TAILIEUCHUNG - Diversity

Communication over a flat fading channel has poor performance due to significant probability that channel is in a deep fade. Reliability is increased by providing more resolvable signal paths that fade independently. Diversity can be provided across time, frequency and space. | 3. Diversity Main story Communication over a flat fading channel has poor performance due to significant probability that channel is in a deep fade. Reliability is increased by providing more resolvable signal paths that fade independently. Diversity can be provided across time, frequency and space. Name of the game is how to exploit the added diversity in an efficient manner. Baseline: AWGN Channel BPSK modulation Error probability decays exponentially with SNR. Gaussian Detection Rayleigh Flat Fading Channel BPSK: Coherent detection. Conditional on h, Averaged over h, at high SNR. Rayleigh vs AWGN Conditional on h, When error probability is very small. When error probability is large: Typical error event is due to channel being in deep fade rather than noise being large. Typical Error Event BPSK, QPSK and 4-PAM BPSK uses only the Q-phase is wasted. QPSK delivers 2 bits per complex symbol. To deliver the same 2 bits, 4-PAM requires 4 dB more transmit power. QPSK exploits the available degrees of freedom in the channel better. A good communication scheme exploits all the available . in the channel. Time Diversity Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods. Coding alone is not sufficient! Example:GSM Amount of time diversity limited by delay constraint and how fast channel varies. In GSM, delay constraint is 40ms (voice). To get full diversity of 8, needs v > 30 km/hr at fc = 900Mhz. Simplest Code: Repetition After interleaving over L coherence time periods, Repetition coding: for all This is classic vector detection in white Gaussian noise. where and Geometry For BPSK Is a sufficient statistic (match filtering). Reduces to scalar detection problem: Deep Fades Become Rarer Performance Beyond Repetition Coding Repetition coding gets full diversity, but sends only one symbol every L symbol times. Does not exploit fully the degrees

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