Multicarrier modulation schemes are gaining momentum in the communications marketplace due to bandwidth efficiency. In particular, orthogonal-frequency-division-multiplex (OFDM) systems allow carriers to be very tightly packed by maintaining strict orthogonality between the various signals across the band. Efficient digital-signal-processing (DSP) implementations of the required signal processing are making this modulation type fast and cost-effective for use in consumer systems. This complex modulation scheme does present some design challenges, however. Fortunately, modern simulation tools can be used to solve some of these design challenges.
Frequency-domain multiplexing using orthogonal carriers was first proposed by Chang.1 Many independent data channels could be packed into a surprisingly small bandwidth. Orthogonality prevents the carriers from interfering with each other, thus obviating the need for guard bands. Although this technique promised great improvements in effective transmission rates, its cost and size limited OFDM to military applications for many years. One of the first OFDM modems was designed for military high-frequency (HF) radios.2 Recently, advances in electronic components and hardware have enabled this and other communications technology, such as code-division multiple access (CDMA), to enter the commercial world.
OFDM is something of a misnomer, since the transmission technique is often employed to spread a single data stream over a band of carriers, with substreams transmitted in parallel. The IEEE 802.11a data transmission standard is designed to carry packetized data over parallel channels at information rates approaching 12 b/s/Hz. The spectrum of an IEEE 802.11a signal is shown in the center of Fig. 1. In IEEE 802.11a wireless-local-area-network (WLAN) systems, 12 carriers at the ends of the spectrum are left "unloaded" to produce a power-spectral density with a steep decline at the band edges.
The high rate efficiencies associated with IEEE 802.11a are made possible through the use of high-order modulation schemes being applied to the individual carriers. Quadrature-amplitude modulation (QAM) of various levels is applied to each carrier. The modulation is normally applied to 64 carriers simultaneously with a computationally efficient Inverse Fast Fourier Transform (IFFT).3 Demodulation can be performed with the FFT. Data-transmission rates corresponding to various options for modulation and coding are shown in the table. These rates are for the HiperLAN 2 standard which employs IEEE 802.11a as the basic modulation type.
Whereas OFDM offers potential for high-data-rate transmission, it also requires additional signal processing for synchronization and other auxiliary receiver (Rx) functions. Some disadvantages of OFDM include susceptability to oscillator phase noise and sensitivity to transmission amplitude/phase distortion. The following section will briefly explore this latter issue.
In an IEEE 802.11a system, data is transmitted in frames, with each frame containing a header which is used for synchronization and control. Although the full description of the header is beyond the scope of this article, suffice it to say that the header contains a correlation word for detection of the start of the frame and also an embedded pilot sequence used for "sounding" the amplitude/phase variation across the wideband OFDM channel.
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The 64 carriers correspond to 48 data channels, 12 unloaded guard channels, and 4 pilot channels. The pilot channels are equally spaced across the OFDM bandwidth, providing the capability to equalize in separate sub-bands. These pilot data are transmitted continuously, interleaved into the modulation stream entering the IFFT. Although data modulation can take many formats, pilot channels and header symbols are transmitted with quadrature-phase-shift-keying (QPSK) modulation.
The purpose of "sounding" the channel is to estimate systematic amplitude/phase variations across the OFDM bandwidth. Since IEEE 802.11a systems have such a large bandwidth, even a small amount of linear distortion imposed upon the signal can cause the various channels to be misaligned in amplitude/phase. This can wreak havoc on the detection process, since in-phase (I) and quadrature (Q) outputs from all channels are serialized and overlaid in the QAM scatter diagram. It is for this reason that equalization becomes critically important for 802.11a-based systems. Figure 2 illustrates a simplified block diagram of an IEEE 802.11a system simulation employing equalization.4 As mentioned earlier, amplitude/phase distortion can present problems in the demodulation/detection process. This distortion can occur over the environmental transmission channel.
