Wireless Measurement Definitions
Introduction
The following sections briefly describe the most commonly used measurements in transmitter and receiver testing for WLAN, TD-SCDMA, and 3GPP FDD.
- Transmission Test Measurements
- Receiver Test Measurements
Transmission Test Measurements
RF Envelope
The RF envelope measurement shows the magnitude of the RF signal's envelope versus time. By observing a signal's RF envelope versus time you can see the signal's frame/burst structure. Some wireless standards specify a mask, to which the signal's RF envelope must conform. The mask is typically specified during the ramp up and ramp down transient of the signal.
Constellation
The constellation measurement shows in a graphical way the general quality of a signal. For a more accurate measurement of a signal's modulation quality an EVM analysis must be performed.
A constellation measurement is most appropriate when a QAM modulation scheme is used (directly or indirectly; for example WLAN 802.11a uses OFDM modulation, where a set of subcarriers is modulated using some QAM scheme). An ideal QAM signal will have a constellation that consists of a set of distinct points on the IQ plane. The following figure shows the constellation for an ideal 16-QAM signal. This constellation has 16 points and is symmetric around the X and Y axes. All points are equally spaced.
Constellation for Ideal 16-QAM Signal
Different signal distortions modify the ideal constellation in different ways and so by looking at the constellation you can get some idea of what types of distortions are present in the signal. The following five illustrations show some examples of how signal distortions appear in the constellation.
The following figure shows the constellation for a 16-QAM signal with gain imbalance. This can be deduced by the fact that in the ideal constellation the span of the points across both axes is the same (approximately 0.425), whereas in the constellation with the gain imbalance the Y axis has a bigger span (approximately 0.475).
Constellation for 16-QAM Signal with Gain Imbalance
The following figure shows the constellation for a 16-QAM signal with phase imbalance. This can be deduced by the fact that in the ideal constellation the points are lined up parallel to the X and Y axes, whereas in the constellation with the phase imbalance the points are lined up parallel to the X axis but not to the Y axis.
Constellation for 16-QAM Signal with Phase Imbalance
The following figure shows the constellation for a 16-QAM signal with ISI (intersymbol interference) and AWGN (additive white gaussian noise). Notice that instead of 16 distinct points there are 16 clusters of points centered around the ideal 16-QAM points.
Constellation for 16-QAM Signal with ISI and AWGN
The following figure shows the constellation for a 16-QAM signal with gain compression (from a nonlinear amplifier). Notice how the outer points (especially the four corner points) that have the highest power have been compressed (moved closer to the center of the IQ plane).
Constellation for 16-QAM Signal with Gain Compression
The following figure shows the constellation for a 16-QAM signal that includes all of the distortions discussed above.
Constellation for 16-QAM Signal with Multiple Types of Distortion
Power
The power measurement is a set of power-related measurements that provides information about a signal's statistical properties. The power measurement includes:
- Power vs. Time shows the instantaneous signal power versus time. Some wireless standards specify a mask, to which the signal's instantaneous power versus time waveform must conform. The mask is typically specified during the ramp- up and ramp-down transient of the signal.
- Total (Average) Power is the average signal power over the measurement duration. For signals that are transmitted in bursts or in slots this measurement should be performed only when the signal is active (on) and not during the idle intervals or inactive slots.
- Peak Power is the maximum instantaneous signal power over the measurement duration. Some standards define the peak power not as the absolute maximum instantaneous signal power but as the power level that is exceeded only for a small percentage (e.g. 1%) of the time.
- Peak to Average Ratio is the ratio of the peak signal power to the average signal power.
- Power Complementary Cumulative Distribution Function is defined as CCDF = 1 - CDF, where CDF is the cumulative distribution function of the signal's instantaneous power. If the probability density function of the signal's instantaneous power is p(x), then
The power CCDF curve shows the probability that the instantaneous signal power will be higher than the average signal power by a certain amount of dB. The X axis of the CCDF curve shows power levels in dB with respect to the signal average power level (0 dB corresponds to the signal average power level). The Y axis of the CCDF curve shows the probability that the instantaneous signal power will exceed the corresponding power level on the X axis.
The following figure shows the CCDF curve for a WLAN 802.11a 54 Mbps signal. In the figure, you can see that the instantaneous signal power exceeds the average signal power (0 dB) for approximately 20% of the time. You can also see that the instantaneous signal power exceeds the average signal power by 5 dB for only 0.7% of the time.
For signals that are transmitted in bursts or in slots this measurement should be performed only when the signal is active (on) and not during the idle intervals or inactive slots.
Power CCDF Curve for a WLAN 802.11a 54 Mbps Signal
- Code Domain Power (CDP)
For signals that use Code Division Multiple Access (CDMA) techniques, CDP is another useful power measurement. CDP shows the distribution of the signal's power in the code domain. The following figure shows the results of a CDP measurement for a 3GPP FDD Test Model 3 signal (based on 2000-12 version of the standard) with 16 DPCHs.
CDP Measurement for 3GPP FDD Test Model 3 Signal with 16 DPCHs
In the preceding figure, you can clearly see the 16 active DPCHs (occupying codes in the 64 to 128 range), as well as the primary CPICH (code 0), the P-CCPCH+SCH (code 1), and the PICH (code 16).
