This post addresses the effect of physical radio impairments on OFDM transmitted signal quality. Designers usually use measurements for error vector magnitude, frequency error, phase noise, and spectrum due to modulation and wideband noise, including adjacent channel power ratio. These measurements are used to identify the sources of degraded system performance. This article won’t cover issues related to inter-carrier interference due to phase noise, IQ gain and phase imbalance, or other similar topics, because the material that follows applies equally for both the single and multiple carrier cases.

## Error Vector Magnitude

Error vector magnitude (EVM) is a direct measurement of modulation accuracy and transmitter performance. By definition, EVM captures the error vector between a measured signal and its corresponding ideal point in the signal constellation display. When combined with measurements of other parameters, EVM encapsulates the effects of many different signal distortions. It can therefore help pinpoint such transmission impairments as:

- phase noise and frequency error
- IQ imbalance, such as gain and phase mismatch, which would result in local oscillator (LO) leakage and unwanted sideband components
- signal compression and nonlinearities
- spurious components

In this post, we’ll relate the EVM to the items listed above. To help assess the EVM calculation process, we’ll also provide a quantitative example based on the Radio420X FPGA mezzanine card from Nutaq.

## Local Oscillator Phase Noise

LO phase noise is demonstrated as random fluctuations around the signal’s center frequency. It can be defined as the single sideband phase noise density, *L(f)*, in dBc/Hz for a given frequency offset, *f* , or aggregately, in terms of root mean square (*rms*) phase noise, *θ _{rms}*, in radians, over the entire bandwidth. Phase noise affects modulation accuracy and contributes to EVM. The impact is visually apparent as a circular distortion of the signal points around the center of the constellation. Let’s take the example of the Radio420X’s local oscillator (LO) phase noise contribution to EVM. The Radio420X’s LO phase noise at 900MHz has typically been measured at -80 dBc/Hz, -88 dBc/Hz, -95 dBc/Hz and -122 dBc/Hz, at offsets of 1 kHz, 100 kHz, 100 kHz and 1 MHz, respectively. The calculated

*rms*phase noise of 0.023

^{o }will translate to -37 dB EVM. The following formula (assuming high SNR and using second-order Tailor series expansion and zero-mean Gaussian distribution for the phase noise) can be used:

where σ is the *rms* LO phase noise.

## DC Offset, and Gain and Phase Mismatch

On the other hand, DC offset, and gain and phase mismatches in the in-phase and quadrature IQ signal paths will directly affect modulation accuracy. These impairments can be seen as LO leakage and unwanted sideband rejection performance. As far as the constellation is concerned, for BPSK pilot symbols in particular, an IQ gain mismatch results in pilot symbols spread mostly along the I-axis, while a phase mismatch would result in the pilot symbols spread along the Q-axis. Most transceivers and vector modulators specify these impairments as LO leakage and single sideband rejection in decibels, dB. Closed form expressions relating to EVM can be used to assess their contributions as follows:

*EVM _{CL}* = 10

^{ACL/20}, and

*EVM _{SSB}* = 10

^{ASSB/20}

_{,}

where *A _{CL} *and

*A*

_{SSB}are the carrier leakage and single sideband rejections in dB. For example, the Radio420X shows a typical carrier leakage and sideband suppression of -45 dB. Both leakages will contribute to about -45 dB in EVM each. You should also note the dB to dB relationship between EVM and carrier leakage and SSB suppressions in high SNR cases.

## Nonlinearities

The last point to discuss is the impact of nonlinearities as represented by third order intermodulation components. These tend to be higher as the transmitter operates near the 1 dB compression point. Nevertheless, the rule of thumb, which would also be dictated by meeting the adjacent channel power ratio (ACPR) specification, is to operate at a backoff equivalent to the OFDM peak-to-average ratio (PAR). Calculating the EVM will not only depend on the intermodulation product level but will also involve the input and the output of the interfering tone levels, *P _{RFIN}* and

*P*. The EVM can be approximated as

_{RFO}*EVM _{IMa}* = 10

^{ -(2OIP3+PRFO-3.PRFIN)/20}

with *OIP3* being the output third-order intercept point. For illustration Radio420X’s output 1dB compression point is typically 10 dBm for low band frequencies below 1.5GHz. Adding 10 dB, one would expect *OIP3* of about +20 dBm. The aggregate EVM for Radio420X is shown in the following table:

Note the following points regarding the scope and accuracy of this analysis:

- It’s based on different assumptions on noise distribution and high SNR signals. However, it establishes a good example of EVM budget analysis as it relates to the different radio transmitter impairments.
- It doesn’t account for the inter-carrier interference that IQ gain and phase imbalance would create on a mirror sub-channel, nor does it account for the LO phase noise and spurious components these impairments would cause on adjacent sub-channels.
- It doesn’t account for the contribution of in-band spurious products, which would be typically caused by reference clock harmonics due to printed circuit board (PCB) substrate finite isolation, for instance.

The literature on topics related to OFDM and MIMO-OFDM receiver performance, as well as techniques for handling IQ imbalance, phase noise, and other related topics, is abundant. We invite you to further explore these topics, and watch our blog for more articles to come.