Description of Modulation System

FCC ID: OIIDTSA1900-2

Operational Description

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Omnipoint Technologies, Inc. Exhibit 9
FCC ID: OIIDTSA1900-2 Page 1 of 2

EXHIBIT 9
DETAILED DESCRIPTION OF MODULATION SYSTEM

A detailed description of the modulation system employed is provided in this exhibit, per the
requirements of § 2.1033(c)(13). The following description is taken directly from Chapter 4 of
Volume 1, Radio Path Physical Layer, in the Personal Communications Services, Air Interface
Specification, J-STD-007.

4.0 Modulation

This chapter defines the theoretical requirements of the modulator, inclusive of the differential encoder.
The modulator receives the bits from the encryption unit and produces and RF modulated signal. The
information bits are first differentially encoded and then passed to the modulator. The modulation is
GMSK (Gaussian Minimum Shift Keying) with a BT product of 0.3.

4.1 Modulation Format

4.1.1 Modulating Bit Rate

The modulating bit rate is 1/T = 1625/6 kb/s (approximately 270.833 kb/s).

4.1.2 Start and Stop of the Burst

The bits contained within a burst are defined in Chapter 2. For the purpose of the modulator specification
at follows, the bits entering the differential encoder prior to the first bit of the burst and following the last bit
of the burst are consecutive logical ones and are denoted by the term dummy bits which define the start
and end points of the useful and active parts of the burst as shown in Figure 4.1. The actual state of
these bits is left to the manufacturer's implementation subject to the requirement that all performance
specifications of this volume are met. Nothing is specified about the actual phase of the modulator output
signal outside of the useful part of the burst. Figure 4.1 depicts the relationship between the active and
useful part of the burst, the tail bits and dummy bits for a normal burst. The useful part of the burst lasts
for 147 modulating bits.

dummy bits
dummy bits 3 tail bits 3 tail bits 1111111...
...1111111 000... ...000

Output Phase

The useful part

1/2 bit 1/2 bit

The active part

Figure 4.: Normal Burst

4.1.3 Differential Encoding

This document contains PROPRIETARY and CONFIDENTIAL information of Omnipoint Technologies, Inc.

Omnipoint Technologies, Inc. Exhibit 9
FCC ID: OIIDTSA1900-2 Page 2 of 2

Each data value di = [0,1] is differentially encoded. The output of the differential encoder is:

d'i = di ⊕ di-1 where ⊕ denotes modulo 2 addition.

The modulating data value αi input to the modulator is: αi = 1 - 2d'i where αi ∈ {-1, 1}

4.1.4 Filtering

The modulating data values αi as represented by Dirac pulses excite a linear filter with impulse response
defined by:

g(t) = h(t) ⊗ rect(t/T)

where the function rect(x) is defined by rect(t/T) = 1/T for t < T/2

rect(t/T) = 0 otherwise

and ⊗ means convolution. h(t) is defined by

 −t2 
 
 2 σ 2T 2 
 
e
h(t ) = where σ = √{ln(2)}/(2πBT) and BT = 0.3
2π σT
where B is the 3 dB bandwidth of the filter with impulse response h(t) and T is the duration of the one input
data bit.

4.1.5 Output Phase

The phase of the modulated signal is:

t ' − iT

ϑ (t ' ) = ∑ αiπh ∫ g (u )du
i −∞

where the modulating index h is ½ (maximum phase change in radiates is ½ per data interval).

The time reference t' = 0 is the start of the active part of the burst as shown in Figure 4. The is also the
start of the bit period of bit number 0 (the first tail bit) as defined in chapter 2.

4.1.6 Modulation

The modulated RF carrier, except for start and stop of the TDMA burst may therefore be expressed as:

2 Ec
x(t ' ) = cos(2πf o t '+ϕ (t ' ) + ϑ0
T
where Ec is the energy modulating bit, fo is the center frequency, and ϕo is a random phase and is
constant during one burst.

This document contains PROPRIETARY and CONFIDENTIAL information of Omnipoint Technologies, Inc.

Document Created: 2001-06-25 16:45:36
Document Modified: 2001-06-25 16:45:36

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