3.6 Mitigation of Fading
3.6.4 Equalization
Equalizers are the most logical alternative for ISI suppression to OFDM, since they don’t require additional antennas or bandwidth and have moderate complexity. Equalizers are implemented at the receiver and attempt to reverse the distortion introduced by the channel. Generally, equaliz- ers are broken into two classes: linear and decision directed (nonlinear).
Alinear equalizer simply runs the received signal through a filter that roughly models the inverse of the channel. The problem with this approach is that it inverts not only the channel but also the received noise. This noise enhancement can severely degrade the receiver performance, especially in a wireless channel with deep frequency fades. Linear receivers are relatively simple to implement but achieve poor performance in a time-varying and severe-ISI channel.
Anonlinear equalizer uses previous symbol decisions made by the receiver to cancel out their subsequent interference and so are often called decision-feedback equalizers (DFEs). Recall that the problem with multipath is that many separate paths are received at different time offsets, so prior symbols cause interference with later symbols. If the receiver knows the prior symbols, it can subtract out their interference. One problem with this approach is that it is com- mon to make mistakes about what the prior symbols were, especially at low SNR, which causes error propagation. Also, nonlinear equalizers pay for their improved performance relative to lin- ear receivers with sophisticated training and increased computational complexity.
Maximum-likelihood sequence detection (MLSD) is the optimum method of suppressing ISI but has complexity that scales like , where M is the constellation size and v is the channel delay. Therefore, MLSD is generally impractical on channels with a relatively long delay spread or high data rate but is often used in some low-data-rate outdoor systems, such as GSM. For a high-data-rate broadband wireless channel, MLSD is not expected to be practical in the foreseeable future, although suboptimal approximations, such as delayed-decision-feedback sequence estimation (DDFSE),
13. Note that the definition of spread spectrum is somewhat loose. The FCC has labeled even the 11Mbps in 20MHz 802.11b system as “spread spectrum,” but this is generally inconsistent with its historical definition that the bandwidth be much larger than the data rate. See, for example, [26, 31, 33] and the references therein.
O Mv
which is a hybrid of MLSD and decision-feedback equalization [7] and reduced-state sequence esti- mation (RSSE) [9] are reasonable suboptimal approximations for MLSD in practical scenarios [12]. 3.6.5 The Multicarrier Concept
The philosophy of multicarrier modulation is that rather than fighting the time-dispersive ISI channel, why not use its diversity? For this, a large number of subcarriers (L) are used in paral- lel, so that the symbol time for each goes from . In other words, rather than sending a single signal with data rate R and bandwidth B, why not send L signals at the same time, each having bandwidth and data rate ? In this way, if , each signal will undergo approximately flat fading, and the time dispersion for each signal will be negligible. As long as the number of subcarriers L is large enough, the condition can be met. This elegant idea is the basic principle of orthogonal frequency division multiplexing (OFDM). In the next chapter, we take a close look at this increasingly popular modulation technique, discussing its theoretical basis and implementation challenges.
3.7
Summary and Conclusions
In this chapter, we attempted to understand and characterize the challenging and multifaceted broadband wireless channel.
•The average value of the channel power can be modeled based simply on the distance between the transmitter and the receiver, the carrier frequency, and the pathloss exponent. •The large-scale perturbations from this average channel can be characterized as lognormal
shadowing.
•Cellular systems must contend with severe interference from neighboring cells; this inter- ference can be reduced through sectoring and frequency-reuse patterns.
•The small-scale channel effects are known collectively as fading. Broadband wireless channels have autocorrelation functions that tell us a lot about their behavior.
•Realistic models for time, frequency, and spatial correlation can be developed from popu- lar statistical channel models, such as Rayleigh, Ricean, and Nakagami.
•A number of diversity-achieving techniques are available for both narrowband and broad- band fading.
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T→LT
B L/ R L/ B L/ Bc
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