Spectrum
The spectrum measurement shows the spectrum of a signal that is the distribution of the signal's power in the frequency domain. Most wireless standards specify a mask, to which the signal's spectrum must conform. The need for the transmitted signal spectrum to conform to a spectral mask is so that the interference to adjacent channels is minimized and kept at acceptable levels. The following figure shows an example of a spectrum measurement and a spectral mask for a WLAN 802.11a signal.
Spectrum Measurement and Spectral Mask for WLAN 802.11a Signal
Some wireless standards specify additional spectrum related measurements. For example, the 3GPP FDD standard defines the following spectrum measurements:
- Adjacent channel leakage ratio (ACLR) is the ratio of the transmitted power to the power measured after a receiver filter in the adjacent channel(s).
- Occupied Bandwidth is the bandwidth that contains 99% of the signal's total transmitted power. The bandwidth is centered around the channel frequency so that the total power outside this bandwidth is split equally (0.5% of the total transmitted power) between the bands below and above it. The following figure shows the definition of the occupied bandwidth.
Occupied Bandwidth Definition
EVM
The EVM (error vector magnitude) measurement provides a metric for the modulation quality/accuracy of a signal. EVM is a measure of the difference between the measured signal and an ideal reference signal. While EVM may be defined differently in each wireless standard, the basic concept is described here.
Let S(k), k = 1, ..., N, be the ideal transmitted signal sampled at one sample per symbol (or chip) at the optimal (zero-ISI) instance. The actual transmitted signal can be modeled as
where:
W = e Dr+jDa, accounts for both a frequency offset (Da radians/symbol phase rotation) and an amplitude change rate (Dr nepers/symbol)
C 0 is a complex constant representing origin offset
C 1 is a complex constant representing the arbitrary phase and output power of the transmitter
E(k) is the residual vector error on sample S(k)
The sum square error vector is
where C 0, C 1, W are chosen such as to minimize the above expression.
EVM (rms) is defined to be the rms value of |E(k)| normalized by the rms value of |S(k)|. Therefore,
In addition to the EVM rms value, the EVM analysis provides other useful results, such as:
- Peak EVM
- Symbol (or chip) where the peak EVM occurs
- rms magnitude error (difference between the magnitudes of the ideal and reference signals)
- Peak magnitude error
- Symbol (or chip) where the peak magnitude error occurs
- rms phase error (difference between the phases of the ideal and reference signals)
- Peak phase error
- Symbol (or chip) where the peak phase error occurs
- Frequency error
- IQ offset (some wireless standards do not remove IQ offset from the measured signal and so this type of distortion is included in the EVM value)
For signals that use code division multiple access (CDMA) techniques, peak code domain error (PCDE) is another useful measurement related to EVM. To get the PCDE value, the error vector E(k) is first projected on the code domain. This is done by calculating the inner-product between E(k) and all the orthogonal vectors in the channelization code set (all codes belonging to the one spreading factor). Then the maximum projection is selected and normalized by the rms value of the reference signal.
Receiver Test Measurements
BER Measurements
A receiver's performance is determined by its ability to receive and demodulate a wanted signal in the presence of noise and/or other interfering signals. Although there are several measurements used to test a receiver's performance, all of them measure the same quantity under different conditions. The measured quantity is the bit error rate. BER is the probability that a transmitted bit will be received and detected in error. Of course, better receivers have a lower BER.
Different wireless standards give different names to various BER measurements such as: Minimum Input Power Sensitivity, Minimum Input Level Sensitivity, Adjacent Channel Rejection, Adjacent Channel Selectivity, Reference Sensitivity Level, Dynamic Range, Blocking, Intermod. As mentioned earlier, all the above measurements are BER measurements under different conditions. These different conditions include additive white gaussian noise (AWGN), modulated interference signals, and CW interference signals. The interference signals can be in band and/or out of band. Typically, the standards specify that the BER should not exceed a certain value for certain power levels of the wanted and interfering signals, and a certain frequency offset (between the wanted signal's channel frequency and the frequency of the interfering signals).
E b /N o Definition
Bit error rate (BER) and frame and packet error rate (FER/PER) are typically reported with respect to E b /N o. This note defines E b /N o and relates it to signal to noise ratio (SNR). Distinction is made of local and system E b /N o. The following discussion is based on similar discussions published by Bernard Sklar (see Eb/No References).
For this discussion, the following figure illustrates a typical RF comm system receiver block diagram.
Typical RF Comm System Receiver Block Diagram
In the diagram above:
- The initial two blocks represent the transmitted signal and the propagation channel between the transmit and receive antennas. The transmitted signal contains data with bit time T b with bit rate R bits/sec. The propagation channel includes significant attenuation and propagation effects (phase, amplitude, multi-path fading, etc.).
- A is the receiver antenna output.
- B is a mid point within the receiver system.
- C is the receiver system pre-detection point.
