# OFDM kills multipath distortion

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High-spectral-efficiency quadrature amplitude modulation (QAM) is used over many communications media such as twisted pair, coaxial cable, fiber optics and radio to carry high-speed digital communications. QAM systems most often employ a single carrier frequency in each direction. However, in recent years systems have been designed using orthogonal frequency-division multiplexing (OFDM), where multiple adjacent narrow-bandwidth QAM signals are combined to fill the same channel bandwidth. So the question is: one carrier or many carriers?

Essentially, QAM is a bandwidth-efficient way to modulate a carrier. It is the sum of two amplitude-modulated double-sideband-suppressed-carrier sinusoidal signals: one DSB-SC cosine wave and one DSB-SC sine wave of the same frequency, each wave carrying totally different information content. Only single-sideband (SSB) modulation is as spectrally efficient as QAM. Implementation of QAM has been preferred over SSB, primarily because of the implementation of carrier recovery in the receiver. Single-carrier QAM has enjoyed great commercial success in telephone, satellite and microwave radio modems. Technical innovations in forward error correction (FEC) and adaptive channel equalization have made it robust in the presence of many channel impairments-linear, nonlinear, stationary and nonstationary.

**Optimal packing**

OFDM, sometimes referred to as multicarrier, employs multiple optimally packed (sub)carrier frequencies, each modulated using QAM. It could just as easily use SSB modulation to the same effect. The superposed QAM signals overlap in frequency but are orthogonal to one another if their carriers are spaced by the symbol rate. For example, in IEEE 802.11a there are 64 implied subcarrier frequencies with a spacing of 312.5 kHz. There are 52 nonzero subcarriers, 48 carrying data and four used as pilot tones. Each subcarrier hums away at 312.5k symbols/second. Data is blocked into 3.2-microsecond frames with an additional 0.8 microsecond of cyclic prefix tacked on for mitigation of intersymbol interference. A 64-point fast Fourier transform is performed over 3.2 microseconds to extract the 48 data symbols on the 48 QAM signals. For binary phase-shift keying (BPSK), with 1 bit per symbol, that is 48 bits in 4 microseconds, for an aggregate data rate of 12 Mbits/s. Half-rate convolutional coding brings the net rate down to 6 Mbits/s. For 64 QAM, the aggregate data rate is six times higher, or 72 Mbits/s. After rate convolutional coding, the net rate is 54 Mbits/s. The entire bandwidth occupancy specified in the standard is 20 MHz.

So what are the merits in using OFDM over single-carrier QAM? The primary reason is robust behavior in the presence of multipath radio propagation.

Such multipath propagation can create deep spectral nulls in the frequency passband of received radio signals due to the destructive interference of two copies of the signal arriving at slightly different times. A null in OFDM can take out one or more subcarriers. The same null in single-carrier QAM might drop a burst of sequentially adjacent symbols, depending on the specific data pattern at that instant. In extreme cases, loss of signal acquisition is even possible. It then gets down to the power of the FEC to recover the original data sequence. Incidentally, narrowband single-carrier interferers create an effect identical to deep nulls. OFDM rides them well, losing only the subcarriers in the vicinity of the interfering signal, whereas single-carrier QAM could fall prey to severe error or lose lock. If the interfering signal, however, is strong enough, OFDM also fails due to automatic-gain-control loop quieting.

**Minimizing multipath**

Multipath propagation effects in fixed-wireless broadband access are minimized by use of high-gain directional antennas with line-of-sight propagation paths. Such antennas will heavily attenuate reflected signals that typically arrive later than the direct signal and at angles well off the central beam lobe. Conversely, use of omnidirectional antennas in nonline-of-sight applications creates the most opportunities for multipath propagation signal degradation. Indoor wireless tests with omnidirectional antennas have seen 5 microseconds of signal dispersion. This suggests very long block sizes for OFDM or long equalizers for single-carrier QAM.

Single-carrier QAM receivers can effectively cancel multipath reflections using decision-feedback equalizer structures combined with preamble headers that sound the channel for the time-varying channel impulse response.

Can we arrive at any conclusions? These would be both application and implementation dependent. Single-carrier QAM operates well in many difficult channel conditions. It is quite tolerant of component impairments that cause phase noise, frequency error and power amplifier nonlinearities. On the other hand, OFDM is demonstrating its robust behavior in multipath and single-carrier interference environments. My guess is that both single-carrier QAM and OFDM will be around for a long time to come.