Performance Improvements Achieved by Equalizing Intermediate Rate FSK Signals

Presented at the 23rd Asilomar Conference on Signals, Systems and Computers
November 2–5, 1998

FSK modems are commonly used for transmission of intermediate data rate signals (1–8 Mbps) in the microwave bands. Link performance can be limited when operating in multipath environments. This paper investigates the performance gains achieved by using equalization and post FM discriminator adaptive filtering for FSK signals to mitigate the effects of multipath. Performance is compared to non-equalized transmissions over a variety of multipath channels.

FSK modems are finding many applications for the transport of intermediate data rate signals (1–8 Mbps) in the telecommunications industry such as short-haul links between cellular basestations and Mobile Telephone Switching Offices (MTSO). FSK modulation is used because cheap, non-linear power amplifiers can be used at the transmitter. The power amplifier is often one the most expensive components in the modem.

As with any radio transmission, FSK signals are subject to multipath distortion. The distortion severity depends on the geometry and geography of local terrain and man-made structures. The FM capture effect provides some margin against multipath, depending on the FM modulation index and the complexity of the demodulator. However, increasing the transmit power has little or no impact because the level of the multipath components are proportional to the transmitted signal power.

This paper explores the performance gains achieved by equalizing FSK signals prior to FM discrimination as well as using post-D adaptive filtering. Adaptive equalization and filtering are routinely used to improve the performance of PSK and QAM modems that operate in multipath environments and is a natural extension of well-established techniques.

Optimum performance for FSK signals is achieved using maximum likelihood sequence estimation [1, 2] but is expensive to implement. Near optimum performance is achieved by match filtering the signal prior to detection [1]. Equalizers provide an estimate of the matched filter and adaptive equalizers, based on decision-directed algorithms, are typically used to track changes in the multipath channel characteristics. Adaptive equalizers also provide another subtle benefit. They allow the use of cheaper, wider tolerance components in both the transmitter and receiver that may change value with time or temperature so could degrade link performance if not compensated. An adaptive equalizer will track these changes minimizing performance degradations and depending on the implementation details, the cost saving achieved by using cheaper parts may more than pay for the additional cost of implementing an adaptive equalizer while providing superior performance.

Before discussing the candidate FSK receivers, we first review FSK transmission systems to define some terms. Figure 1 shows a top level block diagram of an FSK modem. The input data is first mapped to symbols by demultiplexing the data into n-tuples and choosing the appropriate symbol. Typically n=1, 2 and 3 corresponding to 2, 4 and 8-level FSK.

Figure 1. Top level block diagram of an FSK transmission system.

The output of the symbol mapper is 1 of

possible levels. Next, the signal is FM modulated, frequency translated to RF and transmitted. At the receiver, the signal is frequency translated from RF to IF, filtered and FM demodulated (also called FM discriminated) to recover the transmitted symbol stream. Finally, the transmitted symbols are remultiplexed into the received data stream by the symbol-to-bit mapper.

The characteristics of the transmitted signal are dependent on parameters associated with the FSK modulator. Figure 2 shows a block diagram of an FSK modulator where the input signal is either 2-, 4- or 8-level impulses separated by the baud period, T. It is first filtered by v(t) to control the bandwidth of the baseband signal which, in turn, partially controls the FSK signal spectrum. The filter output signal level is then adjusted and input to a phase modulator. The phase modulator centers the signal at frequency

. The choice of a controls the frequency deviation,

, away from the center frequency for each symbol. Different choices of the lowpass filter characteristic and signal gain, a, control the signal bandwidth and intersymbol interference (ISI) on the baseband signal. A common filter characteristic uses a rectangular pulse shape. It does not cause ISI but the bandwidth is relatively wide. Another choice is to use a Nyquist filter [1] that introduces controlled ISI but complicates the demodulator timing recovery. More aggressive filtering, such as Gaussian filters, provide very good bandwidth control but require ISI compensation in the demodulator. Note that baseband-filtering-induced ISI is different from multipath-induced ISI that causes distortion on the FM signal rather than the baseband.

