# Vector Modulation Techniques for Digital RF Systemsâ€”Part One

*In the first part of this two-part set, we examine several of the main modulation techniques being employed in modern digital wireless designs.*

*By: Frank Zavosh, Mike Thomas, David Ngo, Tracy Hall, Motorola Semiconductor Product Sector*

__Contents__

Vector modulation

QPSK/OQPSK

8PSK

p/4 DQPSK

MSK

GMSK

16-QAM

Over the last decade, the deployment of wireless communications in the US and other parts of the world has increased dramatically. Wireless communications technology has evolved from simple first-generation analog products designed for business use to second-generation digital wireless telecommunications systems for residential and business environments.

More recently, demand for portable wireless equipment such as cellular phones and pagers, digital cordless phones, and wireless local-area network (WLAN) systems has rapidly accelerated. This increased demand for mobile communications services is putting a premium on available radio spectrum. In addition, this equipment demands the added features of small size, lightweight, very low power consumption, and fading resilience.

To solve the size and spectrum requirements, engineers are turning to digital modulation techniques. Recent advancements in higher-speed IC processes, innovative high-speed digital-to-analog (D/A) converters and analog-to-digital (A/D) converters, are making it possible for high-speed digital modulation techniques to meet these demands.

This is the first part in a two-part set on vector modulation techniques for digital wireless communication systems. In this part, we will explore the most common modulation techniques used in today's digital RF designs. In part two, we will explore efficiency, digital filtering, and system set up for the measurement of spectral and time domain analysis.

** Vector modulation **

There is a fundamental tradeoff in communication systems. Simple hardware can be used in transmitters and receivers to communicate information at a cost of increased bandwidth and reduced number of users. Alternatively, more complex transmitters and receivers can be used to achieve a spectrally efficient transmission.

Digital modulation can provide high information capacity, compatibility with digital data services, higher data security, better quality communications, and quicker system availability at a cost of increased system complexity. Fortunately, the plethora of modulation schemes developed to date can provide the designer with a wide range of options in trading system complexity for spectral efficiency in order to achieve the best system performance.

Digital modulation methods can be classified into four groups (*Table 1*), depending on the modulation parameter. The characteristics common to digital modulation schemes employed in mobile communications systems include:

- Narrowband performance
- Low required power for information transmission
- Minimal deterioration of transmission characteristics due to Rayleigh fading
- Simplified modem circuits

A further classification of vector modulation schemes commonly used, divides modulations into linear and nonlinear schemes that can be memory-less or with memory. *Table 2* depicts a classification of modulation schemes of interest in digital communications in terms of linearity and memory.

In digital communications, modulation is often expressed in terms of I (in-phase) and Q (quadrature), where the I axis lies on the zero degree phase reference and the Q axis is rotated by 90 deg. The signal vector's projection onto the I axis is its "I" component, and the projection onto the Q axis is the "Q" component. This is known as quadrature (vector) modulation, and nearly all standard modulation schemes are quadrature modulations.

** QPSK/OQPSK **

If we define four signals, each with a phase shift differing by 90 deg., we obtain quadrature phase-shift keying (QPSK). This is implemented by separating the input data stream into two data streams I(t) and Q(t), containing the even and odd bits, respectively. The resulting four states have phase values of p/4, 3p/4, -p/4, -3p/4. If only one component changes sign, a phase shift of 90 deg. occurs. But if both components change sign, then a phase shift of 180 deg. occurs.

If the two bit streams, I(t) and Q(t), are offset by a ½ symbol interval (1-b interval), then the amplitude fluctuations are minimized, since the phase never changes by 180 deg. This modulation scheme, known as orthogonal quadrature phase-shift keying (OQPSK), is obtained by delaying the odd bit stream by a half-symbol interval with respect to the even interval (*Figure 1*).

** 8PSK**

Another commonly used modulation technique is called 8-level phase-shift keying (8PSK). In this scheme, every three consecutive data bits determine one of eight different phase states [0, ±(p/4), ±(p/2), p, ± (3p/4)]. The corresponding I(t) and Q(t), are the cosine and sine of the phase values, respectively.

8PSK modulation is similar to p/4 differential quadrature phase-shift keying (p/4 DQPSK) except that the phase transitions are absolute and not relative to the position of the previous states. Gray coding is generally applied to 8PSK as in most modulation schemes in order to reduce the bit error rate. Note that in this scheme the symbol rate is 1/3 times the original bit rate.

**p/4 DQPSK **

p/4 DQPSK is a compromise solution between the conventional or coincidental transition QPSK and OQPSK methods, because the phase is restricted to fluctuate between ± (p/4) and ± (3p/4) rather than the ± (p/2) or ± (p) in the other schemes. Hence, p/4-DQPSK is essentially p/4-shifted QPSK with differential encoding of symbol phases.

