As discussed in our previous blog post, the quality of a transmitted waveform is usually measured using error vector magnitude, frequency error, output power, and dynamics, as well as time alignment between transmit branches and downlink RS power requirements

[1]. Another key consideration is unwanted emissions, which consist of out-of-band emissions and spurious emissions.

Out of band emissions are unwanted emissions immediately outside the channel bandwidth that result from the modulation process and non-linearity in the transmitter. Spurious emissions are emissions that are caused by unwanted transmitter effects such as harmonic emissions, parasitic emissions, intermodulation products, and frequency conversion products.

The out-of-band emission requirements for the Evolved Node B (eNB) and user equipment (UE) transmitters, for instance, are specified in terms of both adjacent channel leakage power ratio (ACLR) and unwanted emissions on the operating band.

## Relating ACLR to IMD

The increase in ACLR is mainly due to increased adjacent channel occupancy by 3rd and 5th order inter-modulation components [3]. In their application note [4], Maxim Integrated related ACLR to IMD3, calculating an ACLR for n subcarriers using two-tone IMD3 and a correction factor, with the following formula:

ACLRn = IMD3 + Cn

which uses the correction factors listed in the following table:

For a larger number of subcarriers, as in LTE and WiMAX, a set of closed form formulas are presented by Carvalho and Pedro [5]. Their article relates ACPR to the two-tone intermodulation ratio, IMR2, which in turn is linked to the third order intercept point, IP3, and the total output power, POT , as follows:

IMR2 = 2(IP3 – POT) + 6

Following their established theory, Carvalho and Pedro provided the formula for n-tone ACPR related to IMR2 as follows:

ACPR = IMR2 + 10log (n3/(16N + 4M))

with N = (2n3 – 3n2 – 2n)/24 and M = n2/4, where n is an integer multiple of 2.

ACPR will get asymptotically close to IMR2 when the number of subcarriers is high. This approximation can be applied for a 20 MHz LTE signal, for instance, with 2048 subcarriers.

For illustration, the measured 0 dBm two-tone IMR2 for Nutaq’s Radio420X is about -60 dBc. This suggests that the expected ACPR is IMR2, with -24.09 dBm output power per tone, in the case of 5 MHz LTE signal bandwidth. You would also expect such an ACLR level given that Radio420X exhibits a typical P1dB of +15 dBm.

Overall, Radio420X is suitable for LTE radio testing and development at +5 dBm total average output power. When it’s coupled with off-the-shelf pre-driver evaluation boards, such as the SKY77xxx family from Skyworks®, you can expect a clear LTE signal at +15 dBm (leaving typically more than 12 dB backoff) for femtocell applications.

References

1. European Telecommunications Standards Institute. 2012. LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) Conformance Testing (3GPP TS 36.141 version 9.11.0 Release 9). ETSI 3rd Generation Partnership Project (3GPP). http://www.etsi.org/deliver/etsi_ts/136100_136199/136141/09.11.00_60/ts_136141v091100p.pdf
2. European Telecommunications Standards Institute. 2008. Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) Radio Transmission and Reception, (3GPP TS 36.803 version 1.1.0 Release 4).  ETSI 3rd Generation Partnership Project (3GPP). http://www.3gpp.org/ftp/Specs/html-info/36803.htm
3. Sesia, Stefania, Matthew Baker, and Issam Toufik, eds. 2009. LTE, the UMTS Long Term Evolution: From Theory to Practice. West Sussex: John Wiley & Sons. ISBN: 0470697164.
4. Maxim Integrated, Inc. 2006. “Adjacent Channel Leakage Ratio (ACLR) Derivation for General RF Devices.” Application note. http://www.maximintegrated.com/app-notes/index.mvp/id/3902
5. Carvalho, Nuno Borges de, and José Carlos Pedro. 1999. “Compact Formulas to Relate ACPR and NPR to Two-Tone IMR and IP3.” Microwave Journal (December): 70-84. http://www.av.it.pt/nbcarvalho/docs/Revista7.pdf