Figure 2. Block diagram of an FSK modulator.

Figure 3 shows three architectures with increasing complexity that we investigated. Architecture #1 filters the signal with a fixed IF filter followed by an FM discriminator and slicing at the appropriate baud instant, usually accomplished with a bit sync. Architecture #2 adds a decision-directed adaptive (post-D) filter [3] before the slicer. Architecture #3 adds an adaptive IF (pre-D) filter prior to FM discriminating. The pre-D filter is driven by the CMA algorithm [4] to compensate for the multipath. Multipath distorts the constant envelope property of FM signals. The CMA algorithm adapts the filter taps to minimize envelope fluctuations. Other architecture variations such as using just the pre-D filter and eliminating the post-D filter could be, but have not been, considered.

Figure 3. Demodulator architectures under consideration.

We evaluate the performance of the demodulator architectures against a number of different multipath channels. Figure 4 shows the frequency amplitude response and the log of the impulse response envelope. Channels (a), (b) and (c) were derived from snapshot data of real channels. The channels represent mild (a), moderate (b), severe, long delay (c) and severe, short delay (d) multipath environments. A channel with no multipath is an impulse. A single multipath ray would manifest itself as a second impulse somewhere away from the main impulse. The relative time delay indicates the additional transport time of the reflection. The log of the impulse response envelopes in Figure 4 show that there is multipath both before and after the main arrival, the strongest impulse. For moderate and severe channels, there is substantial multipath delay as evidenced by the impulse response. The multipath components are manifest in the frequency amplitude response by the scalloping of the passband. The severe, long delay channel (c) shows both a coarse and fine scalloping corresponding to the short and long delay multipath components. The roll-off is an artifact of the receive filtering in the snapshot collection equipment. The signal bandwidth is within the passband of the channels.

Figure 4. Mild (a), moderate (b), severe, long delay (c) and severe, short delay (d) multipath channels.

We evaluated the performance of the demodulator architectures for operation against data transmitted through the channels. The transmitted signal was a 4-level FSK signal filtered with a 50% square-root-raised-cosine (SRRC) baseband filter. We measured performance using the cluster variance which is the mean-squared-error between the transmitted symbol and the signal input to the “slicer” at the proper baud phase. We used 64 tap FIR filters for the post-D and pre-D filters. The signal was sampled at 4 samples/baud.

The results are shown in Figure 5. When the cluster variance >–5 dB, the signal could not be recovered. For the case where this is no multipath, architecture #1 is useless for SNR <17 dB. Architecture #2 and 3 are capable of recovering signals for SNR’s as low as 10 dB and the cluster variance decreases as a function of the SNR. Similar performance is seen for the mild multipath channel (G401). For the G401 channel, architecture #3 outperforms architecture #2 only when the SNR >16 dB because the additive noise dominates the multipath-induced ISI component when the SNR <16 dB.

Figure 5. Performance of demodulator architectures SNR and multipath channels.

For the moderate and severe, long delay multipath channels, architecture #1 is useless. Architecture #2 and 3 performance is about the same because the pre-D filter does not have enough filter taps to compensate for the multipath delay of these channels. It surprising how well architecture #2 actually does, even for the long delay multipath channels.

Performance against the short delay, severe multipath channel illustrates the power of architecture 3. The multipath delay is substantially shorter but the multipath reflections are quite strong. Architecture #2 is useless while architecture #3 does provide some margin of recovery against this channel.

This paper investigated the application of pre-D equalization and post-D adaptive filters to the recovery of FSK signals in multipath environments. We evaluated three architectures against mild to severe multipath channels in low to moderate SNR’s. Architecture #2 did surprisingly well against multipath, even long delay multipath. Architecture #3 did not perform any better than architecture #2 for long delay multipath. However, for short delay but severe multipath, architecture #3 was able to recover the signal while architecture #2 was not.