Designing a transmitter for telemetry applications requires careful consideration of the modulation scheme. For one such system, a weather-balloon telemetry transmitter was required to send digital data at 384 b/s (48 B) from the output of multiple transducers (sensors) used to measure temperature, pressure, humidity, wind speed and Global Positioning System (GPS) data (coordination and time data). The transmitter operates in the low-UHF band using an allocated bandwidth of 4 MHz from 402 to 406 MHz and 200 20-kHz channels.

The transmitter is comprised of three basic sections: baseband, RF stage with frequency synthesizer, and synchronization circuitry. This article will focus on the transmitter's baseband circuitry, including the processing and preparation of signals for the RF stage, such as pulse shaping, error correction, coding, interleaving, and modulation.

Pulse shaping helps minimize the effects of interference. Pulse shaping typically limits a signal bandwidth for processing through an in-phase/quadrature (I/Q) modulator:

where:

d(n) = the input data (binary or multilevel data),

g(t) = the pulse shape signal, and

s(t) = the shaped signal.

A variety of pulse shapes can be used to limit bandwidth, including raised-cosine and Gaussian forms. In the time domain, the raised-cosine form has the form

where:

r = the rolloff factor (0 < r < 1).

Since the signal-to-noise ratio (SNR) in this application is very low, and the transmitter cannot be stabilized while the balloon is rising, some signal fading is inevitable, requiring the use of error detection and correction. Convolutional coders are usually a good idea for digital transmissions at low SNRs, along with a convolutional interleaver. The interleaver minimizes burst errors by distributing them over a wide range of the data. The convolution coder achieves error-free transmission by adding enough redundancy to the source symbols and process the information serially, or continuously, in short block lengths.

Figure 1 shows a four-state convolutional coder where the rate is defined as the number of input bits to output bits. This system has one input and two outputs, resulting in a coding rate of one-half. The number of states of a convolution coder is determined by the number of delay units (memory); the output is dependent not only on the current input but also on the previous inputs and or outputs. In other words, the encoder is a finite state machine.

In general, a k/n-rate convolutional encoder has k shift registers, one per input information bit, and n output coded bits as determined by the linear combinations (with exclusive-or gates) of contents of the registers and the input information bits. When the ratio is 1/n, then a technique known as puncturing can be applied to achieve higher-rate convolutional encoders.

The shape of the coder is determined by the generators or generator sequences:

The generator can be written as a polynomial in D where D is a unit delay:

The generators can be represented in binary form as g₀ = [1 1 1] and g₁ = [1 0 1] where 1 represents a connection with the exclusive-or adder and 0 represents no connection. They can also be represented in an Octal system as [7, 5]. Different generators were used in the current system, with the convolution of [171, 131] generators realized using the MATLAB mathematical analysis/simulation program from The MathWorks (Natick, MA).

Under multipath conditions, an interleaver is needed in a transmitter to improve the bit-error rate (BER). In the current application, a convolutional interleaver was used with a convolutional encoder. In the interleaving process (Fig. 2), each small cell represents a bit, with adjacent bits distributed for ease of recovery at the receiver.

There are many important criteria in choosing the correct modulation method, including the total cost of the transmitter, the size and power supply, and the required mobility of the transmitter. For the current application, the transmitter is disposable and used only once or twice and so must be low in cost. The transmitter should also be small and light in weight. The transmitter is designed to run on a +9-VDC battery power supply. The limited power supply mandates that the transmitter operate under nonlinear conditions, implying the use of a constant-envelope modulation method.

Due to the mobility (movement) of the transmitter, oscillation and Doppler effects are a concern that can result in dead zones where the receiver has no signal. Convolutional coding helps minimize loss of data due to Doppler, fading, and multipath effects, although it imposes an additional load on the system data processor and rise in power consumption. By careful selecction of modulation format for efficiency, it should be possible to meet the system performance requirements even under +9-VDC battery power.

In amplitude-shift keying (ASK), the amplitude of the carrier fluctuates according to the transmitted data. In binary transmission, the carrier amplitude will exhibit one of two values (Fig. 3). Due to the fluctuation of the signal amplitude, this modulation method by itself is not effective in noisy channels, but is often combined with other modulation schemes to improve system spectral efficiency.

By using frequency as the modulation parameter, frequency-shift-keying (FSK) results. When a carrier frequency is modulated by a binary data, two frequencies are produced (Fig. 4). Frequency separations (frequency deviations) can be chosen such that orthogonal (π/2 phase) transmission is achieved. FSK modulation is quite effective in the presence of noise, but imposes wider spectrum bandwidth requirements compared with other modulation formats such as phase modulation. The bandwidth of binary FSK (BFSK) is BW = 4f_b, where f_b is the baseband data rate, or:

where:

d(t) = +1 or ­1 according to the binary input data and

Ω = a constant offset.

The transmitted signal is either

or

The signal has an angular frequency of w_H = w₀ + Ω or w_L = w₀ ­ Ω. BFSK signals can be generated with the simple modulator of Fig. 5. In this configuration, two balanced modulators are used alternately, one with carrier w_H and the other with carrier w_L. Amplitudes E_H and E_L are generated according to the table so that the modulator functions like a switch. Accordingly, the BFSK signal can be rewritten as Eq. 10, which is comparable to binary phase-shift keying (BPSK). In BFSK, the amplitude of the two terms alternate between 0 and 1 (antipodal), while in BPSK the amplitude alternates between ­1 and +1 (bipolar). The distance between BFSK signal end points is smaller than the distance separating points of BPSK signals. The BFSK and BPSK schemes can be further compared by means of the trigonometric identity of Eq. 11, or the alternate equivalent expression of Eq. 12.

The first term carries no information. The second term in this equation is similar to BPSK, with the minor difference that the data is shaped by sinΩt. As a result, BFSK does not share the noise resistance of BPSK.