WiMAX, which offers high speed data access to large geographical areas — covering distances up to 30 km — is defined by the IEEE 802.16 family of standards. It uses orthogonal frequency division multiplexing (OFDM) to attain the high data rates. Consequently, the composite signal envelopes of the data bursts have significant peaks, which cause large modulation crest factors. Accurate measurement and control of WiMAX signals is challenging, due to the typically high WiMAX crest factors of 12 dB and to its susceptibility to the varying modulation patterns. As WiMAX users move towards or away from the base station, the transmitter changes the waveform composition (or modulation) to optimize data speed and reception reliability. As the waveform changes, the corresponding crest factor variation introduces RF power measurement errors.
This article describes several methods to accurately measure and control the power of WiMAX transmitters. WiMAX transmit signal paths can employ high dynamic range logarithmic amplifiers and accurate rms detectors to ensure accurate control of the transmitted signal across changing modulation types and over temperature. Some of the highlighted topics will cover the difficulties in dealing with changing crest factors and rapid envelope changes.
WiMAX Standards
IEEE 802.16, the formal specification of WiMAX, is targeted at providing broadband wireless access beyond that which is currently available using IEEE 802.11x (WLAN). 802.16-2004 (sometimes called 802.16d), the latest full revision of the WiMAX standard, focuses primarily on fixed position point-to-point or point-to-multipoint networks. The standard defines OFDM modulation, a frequency range of 2 to 11 GHz, and data rates up to 70 Mbps. OFDM modulation in 802.16d utilizes up to 256 subcarriers with bandwidths from 1.25 to 28 MHz. The subcarriers are spaced such that they are orthogonal to each other, thus reducing signal interference. The choice of signal bandwidth can be determined in multiple ways. The base station can change the signal bandwidth based on transmission distance and signal environment, or network providers may determine the bandwidth available to a user, based on various pricing plans. Figure 1 shows a basic diagram of the signal structure for an 802.16d network.
A recent amendment to 802.16-2004 focuses on the OFDMA physical layer. This updated standard, 802.16e-2005 (or Mobile WiMAX), introduces specifications that allow for mobility in a WiMAX network at speeds up to 75 MPH (120 kPH). In order to accomplish this, 802.16e increases the number of available carriers from 256 to 2048, with the BPSK pilot tones no longer at fixed intervals during each data burst. The bandwidth for each data burst includes 1.25, 5, 10 and 20 MHz. It is also possible that additional bands at 3.5, 5.5 and 7 MHz will be made available for use in Europe. While the 802.16d standard includes specifications for the entire 2 to 11 GHz band, 802.16e focuses on licensed bands below 4 GHz. Figure 2 shows how the data bursts for an OFDMA network overlap in time, as opposed to the individual bursts of OFDM. This added complexity allows for a larger number of users and handles the necessary complexity for a multi-path mobile environment. 802.16e also merges WiBro under this IEEE standard. WiBro, a Korean system for wireless broadband access, was introduced in February 2002 when the Korean government allocated 100 MHz of spectrum from 2.3 to 2.4 GHz. This band was then standardized by the Korean Telecommunications Technology Association (TTA) in late 2004. WiBro base stations offer a theoretical data rate up to 50 Mbps and cover a radius of 1 to 5 km, allowing the use of portable and mobile Internet devices within the range of a base station. Under 802.16e, WiBro is defined as one of the available system profiles and consists of 1024 subcarriers within an 8.75 MHz bandwidth.
As shown in the figures, WiMAX is transmitted using OFDM and is made up of 256 to 2048 subcarriers, each of which is modulated using BPSK, QPSK, 16QAM or 64QAM. The combination of all these subcarriers and different modulation schemes results in the potential for large peaks and troughs during each signal burst. In theory, it is possible for these extremes to fall on top of each other causing a large peak-to-average ratio (PAR) or crest factor (CF). Variations in data rate and burst length will affect the overall signal crest factor. This can cause issues even in the simplest of WiMAX systems. For example, a system which utilizes 256 subcarriers will have a theoretical crest factor of 10 log(256) = 24 dB. In practice, it is more likely to only have a peak crest factor of 12 dB because the probability that the phase of every subcarrier will add together is very low. A crest factor of 12 dB still poses significant design considerations with regards to the selection of high linearity devices (mixers, modulators, power amplifiers, etc.) in the RF signal chain. Because WiMAX systems can be used for non-line-of-sight applications, gain control of the transmitter is necessary to adjust the output TX level depending on the channel quality. It is also necessary to accurately control the power amplifier’s output in order to avoid signal clipping and increased distortion. Some systems employ crest factor reduction schemes, typically in the digital baseband processing, to minimize these effects.