In DQPSK-based designs, the differential encoding mitigates loss of data due to phase slips. However, differential encoding results in the loss of a pair of symbols when channel error occurs, which translates to approximately 3-dB loss in signal-to-noise relative to coherent p/4-QPSK [1].

The phase transition states for p/4-DQPSK are given in *Table 3*.

The I and Q components can be mathematically represented as a function of the previous symbol phase and the relative transition phase of *Table 2,* yielding

Note: the symbol rate for p/4-DQPSK modulation is 1/2 the bit rate.

** MSK **

Minimum shift keying (MSK) is a special class of frequency-shift keying (FSK) where the modulation index, *m*, is equal to 0.5. It can be generated using a voltage-controlled oscillator (VCO) structure as in FSK, or using a quadrature structure as pre-modulation filtered OQPSK. The modulation index of 0.5 value corresponds to frequency deviation D f=1/4T_{b}. Thus, the MSK signal can be represented as:

Note that cos(± p t/2 T_{b}) and sin(± pt/2 T_{b}) represent independent and uncorrelated data streams that correspond to the I(t) and Q(t). The implementation of the quadrature structure for the MSK modulator uses the same OQPSK modulator structure except for the addition of sinusoidal pulse-shapers (*Figure 2*).

In a pure MSK system, the Gaussian filters are not used, since they disturb the sine/cosine relationship between the I(t) and Q(t) channel, which provides the constant envelope. Addition of the filter enhances the spectral efficiency at a cost of modulating the carrier envelope.

** GMSK **

Gaussian minimum-shit keying (GMSK) is derived from continuous-phase FSK (CPFSK) by selecting the frequency deviation to be the minimum (MSK) and filtering the baseband modulating signal with a Gaussian filter. In most common GMSK systems this is done by performing a direct frequency modulation (FM) of the filtered baseband signal onto the carrier (*Figure 3*).

Where g(t) is the filtered pulse stream and h(t) is the filter impulse response. Modulation of the carrier wave frequency by the baseband signal g(t) around a center frequency f_{c}implies modulating its phase

Where f_{m} = f_{b}/4

Using a VCO, the modulated carrier is then generated

y(t)=cos(F(t))

An alternative method to direct FM modulation is the quadrature implementation. Since the desired signal y(t) can be written as:

The complex phase function u(t) can be expressed as a train of baseband pulses, similar to what is done in simple FSK signals:

After some extensive manipulations, we can represent u(t) as a function of phase trajectories, hence:

Where corresponds to a set of discrete boundary phases at the symbol boundaries, and are phase trajectory functions defined in *Table 4*.

The above formulation is valid for B_{b}T > 0.3 since the inter-symbol interference (ISI) between non-adjacent symbols is ignored. The effect of this approximation is to underestimate the curvature of the trajectories for B_{b}T < 0.3 resulting in a non-constant envelope.

Note the quadrature formulation for GMSK is easy to implement in hardware, since only four distinct phase trajectories and four distinct initial phase states need to be evaluated or stored in read-only memory (ROM) tables.

** 16-QAM **

Sixteen-level quadrature amplitude modulation (16-QAM) can be viewed as an extension of multiphase PSK modulation, wherein the two baseband signals are generated independently of each other. Thus, two completely independent (quadrature) channels are established.

In the case where two levels (±1) are used on each channel, the system is identical to 4-level PSK. QAM trades off increased spectral efficiency (bits transmitted per second per Hz of bandwidth) for reduced tolerance to noise and other channel impairments when compared to the QPSK modulation discussed previously.

In 16-QAM, the data stream is separated into odd and even bits represented by I(t) and Q(t), respectively (*Figure 4*).

Every two bits of I(t) and every two bits of Q(t), are selected to represent one of four possible states. Since the four states of I(t) and Q(t), are uncorrelated, there are 16 possible states for the signal. There can be transition from any state to any other state at every symbol period. The symbol rate is 1/4 the original bit rate, hence, this modulation is spectrally efficient.

Extensions in the form of 32-, 64-, 128-, and 256-QAM are also commonly used in high data rate systems. However, due to noise sensitivity they are not as common in wireless systems.

**Wrap-up**

This concludes part one of this two-part series. Over the next few weeks, part two of this piece will appear. Part two will focus on efficiency, digital filtering, and system set up issues.

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**About the authors:***Frank Zavosh, RF Design Engineer; Mike Thomas, RF Design Engineer; David Ngo, RF Design Engineer; and Tracy Hall, RF Design Engineer, Motorola Semiconductor Product Sector, 210 East Elliot Road, Phoenix, AZ, 85284. Phone: 480-413-6617; Fax: 480-413-4433.*