WiMAX signals suffer from the effects of multipath and exhibit broadband fading characteristics that are very apparent in the spectrum of the received WiMAX signal (see Figure 1). It’s not a trick; OFDM modulation does not eliminate fading and is not always received with a flat spectrum. Processing of the received OFDM signal can flatten the spectrum with a relatively simple channel estimator.

Multipath, delay spread inter-symbol interference and the cyclic prefix all determine the complexity of, and the performance of the algorithms needed at the receiver to flatten the spectrum. Let’s examine and differentiate these and how they apply to WiMAX.

##### Considering the Effects of ISI

click to enlarge Figure 1. A BVS YellowFin™ spectrum shot of an 802.16e signal propagating through a broadband fading channel due to multipath. |

Combining any number sinusoids of the same frequency with any arbitrary phase still results in a sinusoid of the same frequency, but it may have a different amplitude and phase. These sinusoids, the RF carriers, are OFDM modulated in both amplitude and phase to carry data and this modulation requires that we also consider the effects of ISI, if present, on the received spectrum.

click to enlarge Figure 2. A YellowFin™ multipath display. This multipath creates the broadband frequency selective fading shown in Figure 1. |

The WiMAX system must be set-up so that Tcp > Td and ISI is not present. If ISI exists, the receiver would need knowledge of both the multipath and the data modulated onto the RF carrier to flatten the received spectrum, and this requires a more complex equalizer that typically suffers from poorer performance when compared to a system that does not need to correct for ISI.

##### Mobile WiMAX 802.16e

Figure 1 is a spectrum plot of a received 802.16e Mobile WiMAX downlink signal experiencing broadband fading. This frequency selective fading is quite severe, over 10 dB, in some frequency bins. The spectrum data was a “snap-shot” and synchronized exactly across one OFDM symbol of a WiMAX packet. A channel frequency response estimate is calculated from reference signals that are placed into WiMAX packets.Mobile WiMAX 802.16e has several reference signals that can all be used for channel estimating. The preamble index is contained in 1 OFDM symbol at the start of a packet and pilot subcarriers are placed on a few subcarriers per OFDM symbol, but throughout the WiMAX packet. These reference codes are known as a priori and are compared to received frequency bins that contain the reference code. A channel estimate is generated for each frequency bin that contains a reference code. Bins that do not contain a reference code are interpolated to calculate a complete channel estimate for all frequency bins.

The channel estimator may use linear interpolation across the frequency bins, interpolation across frequency bins and time (successive channel estimates) or adaptive estimates that also require some statistical knowledge of the channel. The channel estimate for each frequency bin is then multiplied onto the received signal’s corresponding frequency bin to correct for both amplitude and phase.

Multipath has faded the signal strength of some frequency bins due to destructive combining (see Figure 1.) The channel estimate may perfectly correct the magnitude and phase of each subcarrier, but subcarriers that are received (assuming equally distributed noise across the band) with lower signal strength will have a lower carrier-to-interference plus noise ratio (CINR), since both the signal and noise are amplified. This is one reason why WiMAX utilizes interleaving and forward error correction (FEC).

##### Conclusion

The delay spread in a WiMAX system must be less than the length of the cyclic prefix (Td Tcp) to avoid ISI. WiMAX channel estimators are designed to correct for the effects of multipath and ISI will compromise WiMAX performance.Multipath can reduce the signal strength of frequency bins that experience a fade and compromise performance since the bins experiencing the fade (assuming uniform noise across the band) will have a lower CINR.

CINR, multipath and delay spread are all important measurements for deploying, debugging and optimizing WiMAX networks.

Ray Chadwick is Chief Engineer at Berkeley Varitronics Systems, Inc, in Metuchen, NJ.

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