UK EE 422G - Lab 7 Bit Detection with the Correlation Receiver

Unformatted text preview:

EE 422G - Signals and Systems Laboratory Lab 7 Bit Detection with the Correlation Receiver Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 October 30, 2011 Objectives: - Know the basic operation of the optimal matched filter and correlation receivers for detecting known/deterministic waveforms in noise. - Implement the correlation receiver for detecting signals in noise. - Implement the match filter for decoding bit streams received from noisy, bandlimited channels, and computing bit error rates. 1. Background: In modern digital communication systems information from signals, such as speech, video, and text must be transferred to other locations. Noise corrupts the signal during transmission, which arises from many sources, including interference from other transmitters and thermal motion of the electrons. The purpose of the receiver is to accurately recover the transmitted information, even in the presence of noise and distortion. The problem of recovering signals corrupted by noise has several solutions. The correlation receiver can be shown to be the best solution (optimal) for recovering digital data encoded with a known waveform in the presence of additive white Gaussian noise (AWGN). A correlation receiver basically compares the received signal to the waveforms it expects to receive. This applies directly to a digital communication problem since each bit (or bit sequence) can be encoded to a set of distinct waveforms known to both the transmitter and receiver. For example, consider the signal of Fig. 1a. If the transmitted waveform is corrupted by noise, the received signal may look like the solid-lined plots of Figs. 1b and c. For a correlation operation, the received signals values are aligned with a template (shown in the dashed lines of Figs. 1b and c), and the sum of products between the received signal and template are taken over an interval equal to the ideal waveform duration. The correlation will be greatest when the template is aligned with the received signal, as shown in Fig. 1b. A lesser response occurs as the misalignment increases. Fig. 1c shows a misalignment that results in the minimum response (largest negative number). The correlation receiver often uses signals that are zero-mean to exploit the cancellation between positive and negative values in the correlation sum.(a) (b) (c) Figure 1. (a) Ideal transmitted waveform. (b) Matched alignment with noisy received waveform for maximum correlation receiver response. (c) Mismatched alignment with noisy received waveform for minimum correlation receiver response. A correlation receiver therefore segments the signal into intervals that are synchronized with the bit intervals, and integrates the product of the received signal and template over the interval to produce correlation values. The correlation values become detection statistics used to decide on the most likely bit value that was transmitted for each interval. In the case of binary signaling (0 or 1) there are only 2 possible symbols, so 2 correlation receivers would operate in parallel corresponding to waveforms associated with each bit. The bit channel with the greatest correlation value corresponds to the detected bit. The synchronization of the segment intervals requires that both the source and receiver have the same clock signal or some way to synchronize before applying the correlation receiver, since the alignment of the correlation interval affects the result. An example of this receiver is shown in Fig 2, where )(0tf is the template for the 0 bit,)(1tf is the template for the bit 1, and T is the synchronized bit interval. Every T seconds the input is correlated with the template and the correlation output is sampled to obtain the detection statistics. In this case the decision rule is to simply decide on the bit whose template has the best match (largest value). A bit error occurs when noise or bandwidth limitations result in an incorrect decision. The numbers of errors per bit is referred to as the bit error rate, or equivalently the percentage of errors.Figure 2. Correlation receiver synchronized to waveform intervals for bit sequence detection. For applications where a physical event emits signals, apart from a clock synchronization (such as a blood pressure drop, or an echo from an active sonar), the receiver must detect the signals as well as estimate when the signal was received. This is typically the case for sonar or radar systems, where the time of the received echo depends on the distance between the target and receiver (which can vary as the target moves through the space of interest). The detection of the echo signal indicates the presence of a target, and the time at which the echo returns indicates the distance between the target and receiver. In this case, intervals for correlation cannot be predetermined. Therefore, the signal template is slid continuously over the received signal producing a continuous output from which decisions are made on whether a target is present. This is typically done with a simple threshold. If there is a match with the signal of interest, the output will exceed typical values corresponding to the no-signal case. An example of the correlation filter implemented as a matched filter for this case is shown in Fig. 3. The signal of interest is a tapered sine wave. The top set of 3 waveforms in Fig. 3 show the signal, added noise, and the continuous sequence of detection statistics for the template that matches the signal. The lower 3 waveforms show the case when no signal is present (noise only). Note that detection statistics near 0.2 seconds reach a maximum for the case when a signal is present. This value is at least one order of magnitude greater than any of the outputs for the noise only signal. If accurate statistics of the noise fluctuations are available, the threshold can be set to achieve a specific false-alarm rate. In general, there is a trade-off between the false-alarm rate (the likelihood that noise is detected as the signal – false detection) and the detection rate (likelihood that a target will be detected when present – true detection). A high threshold results in lower false-alarm rates but also lower detection rate, and vise versa. TChannel 0 )()()( tntstx )(0tf)(1tftTtTtTtTDecision Rule: If Channel 0 greater than Channel 1, decide bit 0.


View Full Document

UK EE 422G - Lab 7 Bit Detection with the Correlation Receiver

Documents in this Course
Load more
Download Lab 7 Bit Detection with the Correlation Receiver
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lab 7 Bit Detection with the Correlation Receiver and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lab 7 Bit Detection with the Correlation Receiver 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?