The integrate-and-dump detector is fundamental to coherent detection, the optimal receiver technique that minimizes bit error rate (BER) for a given signal-to-noise ratio Eb/No. In this project develop a pulse amplitude (PAM) transmitter based on a transmit filter to map a bitstream onto a signaling waveform (rectangular and Manchester pulse shapes), an additive white Gaussian noise (AWGN) channel, and a receiver that implements integrate-and-dump detection. All waveforms throughout the signal processing chain are presented as a stacked chart indicator with a speed control to permit generated waveforms to be studied slowly (i.e., the integrator output ramping up or down) or quickly to process long message bitstreams. Visualizing the critical system signals as waveforms facilitates exploration of the effects of specific values of BER and Eb/No, and promotes deeper understanding of coherent detection.

Refer to the following textbooks for additional background on the project activities of this module; see the "References" section below for publication details:

If you are relatively new to LabVIEW, consider taking the course LabVIEW Techniques for Audio Signal Processing which provides the foundation you need to complete this project activity, including: block diagram editing techniques, essential programming structures, subVIs, arrays, and audio.

Noise represents the most widely-known channel impairment in a communication system. No doubt you have heard "static" while listening to AM radio during a thunderstorm, soft hissing during a telephone conversation, and other types of background noise. Digital communication system noise causes errors in the recovered (regenerated) bit stream at the receiver.

In general, digital receivers rely on one of two detection techniques to regenerate the transmitted bit stream: coherent detection and non-coherent detection. "Coherent" means the receiver maintains synchronism with the transmitter, normally by using special subsystems that extract timing signals directly from the transmitted bit stream. Transmitting timing pulses in a separate channel is usually too expensive for long-haul comm links. The synchronizer establishes the precise beginning and ending of each bit interval. A synchronizer increases the receiver's cost and complexity, but also achieves the lowest bit error rate (BER) of the two techniques for a given signal-to-noise ratio (SNR). Incoherent detection, on the other hand, uses a lower-complexity approach to recover the bit stream, but does not perform as well in terms of BER. In this project the correlation detector scheme is studied in detail.

Figure 1 illustrates a generic communication system (transmitter, channel, and receiver) and a comparator to compare the original source bitstream to the output bitstream and report bit error.

Figure 1: Generic communication system with comparator

This project implements Figure 1 at a moderately realistic level:

Figure 2 illustrates the detailed block diagram of the binary pulse amplitude modulation (PAM) transmitter.

Figure 2: PAM transmitter block diagram

The bitstream 1 and 0 values map to the amplitudes E b / T b E b / T b MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaGcaaqaamaalyaabaGaamyramaaBaaaleaacaWGIbaabeaaaOqaaiaadsfadaWgaaWcbaGaamOyaaqabaaaaaqabaaaaa@3940@ and − E b / T b − E b / T b MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGHsisldaGcaaqaamaalyaabaGaamyramaaBaaaleaacaWGIbaabeaaaOqaaiaadsfadaWgaaWcbaGaamOyaaqabaaaaaqabaaaaa@3A2D@ , where E b E b MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbWaaSbaaSqaaiaadkgaaeqaaaaa@3724@ is the energy per bit and T b T b MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGubWaaSbaaSqaaiaadkgaaeqaaaaa@3733@ is the bit interval. The amplitudes are applied to the prototype pulse shape p(t) p(t) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaaiikaiaadshacaGGPaaaaa@388E@ with unit amplitude to generate a pair of signaling waveforms s 1 (t)= E b / T b p(t) s 1 (t)= E b / T b p(t) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGZbWaaSbaaSqaaiaaigdaaeqaaOGaaiikaiaadshacaGGPaGaeyypa0ZaaOaaaeaadaWcgaqaaiaadweadaWgaaWcbaGaamOyaaqabaaakeaacaWGubWaaSbaaSqaaiaadkgaaeqaaaaaaeqaaOGaamiCaiaacIcacaWG0bGaaiykaaaa@41D2@ and s 0 (t)=− E b / T b p(t) s 0 (t)=− E b / T b p(t) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGZbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiaadshacaGGPaGaeyypa0JaeyOeI0YaaOaaaeaadaWcgaqaaiaadweadaWgaaWcbaGaamOyaaqabaaakeaacaWGubWaaSbaaSqaaiaadkgaaeqaaaaaaeqaaOGaamiCaiaacIcacaWG0bGaaiykaaaa@42BE@ . This signaling scheme is called binary antipodal signaling.