This type of distortion can also occur even in various filters placed within the transmission chain by the system designers. Furthermore, filter characteristics can change with time or may not be known before a signal is received (e.g., the precise characteristics of a transmit filter are not known to the Rx). For this reason, equalization requires that the overall transmission channel frequency characteristics be measured and corrected on a dynamic basis. Fortunately, frequency-domain equalization is relatively simple and is efficiently implemented in OFDM systems. The purpose of the sounder in Fig. 2 is to use the known sounding or training sequence to estimate the variation in amplitude/phase in the various channels. The result of this operation is a vector of complex numbers, or coefficients, that represent the estimated amplitude/phase for each channel. These estimates can be used by a simple equalizer, which only performs a channel-by-channel complex multiplication against the inverse of the complex amplitude/phase estimates. As is the usual case on fading channels, certain frequencies can exhibit low amplitudes, or spectral "nulls." In this situation, information about the reliability of these frequency channels can be passed on to error-control-decoding algorithms. Many coding schemes can accept "soft-decision" information to make better estimates of the original transmitted bits, even in severe fading.
Figure 3 shows the effect of amplitude/phase distortion on the demodulated scatter diagram of an IEEE 802.11a signal operating in 64QAM mode. The signal points shown in squares represent the ideal, or nominal constellation points. These points are actually collected at the output of the equalizer. In this simple experiment, the simulation was run with no noise or fading, so the sounder could obtain perfect estimates of channel amplitude/phase variations. In this experiment, the amplitude/phase variations were created by the introduction of a seven-pole Butterworth filter at the transmitter (Tx) output. The filter amplitude and group-delay response is shown overlaid on the 802.11a spectrum in Fig. 1. The response corresponds to a nonideal Butterworth implementation where some of the resonators have a noninfinite quality factor (Q). This response is generated from a circuit model that runs simultaneously with the communication-link simulation. Although the filter band edges are well-outside the IEEE 802.11a signal spectrum, even the small amount of group-delay distortion within the IEEE 802.11a transmission band causes problems with constellation phase skew. This effect is evident in the unequalized scatter plot, shown as triangles, in Fig. 3. In practice, equalization will not be perfect, since the channel sounder must estimate the channel characteristics in the presence of noise. Even if noise is limited to additive white Gaussian noise (AWGN), the estimated equalization coefficients will have some inaccuracy.
Software simulations can also be used to model performance in the nonideal situation of an AWGN channel. An error rate plot can be created where Es is the energy transmitted per data channel and N0 represents the channel-noise power spectral density, normalized to an individual data channel. With such normalization, ideal symbol error probability will be the same as ordinary QAM. In using the software to generate a plot, a bound on ideal symbol-error probability for 64QAM can be overlayed on the simulated results. When such simulations were performed (results not shown here) the error probability for the unequalized system hangs up at a high value, as expected. The error probability for the equalized system is close to ideal, although there is some performance loss due to nonideal equalization.
In summary, the Visual System Simulator 2002 software from Applied Wave Research (El Segundo, CA) can be used to effectively reveal and diagnose potential pitfalls in communication-system designs. This is only possible, however, when software tools provide not only extensive application-specific libraries, but also links to practical hardware models. Only in this case can realistic operational scenarios be accurately assessed.
REFERENCES
- R. Chang, "Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission," BSTJ, Vol. 46, pp. 1775-1796, December 1966.
- M. Zimmerman and A. Kirsch, "The AN/GSC-10/KATHRYN Variable Rate Data Modem for HF Radio," IEEE Transactions on Communications Technologies, Vol. COM-15, pp. 197-205, April 1967.
- S. Weinstein and P. Ebert, "Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Fourier Transform," IEEE Transactions on Communications Technologies, Vol. COM-19, pp. 628-634, October 1971.
- Visual System Simulator Modeling Manual, Applied Wave Research, Inc., El Segundo, CA.