Wireless applications using WiMAX high-date-rate technology are poised for growth in the next several years. Based on orthogonal-frequencydivision-multiplexing (OFDM) techniques, WiMAX holds the promise of broadband wireless access (BWA) as part of the "last mile" of multimedia services networks. Last month, this three-part article series on WiMAX testing opened with a review of the WiMAX physicallayer (PHY) and media-access-control (MAC) protocols as outlined in the IEEE 802.16-2004 standard, and the fundamental features of a baseband transceiver for WiMAX. In this second part, a baseband WiMAX receiver will be proposed, along with the key algorithms for its various measurement capabilities.

Last month, various elements of the WiMAX baseband receiver model were introduced, including the effects of inphase/quadrature (I/Q) gain imbalance (see Fig. 7 from Part 1, Microwaves & RF, July 2006, p. 76) and the effects of quadrature error (see Fig. 8 from Part 1, Microwaves & RF, July 2006, p. 76). In the baseband transmitter and channel model, the effects of I/Q origin offset and I/Q gain imbalance are introduced into time-domain signal as:

When Iscale = Q_scale, the I/Q imbalance will be zero. When both I_of and Q_of are zero, there is no I/Q offset. Figure 7 shows the effect of IQ gain imbalance in the constellation of the received symbols.

Quadrature skew error indicates the orthogonal error between the I and Q signals. Ideally, I and Q channels should be exactly orthogonal (90 degrees apart). When the orthogonality is not ideal (less or more than 90 deg. apart, or 90 ± , then a quadrature error can be observed. In the baseband signal model, the Q offset is introduced into the time-domain signal as:

where:

α = the quadratic error.

When α is equal 0 deg., y_m(n) will be equal to x_m(n) (no quadrature error). Figure 8 shows the effect of quadrature error in the constellation of the received symbols.

The received signal can be modeled (without the I/Q impairments) as:

where:

= the common phase error which could be caused by the remaining part of frequency offset (after frequency-offset compensation) and other possible sources as described earlier;

θ_m(k)^{carrier dep} = the carrier-dependent phase rotation which is mainly caused by sample timing offset; and

Γ_m = the common gain offset which can be due to the variation of the gain of the amplifiers.

All the other noise sources are either folded into the AWGN term , zm(k), (if additive) or into the channel-frequency response, H(k), (if multiplicative).

Figure 9 shows a block diagram of the proposed WiMAX test receiver. The receiver is designed for test and measurement purposes, and there are some differences from the actual receiver algorithms that would be used in a WiMAX product. Note also that the receiver is a digital baseband receiver that processes the I/Q data that is provided by the analog front end of any receiver or vector signal analyzer. The received signal is also passed through the channel emulator to add the desired impairments (for test purposes) that are mentioned above. Therefore, the received signal represents I/Q samples that include the possible impairments due to the actual hardware (at the transmitter and receiver front-end) as well as the intentional impairments that are included in the channel emulator.

The transmitter can be any signal source that is transmitting standard WiMAX signals. It can be a vector signal generator (VSG) or a simulator. The authors have developed a standardsbased digital baseband transmitter in MATLAB software in order to test WiMAX performance in stand-alone mode. The simulated transmitter includes functions like channel coding, all possible modulation (BPSK, QPSK, 16QAM, 64QAM) and coding options (except turbo coding), all possible cyclic prefix options, uplink and downlink burst generation, all possible sampling rate and bandwidth options, flexible number of symbols within a burst, and ability to generate random and standard test data. However, as mentioned above, it is not necessary to use the transmitter simulator. The main goal is to test third-party transmitter products with the proposed receiver. However, it is desirable to have the option of using synthetic data from the simulated transmitter as well for debugging and cross-checking purposes. No matter which transmitter is used, as long as it is a IEEE 802.16-2004 standard based transmitter, the proposed receiver is designed to function properly, and all the blocks that are necessary to test and measure the transmitter quality are included as shown in Fig. 9.