0.14 Mix’n’match receiver design  (Page 2/9)

This section describes the construction of the sampled IF signal that must be processed by the ${\mathcal{M}}^6$ receiver. The system that generatesthe analog received signal is shown in block diagram form in [link] . The front end of the receiver that turns thisinto a sampled IF signal is shown in [link] .

The original message in [link] is a character string of English text. Each character is converted into a 7-bit binary stringaccording to the ASCII conversion format (e.g., the letter “a” is 1100001 and the letter “M” is 1001101), as inExample  [link] . The bit string is coded using the (5,2) linear block codespecified in blockcode52.m which associates a 5-bit code with each pair of bits. The output of the block codeis then partitioned into pairs that are associated with the four integers of a 4-PAM alphabet $\pm 1$ and $\pm 3$ via the mapping

as in Example  [link] . Thus, if there are $n$ letters, there are $7n$ (uncoded) bits, $7n\left(\frac{5}{2}\right)$ coded bits, and $7n\left(\frac{5}{2}\right)\left(\frac{1}{2}\right)$ 4-PAM symbols. These mappings are familiar from [link] , and are easy to use with the help of the M atlab functions bin2text.m and text2bin.m . Exercise  [link] provides several hints to help implementthe ${\mathcal{M}}^6$ encoding, and the M atlab function nocode52.m outlines the necessary transformations from the original text into a sequence of 4-PAMsymbols $s\left[i\right]$ .

In order to decode the message at the receiver, the recovered symbols must be properly grouped and the start ofeach group must be located. To aid this frame synchronization, a marker sequenceis inserted in the symbol stream at the start of every block of 100 letters (at the start of every 875 symbols).The header/training sequence that starts each frame is given by the phrase

which codes into 245 4-PAM symbols and is assumed to be known at the receiver.This marker text string can be used as a training sequence by the adaptive equalizer.The unknown message begins immediately after each training segment. Thus, the ${\mathcal{M}}^6$ symbol stream is a coded message periodically interrupted by the same marker/training clump.

As indicated in [link] , pulses are initiated at intervals of $T_t$ seconds, and each is scaled by the 4-PAM symbol value.This translates the discrete-time symbol sequence $s\left[i\right]$ (composed of the coded message interleaved with the marker/training segments)into a continuous-time signal

The actual transmitter symbol period $T_t$ is required to be within $0.01$ percent of a nominal ${\mathcal{M}}^6$ symbol period $T=6.4$ microseconds. The transmitter symbol period clock is assumed to besteady enough that the timing offset ${ϵ}_t$ and its period $T_t$ are effectively time-invariant over the duration of a single frame.

Details of the ${\mathcal{M}}^6$ transmission specifications are given in [link] . The pulse-shaping filter $P\left(f\right)$ is a square-root raised cosine filter symmetrically truncated to eight symbol periods.The rolloff factor $\beta$ of the pulse-shaping filter is fixed within some range and is known at the receiver,though it could take on different values with different transmissions.The (half-power) bandwidth of the square-root raised cosine pulse could be as large as $\approx$ 102 kHz for the nominal $T$ . With double sideband modulation, the pulse shape bandwidthdoubles so that each passband FDM signal will need a bandwidth at least 204 kHz wide.