Many different pulse shapes are used in practice, based on the application. This project considers two specific pulse shapes, namely, rectangular and Manchester. Both of the pulse shapes are of the polar NRZ (non return to zero) type. The Figure 3 screencast video continues the discussion by describing these two pulse shapes in more detail.

Figure 3: [video] Rectangular and Manchester polar NRZ pulse shapes

The signal point mapper and pulse generator of Figure 2 describe the desired amplitudes and pulse shape, while the transmit filter converts the message bitstream into a sequence of signaling waveforms. The transmit filter is an FIR filter driven by an impulse train derived from the signal point mapper amplitudes; the FIR filter coefficients are the pulse shape values. Refer to the screencast video in pam_TransmitFilter.vi for full implementation details.

The bit sync generator block sends pulses to the receiver to indicate the beginning and ending a bit interval.

Additive white Gaussian noise (AWGN) impairs signals as they pass through an electromagnetic medium, including the electronics in the transmitter and receiver. Adding the output of a Gaussian random number generator to the transmitted signal simulates the AWGN impairment of a real channel.

The degree of signal impairment is reported as a ratio of signal strength to noise ratio (SNR). Digital communication systems define signal-to-noise ratio as E b / N 0 E b / N 0 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcgaqaaiaadweadaWgaaWcbaGaamOyaaqabaaakeaacaWGobWaaSbaaSqaaiaaicdaaeqaaaaaaaa@38FD@ (pronounced "ebb know"), where E b E b MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbWaaSbaaSqaaiaadkgaaeqaaaaa@3724@ is the energy per bit and N 0 N 0 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGobWaaSbaaSqaaiaaicdaaeqaaaaa@3700@ is twice the power spectral density of thermal noise at room temperature. The ratio is dimensionless, and is normally reported in decibels. Refer to the screencast video in util_AWGNchannel_PtByPt.vi to learn how to convert a specified E b / N 0 E b / N 0 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcgaqaaiaadweadaWgaaWcbaGaamOyaaqabaaakeaacaWGobWaaSbaaSqaaiaaicdaaeqaaaaaaaa@38FD@ ratio into the standard deviation parameter of a Gaussian random number generator.

Figure 4 shows the block diagram of a receiver that implements coherent detection with a correlator, also called an integrate-and-dump detector.

Figure 4: Block diagram of PAM receiver based on coherent detection

The correlator multiplies the received signal by the same pulse shape used by the transmitter, and then integrates this product signal over one bit interval. The correlator output is sampled at the end of the bit interval by the sample-and-hold device, and then compared to the zero threshold. If the sampled correlator output is greater than the threshold, the received bit is declared a 1, otherwise the received bit is declared a 0. The integrator is reset to zero at the beginning of each bit interval.

The receiver requires precise synchronization with the transmitter in two respects: the correlator must multiply the received signal by the pulse shape in the same time location, and the integrator must be reset precisely at the beginning of a new bit interval. These requirements are easy to achieve within a simulation, since the transmitter can send pulses to signal the beginning and ending of the bit interval. In a real system, synchronization subsystems extract these timing pulses directly from the received signal, adding cost and complexity to the receiver.

Digital communication system performance in the face of AWGN channel impairment is measured in terms of bit error rate (BER) for a given signal quality E b / N 0 E b / N 0 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcgaqaaiaadweadaWgaaWcbaGaamOyaaqabaaakeaacaWGobWaaSbaaSqaaiaaicdaaeqaaaaaaaa@38FD@ . Coherent detection with binary antipodal signaling as used in this project has a theoretical BER of

where the Q-function Q(x) Q(x) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGrbGaaiikaiaadIhacaGGPaaaaa@3873@ describes the area under a zero-mean unit-variance Gaussian probability density function from x x MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG4baaaa@3644@ to positive infinity, i.e., the area under the positive tail of the Gaussian. Equation Equation 1 serves as the benchmark for the simulated BER of the system constructed in this project.