GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

Multi-carrier Waveform Examples EXAMPLE 1: 4 carrier EDGE Waveform with 4 Frames of Continuous data, PN15 modified, 80000 points. RF Initial Phase = 0 for all, data offset = 0 Repetition interval 4*4.6ms -> 18.4ms

CCDF Complementary Cumulative Distribution Function (Power distribution)

Spectrogram (Spectrum versus time)

The markers show the expected repetition interval. There is no sign of spectrum splatter (baseband elevation) at repeat points.

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

Measured CCDF and Auto-correlation The CCDF matches Signal Studio. The auto-correlation peak at 18.46ms shows the expected waveform repetition. Notice the slow amplitude variation superimposed on the power versus time signal (bottom right)

Spectrum Average showing expected EDGE shape

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

EXAMPLE 2: Same waveform used in Example 1 with a Data Offset of 10 symbols between carriers: Carrier 1: data offset = 0 Carrier 2: data offset = 10 Carrier 3: data offset = 20 Carrier 4: data offset = 30 CCDF (looks similar to ESG) Yellow trace. The white is from example 1 for comparison

Spectrogram

No evidence of baseband elevation

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

Measured CCDF and auto-correlation

Spectrum Average

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

EXAMPLE 3: GMSK 8 carriers with 4 frames and 15325 data offset with 10 symbol increments. Initial RF phase = 0 degrees for all carriers Note: This is a large waveform (8M points) because of the large frequency offsets and therefore high sampling rate (69.33MSa/sec).

CCDF

SPECTROGRAM In order to look at the spectrum over the whole waveform, we focus on the signal for just one of the carriers

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

Measured CCDF and auto-correlation

As expected, the CCDF of an individual GMSK carrier is 1. SPECTRUM AVERAGE showing classic GMSK filtered shape

GSM / EDGE Multi-carrier: Waveform Characteristics Power Distribution (CCDF) and Spectrum

Agilent Technologies October 2006

EXAMPLE 4: Same signal as example 3, but RF Initial Phase randomized. Data offset 0 for all carriers CCDF

The yellow curve shows the dramatic reduction in the peak-to-average power ratio. Randomizing the initial phase but keeping the data offset between carriers leaves the CCDF largely unchanged.