RF Power Detection in the Transmit Signal Chain
Figure 3 shows the block diagram of a typical WiMAX transmit signal chain. The transmit signal path consists of three consecutive stages: digital baseband processor or digital signal processor, radio and power amplifier. A portion of the transmitted signal is sampled by the directional coupler before it reaches the antenna. The sampled RF power is delivered to the power detector where it is converted to a DC voltage. The output voltage of the power detector is digitized and fed to the digital signal processor (DSP). Once the power measurement is available as a digital level, a decision is made based on the measured output power versus the desired output power. The DSP will adjust the output power using a digital-to-analog converter to drive the signal path power control, either at the baseband, radio or power amplifier. The RF power management loop will reach a steady-state once the measured output power and the desired output power are balanced. A temperature sensor can also be introduced as an input to the DSP to add temperature compensation capabilities. This RF power management configuration is not limited to a particular application. Both base stations and subscriber stations alike may incorporate variations of this same RF power control system.
There are two basic methods by which the RF power detector and the DSP can interact to control the power of the WiMAX burst. The first method, which is similar to the technique used in envelope ramping in GSM applications, shapes the RF burst instantaneously. It uses the feedback of the detector to shape the envelope of the RF burst, made up of the preamble, frame control header and data. This envelope shaping method requires high speed detectors and fast feedback paths. A more commonly adopted method is that of output power monitoring. This method takes a power measurement during a burst and adjusts the RF power accordingly during the subsequent burst. The power adjustments are highly dependent on the linearity of the radio components to scale and shape the RF burst. A single measurement of RF output power can be affected by the high frequency components in the measured signal, which can manifest themselves as noise or AC-residual on the detector’s DC output. To mitigate this effect, multiple measurement points can be taken throughout the burst to average out the AC-residual error.
Detector Background
Historically, diode detectors have been used in RF power control circuitry to regulate transmitted power. The simple diode circuitry offers a small dynamic range with poor temperature stability. Even with temperature compensation circuitry, a diode detector can only offer a small detection range with worsening temperature performance at low input powers.
A popular alternative to the diode detector is the demodulating logarithmic amplifier (log amp). The log amp offers an easy to use linear-in-dB RF power detection response, a wide dynamic range, temperature stability and nanosecond response times. The newest RF power measurement alternative is the TruPWR rms-responding detector, which offers wide dynamic ranges and temperature stability. In addition, rms detectors are insensitive to changes in the peak-to-average ratios, whereas diodes and log amps are both waveform dependent.
Each WiMAX application has diverse power control and RF detection needs. Subscriber stations can be designed with dynamic ranges as small as 30 dB, but are susceptible to supply power consumption. Base stations have more allowance for power consumption, but need to control dynamic ranges of up to 60 dB. Both, similarly, require temperature stability for improved accuracy. Only log amps and rms detectors are able to meet those needs.
Logarithmic Amplifiers
The first detection method to be looked at is a peak-detecting device, the logarithmic amplifier. A wide variety of log amps is available with detection ranges from 40 to 100 dB, and frequencies from DC to 10 GHz. A typical block diagram of a log amp is shown in Figure 4.
The core architecture of a log amp is a cascaded chain of linear amplifiers. Each amplifier has a gain of 5 to 20 dB. The combination of gain and number of amplifiers determines the detection range of the log amp. The output of each amplifier stage is fed into a full wave rectifier (marked DET). The outputs of each rectifier are summed together, and the summer’s output is applied to a low pass filter to remove the ripple of the rectified signal. This yields the logarithmic output (often referred to as the “video” output), which will be a steady-state DC output for a steady-state AC input signal. It is the bandwidth of this video output that is particularly important in a WiMAX system. The wider the video bandwidth, the faster the log amp is able to respond to changes in the peak voltage, or amplitude, of the input signal. This makes the log amp particularly suited to accurately keep up with the envelope of the WiMAX burst. With response times as low as 8 ns, log amps can easily keep up and measure small periods of the RF burst, such as the preamble, which last about 26 ms.