- RX DUT 1 is the receiver RF frontend and contains any lossy lines before the receiver and receiver front-end amplifiers, filters, and mixers. For this discussion it is defined with gain in dB (G 1 ) and noise figure in dB (NF 1 ).
- RX DUT 2 is the receiver backend and contains content before detection and includes amplifiers, filters, matched filter, and sampler. For this discussion it is defined with gain in dB (G 2 ) and noise figure in dB (NF 2 ).
- BER is then measured, typically with suitable DSP algorithms.
At each A, B, and C point in the system, there is a measurable value for the signal (S A, S B, S C ) and noise density (N OA, N OB, N OC ), where the signal is in Watts (W) and noise density is in Watts/Hz (W/Hz).
In this system (and for discussion purposes) the received desired signal has additive thermal noise contributions from the propagation path available at the receiver antenna output and from the receiver noise figures. Other noise contributors are ignored, such as interfering signals and nonlinear intermodulation products.
Thermal noise at the receiver antenna output is typically defined in terms of noise temperature in Kelvin. Call this T A. Note that 290 K (16.85 o C) corresponds to a noise power density of -173.975 dBm/Hz value.
The receiver antenna output noise power density is:
N 0A = k T a, where k is Boltzmann's constant.
Receiver noise figures can also be represented in terms of noise temperature in Kelvin: T = 290 (F-1) where F = 10 (NF/10).
The RF DUT 1 and 2 have associated noise temperatures at T 1 and T 2 respectively.
T 1 = 290 (F 1 -1); F 1 = 10 (NF 1 ^/10)
^ T 2 = 290 (F 2 -1); F 2 = 10 (NF 2 /10)
T 1 represents the equivalent noise temperature due to RF DUT 1 defined at the input of RF DUT 1 and has associated noise power density: k T1. This results in definition for N 0B as:
N 0B = G 1 (k T a ) + G 1 (k T 1 ) = G 1 k (T a +T 1 )
T 1 represents the equivalent noise temperature due to RF DUT 2 defined at the input of RF DUT 2 and has associated noise power density: k T 2. This results in definition of N 0C as:
N 0C = G 1 G 2 (k T a ) + G 1 G 2 (k T 1 ) + G 2 (k T 2 ) = G 1 G 2 k (T a +T 1 +T 2 /G 2 )
SNR is related to E b /N o in the following way:
where:
SNR = signal-to-noise ratio (unitless)
S = signal power (W)
N = noise power (W)
E b = bit energy (W / sec)
T b = bit time (sec)
N BW = receiver noise bandwidth (Hz)
N 0 = noise power density = N / N BW (W/Hz)
R = data rate = 1/ T b (1/sec)
E b /N 0 = E b over N 0 (unitless)
To provide a signal-to-noise figure that is independent on the receiver noise bandwidth, the signal-to-noise density is typically used.
Thus, we now see the relationship between E b /N 0 and S/N o and S/N.
S/N o and E b /N 0 values may be considered as local or system values. Local values are specific to the receiver system point where they are evaluated (points A, B, or C in the diagram); system values are independent of the receiver system point where they are evaluated.
Local values of S/N o and E b /N 0 are directly measurable at each point in the system and are typically the preferred S/N o and E b /N 0 values used by RF/analog designers.
At points A, B, and C, the local S/N o values are:
S A /N OA = S A /(k T a )
S B /N OB = (S A G 1 )/(k (T a +T 1 ) G 1 ) = S 1 /(k (T a +T 1 ))
S C /N OC = (S A G 1 G 2 )/(G 1 G 2 k (T a +T 1 )+G 2 k T 2 ) = S A /(k (T a +T 1 +T 2 /G 1 )
System values of E b /N 0 and S/N o are directly measurable only at the pre-detection system point (point C in the diagram). These are the system values because they characterize the overall system performance. The system values are typically the preferred S/N o and E b /N 0 values used by System/DSP designers.
In all cases,
E b /N 0 = S/N o /R
At point C, the local E b /N 0 and S/N o values are the same as the system E b /N 0 and S/N o values.
Summary
- Local S/N o and E b /N 0 values are not the same at all points of measurement in the receiver.
- System S/N o and E b /N 0 values are only measurable at the receiver pre-detection point (point C in the diagram), may be inferred at the other receiver points (points A and B) and have only one value defined for the system.
- Always specify if the S/N 0 or E b /N o you are using is the Local or the System value.
In the Wireless Test Bench data displays, the E b /N o value used is the local E b /N o value at the receiver input, equivalent to point A in the diagram.
E b /N o References
- Sklar, Bernard, Digital Communications: Fundamentals and Applications, 2nd Edition, Prentice-Hall, N.J., 2001.
- Sklar, Bernard, "RF Resign: Will the Real E b /N o Please Stand Up," Communication Systems Design, April, 2003.
References
- Agilent Application Note "Characterizing Digitally Modulated Signals with CCDF Curves."
http://literature.agilent.com/litweb/pdf/5968-6875E.pdf - Agilent PN (Product Note) "Using Error Vector Magnitude Measurements to Analyze and Troubleshoot Vector-Modulated Signals."
http://literature.agilent.com/litweb/pdf/5965-2898E.pdf
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