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 = and g1 = 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 . Different generators were used in the current system, with the convolution of 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 = 4fb, where fb 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 wH = w0 + Ω or wL = 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 wH and the other with carrier wL. Amplitudes EH and EL 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.
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Multifrequency shift keying involves the transmission of multilevel rather than binary data. The total required bandwidth (B) in this case is B = 2Mf where M is the number of symbols and fs is the symbol rate. As a result, M-ary FSK requires more bandwidth than other modulation schemes such as M-ary PSK. The probability of error decreases as M increases, compared to other modulation schemes, such as BPSK.
In phase-shift keying (PSK), the phase of the carrier is altered according to the data. By maintaining roughly constant amplitude, the approach provides good noise resistance. The spectrum efficiency can be dramatically improved by combining both PSK with ASK. BPSK, which can be thought of as an AM signal, can be generated by sending a waveform as a carrier to a balanced modulator and applying the baseband signal as the modulating waveform. A typical PSK signal spectrum reveals about 14 dB difference between the sidelobe and mainlobe levels (where more than 90 percent of the signal power is found). Such high sidelobes can cause adjacent-channel interference so they must be reduced. Lowpass filtering of the baseband signals helps to suppress (although not eliminate) the unwanted sidelobe signals. Unfortunately, spectrum suppression tends to distort the desired signal, resulting in a partial overlap of a data bit and its adjacent bits in a single channel, a phenomenon known as intersymbol interference (ISI). ISI can be minimized through equalization filters.
Figure 6 shows how a single mixer can be used to modulate a carrier by alerting its amplitude or phase or frequency, resulting in two information states, where one represents one or zero. In contrast, quadrature modulators offer the advantage that any parameter of a carrier can be simultaneously manipulated to represent the information. A quadrature modulator is implemented with a phase shifter, two mixers, and signal-combining stage.
The representation of a quadrature modulator generating a quadrature-phase-shift-keying (QPSK) signal is Eq. 13, where:
de(t) = even indexed data and
do(t) = odd indexed data.
The abrupt changes in phase of a QPSK baseband signal give rise to spectral components at high frequencies and relatively wide spectral width. The baseband spectral range is large and multiplication by the carrier translates the spectral pattern without changing its form. The abrupt phase changes in QPSK (which can be as large as 180 deg.) occur at the symbol rate 1/Ts = 0.5Tb, where Tb is the data rate.
Such abrupt phase changes can cause substantial changes in the amplitude of the waveform, causing problems in QPSK communication systems. Most systems employ nonlinear power output stages in their transmitters to suppress the amplitude variations. Because of their nonlinearities, however, these stages generate spectral components outside the range of the main signal lobe thereby undoing the effect of the band-limiting filtering and causing interchannel interference. Staggered or offset QPSK (OQPSK), with phase changes limited to 90 deg., is often substituted for 180-deg. QPSK. By limiting shifts to 90 deg., the data arms are delayed to each other by one-half period of the data rate and the signal envelop never goes to zero. BERs for QPSK and OQPSK are the same as for BPSK (Fig. 7).
An important feature of minimum-shift keying (MSK) is its phase continuity. MSK is generated in the same manner as offset QPSK provided that the transmitted data is shaped using a one-half-cycle sinusoid. The MSK signal has constant signal envelop and avoids the 90-deg. abrupt phase shift that occurs in OQPSK. In MSK, the baseband waveform, which multiplies the quadrature carrier, is much smoother than the abrupt rectangular waveform of OQPSK. While the spectrum of MSK has a main lobe which is 1.5 times as wide as the main lobe of QPSK, the side lobes in MSK are smaller (Fig. 8), making filtering much easier.
An MSK signal can be represented mathematically by Eq. 14. An MSK signal is a quadrature signal where each term is multiplied by the data. This data is shaped by a sinusoid for the purpose of smoothing. As it appears as a modified version of OQPSK, it can be called "shaped OQPSK." MSK signals can be formatted to appear as FSK signals.
By using the trigonometric identity, the MSK equation can be written as Eq. 15. The magnitudes of the two terms can be replaced by EH and EL in Eq. 16, and the MSK signal appears as Eq. 17.
When the data de(t) and do(t) are the bipolar values +1 and 1, then EH and EL simultaneously take on the values of 0 and 1, respectively. The transmitted signal appears as FSK with angular frequency of wH or wL although maintaining constant amplitude. For orthogonality over the bi interval Tb, the following must be satisfied:
Recalling the trigonometric identity 2sin(A)sin(B) = cos(A + B) cos(A B), it can be seen that orthogonality is preserved when
resulting in Eq. 21.
The minimum difference between fL and fH is obtained when m n = 1 and when fL ≠ 0. For the minimum n = 1 and m = 2, the result is fH = 3fb/4 and fL = fb/4. When wL wH = 2 Ω, then Ω = 2π(fb/4). For this reason, this modulation scheme is called minimum-shift keying (MSK).
So far, input data has been half-sinusoidal shaped. With Gaussian MSK (GMSK), input data are shaped using a Gaussian pulse shape so that phase oscillation is reduced to less than π/2 compared to MSK and transitions between phase states are smoother.
The mathematical representation of the Gaussian pulse shape is
where:
β = the 3-dB bandwidth.
In a continuous-phase-modulation (CPM) scheme, the phase of the carrier is changed even more smoothly. To maintain this smooth phase continuity, however, the history of previous symbols must be stored in memory (L). When L = 1, this modulation scheme is known as a full-response system or binary CPM (which defines an MSK scheme). A partial response CPM scheme is when L is greater than 1. This has advantages compared to OQPSK or MSK in that it ensures rapid spectral rolloff as well as a narrower spectrum (Fig. 9).
When the MSK and GMSK modulators were simulated with MATLAB and Simulink, the power levels at the channel boundaries were better than 80 dBc for a case where the maximum allowable level of adjacent-channel power must be better than 60 dBc according to wireless regulations. From these simulations, both modulators meet the requirements.