Using a peak-detecting device like a log amp is advantageous when measuring the signal power of a waveform at an exact point in time. Because the log amp is able to track the envelope of its input, provided the modulation rate is lower than the video bandwidth of the log amp, the DC output will be an instant-by-instant measurement of the peak amplitude of the input signal. This kind of measurement is useful in a WiMAX system to detect high crest factor signals during a burst and make the appropriate adjustments in power amplifier biasing or implement a crest factor reduction scheme in the next burst. Figure 5 shows the output voltage and linearity error of a log amp at various 2.35 GHz OFDM modulations, 256 subcarrier signals with 10 MHz bandwidth. The error, normalized to QPSK with 3/4 encoding rate, is graphed on the secondary y-axis, scaled in dB. While the log amp is able to maintain approximately 50 dB of measurement range within ±1 dB or error for each modulation, there is an obvious shift in the intercept of the transfer function. The intercept is the point on the x-axis through which the transfer function would pass if the output voltage could go to 0 V. This intercept shift is a byproduct of the successive detection architecture of a log amp. The amount of intercept shift is based on the crest factor of the signal. Because the log amp behavior is repeatable over manufacturing process variations, the intercept shift of the log amp for a sine wave versus a modulated input signal can be easily characterized. The DSP can then use an offset correction to compensate for the detector’s output voltage and yield accurate RF power measurement.
The low power consumption, of the order of 15 to 30 mA, makes log amps viable in both base stations and subscriber stations alike. The well-established log amp architecture offers excellent temperature stability across large dynamic ranges as well as fast response times for burst tracking and peak sampling. However, as the peak-to-average ratio of the RF signal varies, the output response of a log amp will also vary. This introduces an uncertainty that in many cases must be compensated for by the DSP.
RMS-responding Detectors
Unlike diodes and log amps, mean power detectors (or rms detectors) have responses which are independent of waveform. The waveform-independence is particularly useful as WiMAX systems optimize the quality of the link by dynamically adjusting the signal modulation. The composite signal envelopes of the data bursts may have significant peaks that can drastically change over time and throw off measurement accuracy. Using log amps in the RF power control system require some method of compensation; however, rms detectors simplify the complexity of the system by reducing and in some cases eliminating compensation schemes.
Figure 6 shows the block diagram of a 30 dB rms detector. It achieves independence from peak-to-average ratios by computing the square, mean and root functions of an rms calculation. The RF input is fed to one of two identical squaring-cells. The squared signal is then averaged through a low pass filter network. The signal is fed to a high gain error amplifier that has the second squaring-cell in its feedback path. This feedback loop performs the square-root function, thus completing the rms calculation. The output is a linear-responding DC voltage whose conversion gain has units of VDC/Vrms. The linear-in-volts rms detector is able to operate at frequencies as high as 6 GHz. The rms-responding detector allows the RF power control system to monitor and dynamically adjust the transmitter’s output power even as the peak-to-average ratio of the transmitted signal changes. Figure 7 illustrates the accuracy in measuring various OFDM waveform types. The method used to calculate the error is similar in nature to that used in the log amp error calculation. The linearity error of the detector is within ±0.5 dB across the dynamic range of the device. The various waveforms lie on top of each other with a deviation of a couple tenths of a dB. This 30 dB dynamic range and low 1 mA power consumption is useful for subscriber applications. The slower response time, in the range of 25 μs, limits the rms detector use to output power monitoring. Figure 8 shows the block diagram of a 60 dB rms detector, which is appropriate for wider dynamic range base station applications. The input signal is applied to a 12-step, continuously variable gain amplifier, which is controlled by the setpoint, a logarithmic control voltage. The output of the VGA is fed to an accurate squaring-cell. The fluctuating output is filtered and compared with the output of an identical squarer. At this point, the square and mean operations of the rms calculation are complete. The output is fed back to the VGA setpoint, making the output proportional to the logarithm of the rms value of the input. The detector response is linear-in-dB, allowing the device to measure RF signals in a 60 dB dynamic range. The final step of performing the square-root function is not needed for accurate rms detection. Figure 9 shows the performance of the 60 dB rms detector when measuring various OFDM modulated input signals. Again, the various waveforms lie on top of each other with negligible deviation. The humps in the linearity error curve correspond to the steps of the logarithmic VGA. Still, the linearity error across the dynamic range stays well within ±0.5 dB. As in the case of the linear-in-volts detector, the 70 μs response time of this 60 dB detector also limits this detector application to output power monitoring.
Conclusion
The emerging WiMAX standard has great potential to offer wide area coverage and mobile access to high speed networks. The large crest factors associated with the OFDM modulation scheme require accurate transmit power measurements for PA control and the implementation of crest factor reduction algorithms. Designs requiring fast response to the OFDM envelope should consider the accuracy of log amps. The waveform-independence provided by rms detectors can reduce, or even eliminate, the need for compensation schemes in these networks, simplifying the overall design of the transmit chain.
Carlos Calvo received his BS and MS degrees in electrical engineering from Worcester Polytechnic Institute. He is an applications engineer in the Advanced Linear Products Division at Analog Devices Inc.
Matthew Pilotte received his BS degree in electrical engineering from Worcester Polytechnic Institute. He is an applications engineer in the Advanced Linear Products Division at Analog Devices Inc.
