The Office of Spectrum Management (OSM) in NTIA is responsible for managing the radio spectrum used by the Federal Government. ITS supports OSM by establishing a methodology for specifying spectrum requirements of various modulations employed by the Government. With the continuing development of new digital modulations, it is essential to analyze the spectra of the modulations to determine their bandwidth requirements. Allocating spectrum for a modulation without knowing the width and shape of its spectrum could cause one system's spectrum to overlap onto an adjacent channel spectrum occupied by another system, resulting in potentially serious interference problems.
The flowchart in Figure 1 shows the steps used in analyzing the spectrum and establishing the Occupied Bandwidth (OBW) and Necessary Bandwidth (NBW) formulas. After a modulation is selected, its spectra is calculated from an analytic equation. Alternatively, the transmitter can be simulated and the spectra can be calculated from the waveform. Then the total power contained in a bandwidth (BW) is calculated, and the 99% power BW is specified parametrically. The next step is to spline interpolate between spectral peaks to establish the spectral envelope. Following that, the OBW is specified in terms of the 99% power BW, and the NBW is specified in terms of the spectral envelope 20 dB down frequency. With these new results, the OBW and NBW can be specified in terms of system and modulation parameters and can be explicitly calculated from the power spectral density (power spectrum), thus providing a methodology for efficient management of the changing spectrum environment.
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| Figure 1. Spectral analysis of modulations flowchart. |
In FY 99, this analysis was applied to minimum-shift keying (MSK) that provides an analytically tractable baseline for comparison with other modulations, orthogonal frequency division multiplex (OFDM) also referred to as multicarrier modulation (MCM) and Gaussian minimum-shift keying (GMSK).
A transmitter block diagram and analysis results for GMSK are shown in Figures 2-5. Figure 2 describes the major blocks of the transmitter where a non-return to zero (NRZ) data stream is employed, and T is the symbol duration which is used in normalizing the analysis results. All results are shown for a Gaussian filter with a 3dB bandwidth B and a normalized bandwidth of BT=0.25. Sidelobe ripple increases with increasing BT.
The one-sided linear power spectrum of the transmitter output is shown in Figure 3, demonstrating the effect of the Gaussian filtering on the input data stream. The log of the power spectrum is given in Figure 4, along with the calculated 3 dB and 20 dB down bandwidths of 0.207 and 0.504. The BW where the spectral envelope has rolled off by 20 dB is proposed as the NBW. All bandwidths are one-sided and normalized to the symbol duration.
The spectrum in Figure 3 was integrated to obtain the total power in the BW specified by the abscissa and given as a percentage of total power contained in a BW. This is shown in Figure 5. The BW containing 99% of the total power (also OBW) was calculated to be 0.430.
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| Figure 2. GMSK transmitter. |
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| Figure 3. GMSK linear power spectrum. |
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| Figure 4. GMSK log power spectrum. |
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| Figure 5. GMSK total power within a bandwidth. |