SYSTEM MODEL AND PREAMBLE DESIGNwhere hi is the i-th channel coefficient, Xi is the i-th transmit data symbol and Wi is the white Gaussian noise.The upstream cable modem consists of Reed-Solomon (RS) encoder, byte interleaver, scrambler (or randomizer), preamble prepending block, symbol mapper, pre-equalizer and transmit filter as can be seen in Fig. 1. In DOCSIS specification, the preambles consist of QPSK symbols with maximum length of 1536 bits and data symbols that could be QPSK, 8-16-, 32-and 64-QAM symbols. The scrambler of the upstream cable modem has the arbitrarily programmable I5-bit seed value. The pre-equalizer has 24 taps and it is operated in traffic mode. Transmit filter is square root-raised cosine filter with 0.25 roll-offThe receiver detects the data by matched filter and its output is

The upstream of digital cable modem is a burst mode transmission system, where a burst contains the preamble and data. In this paper, we consider algorithms for the symbol timing, carrier frequency-and phase-offset recovery for the upstream cable modem, that are compliant to DOCSIS 2.0. Several algorithms are tested and verified to find the best algorithm for each of the three recovery blocks, respectively. To fit to the DOCSIS specification, Oerder & Meyr's is chosen for the timing recovery algorithm, Mengali & Morelli's is chosen for the carrier frequency-offset recovery algorithm and Cartwright's is chosen for blind carrier phase recovery. We decide the optimal preamble length for these algorithms and check the error variance. Finally, we show the error performance of the entire system. also consider the carrier phase offset recovery algorithm [7], [8].The system model is shown in Figure 1. The transmitter of the upstream cable modem consists of Reed-Solomon (RS) encoder, block interleaver, scrambler (randomizer), symbol mapper, transmit equalizer, and transmit filter. System descriptionThe upstream Physical Media Dependent (PMD) sublayer uses a Time Division Multiple Access (TDMA) burst type format. In upstream cable modem, required parameter values are summarized in Table 1.