cients {Wl}(which compensate for the frequency- selective channel’s variations of amplitude and phase with frequency). An IFFT is applied to the M weight-equalized complex-valued samples, and the resulting time-domain sequence is passed to a data symbol decision device — or, in the case of a DFE, the estimated ISI due to pre- viously detected symbols is computed using B feedback taps {fk}, and subtracted off, symbol by symbol. FDE can also be combined with spatial processing to provide interference suppression and diversity [9]. COEXISTENCE OF SINGLE-CARRIER AND OFDM SYSTEMS Figure 6a shows block diagrams for OFDM and SC systems with linear FDE. It is evident that the two types of systems differ mainly in the placement of an IFFT operation: in OFDM it is placed at the transmitter to multiplex the data into parallel subcarriers; in SC it is placed in the receiver to convert FDE signals back into time domain symbols. The signal processing complexi- ties of these two systems are essentially the same for equal FFT block lengths. � Figure 4. Complexity comparison of time and frequency domain linear equalizers with LMS adaptation. Length of channel response (symbol intervals) Complexity comparison — time and frequency domain equalizers 10 20 30 40 50 60 70 80 90 1000 101 100 102 103 N um be r of m ul ti pl ie s pe r sy m bo l Time domain linear equalizer Frequency domain linear equalizer or OFDM � Figure 5. SC-FDE decision feedback equalizer. Detect + Multiply by coefficient {Wl} FFT {rm} {RL} {zm} {am} Process block of M samples at a time Symbol-by-symbol subtraction of feedback components IFFT B feedback taps {fk} IEEE Communications Magazine • April 200262 A dual-mode system, in which a software radio modem can be reconfigured to handle either SC or OFDM signals, could be imple- mented by switching the IFFT block between the transmitter and receiver at each end of the link, as suggested in Fig. 6b. There may actually be an advantage in oper- ating a dual mode system, wherein the base sta- tion uses an OFDM transmitter and an SC receiver, and the subscriber modem uses an SC transmitter and an OFDM receiver, as illustrat- ed in Fig. 7. This arrangement — OFDM in the downlink and SC in the uplink —has two poten- tial advantages: • Concentrating most of the signal processing complexity at the hub or base station. The hub has two IFFTs and one FFT, while the subscriber has just one FFT. • The subscriber transmitter is SC, and thus inherently more efficient in terms of power consumption due to the reduced power backoff requirements of the SC mode. This may reduce the cost of a subscriber’s power amplifier. EQUALIZER TRAINING USING LEAST SQUARES MINIMIZATION The FDE parameters {Wl} and {fk} are adapted, or trained from the reception of N consecutive training blocks, each consisting of a sequence of P known transmitted training symbols. The length of a training block, P, may be equal to or less than the length of a data block M and is preceded by a cyclic prefix. If it is less than M, P is picked to be at least equal to the maximum expected channel impulse response length in data symbol intervals. If P < M, the forward filter parameters derived from training, {Wl, l = 0, 1, …, PI} can be interpo- lated to values to be used for blocks of M. The sequence of P transmitted training sym- bols is known as a unique word (UW). Ideally, its frequency spectrum (FFT) should have equal or nearly equal magnitude for all frequencies. Such an ideal training sequence ensures that each fre- quency component of the channel is probed uni- formly. For unique word lengths P that are powers of two, such as 64 or 256, polyphase Frank-Zadoff sequences [10] or Chu sequences [11] are suit- able. If binary-