### Abstract

Unlike many other cellular standards, NCDMA is required by the 3GPP2 standard to perform spectrum inversion in the physical layer before transmission and after reception. With today’s vast selection of radio frequency (RF) transceivers and baseband processors, it is easy to imagine how one could come across a set of RF transceiver and baseband processor that have mismatched spectrum in the transmit and receive paths. This simple oversight will result in noncompliance to the 3GPP2 standard and failure to demodulate. However, there are a few simple techniques that can help determine if spectrum inversion has been performed on a signal.

*microwaves&rf*, October 11, 2013.

### Introduction

### How to Detect Spectrum Inversion

*has*been inverted.

**Figure 1**).

*Figure 1. WCDMA I/Q modulation and demodulation format. Note that the Q channel is multiplied by a negative phase LO, i.e., -sin(ω*

_{LO}t), as shown in red.### Transmitter Signals

_{m}= e

^{jωmt}= cos(ω

_{m}t) + jsin(ω

_{m}t)

_{ITX}= cos(ω

_{LO}t) and LO

_{QTX}= -sin(ω

_{LO}t)

_{TX}= cos(ω

_{m}t)cos(ω

_{LO}t) - sin(ω

_{m}t)sin(ω

_{LO}t)

_{TX}= ½cos((ω

_{m}- ω

_{LO})t) + ½cos((ω

_{m}+ ω

_{LO})t) - ½cos((ω

_{m}- ω

_{LO})t) + ½cos((ω

_{m}+ ω

_{LO})t)

_{TX}= cos((ω

_{m}+ ω

_{LO})t)

### Received Signals

_{RX}= cos(ω

_{RX}t), with ω

_{RX}= ω

_{m}+ ω

_{LO}

_{LO}= e

^{-jωLOt}= cos(ω

_{LO}t) - jsin(ω

_{LO}t)

_{BB}= cos(ω

_{RX}t)cos(ω

_{LO}t) - jcos(ω

_{RX}t)sin(ω

_{LO}t)

_{BBI}= ½cos((ω

_{RX}- ω

_{LO})t) and V

_{BBQ}= ½sin((ω

_{RX}- ω

_{LO})t)

_{RX}with ω

_{m}+ ω

_{LO}, the I and Q baseband outputs are the same as the I and Q of the TX baseband inputs:

_{m}= cos(ω

_{m}t) and Q

_{m}= sin(ω

_{m}t)

### Perform Spectrum Inversion

### Method 1

**Figure 2**).

*Figure 2. NCDMA I/Q modulation format. Note how the Q channel is multiplied by LO with positive phase, i.e., sin(ω*

_{m}t), as highlighted in red._{m}= cos(ω

_{m}t) and Q

_{m}= sin(ω

_{m}t)

_{ITX}= cos(ω

_{LO}t) and LO

_{QTX}= sin(ω

_{LO}t)

_{TX}= cos(ω

_{m}t)cos(ω

_{LO}t) + sin(ω

_{m}t)sin(ω

_{LO}t)

_{TX}= ½cos((ω

_{m}- ω

_{LO})t) + ½cos((ω

_{m}+ ω

_{LO})t) + ½cos((ω

_{m}- ω

_{LO})t) - ½cos((ω

_{m}+ ω

_{LO})t)

_{TX}= cos((ω

_{m}- ω

_{LO})t)

### Method 2

_{m}= cos(ω

_{m}t) and Q

_{m}= -sin(ω

_{m}t)

_{ITX}= cos(ω

_{LO}t) and LO

_{QTX}= -sin(ω

_{LO}t)

_{TX}= cos(ω

_{m}t)cos(ω

_{LO}t) + sin(ω

_{m}t)sin(ω

_{LO}t)

_{TX}= cos((ω

_{m}- ω

_{LO})t)

### Method 3

_{m}= sin(ω

_{m}t) and Q

_{m}= cos(ω

_{m}t)

_{ITX}= cos(ω

_{LO}t) and LO

_{QTX}= -sin(ω

_{LO}t)

_{TX}= sin(ω

_{m}t)cos(ω

_{LO}t) - cos(ω

_{m}t)sin(ω

_{LO}t)

_{TX}= ½sin((ω

_{m}+ ω

_{LO})t) + ½sin((ω

_{m}- ω

_{LO})t) - ½sin((ω

_{m}+ ω

_{LO})t) + ½sin((ω

_{m}- ω

_{LO})t)

_{TX}= sin((ω

_{m}- ω

_{LO})t)

### Conclusion