Wireless Communication Lecture 4 Omar Abu-Ella

Channel Capacity Omar Abu-Ella

Shannon Capacity Defined as the maximum mutual information of channel Maximum error-free data rate a channel can support. Theoretical limit (usually don’t know how to achieve) Depends on the channel characteristics We focus on AWGN channel with fading Omar Abu-Ella

AWGN Channel Capacity Omar Abu-Ella

Power and Bandwidth Limited Regimes Omar Abu-Ella

Band limited regime SNR>>1 N0=1 assumed Omar Abu-Ella

Power limited regime SNR<<1 N0=1 assumed Omar Abu-Ella

Capacity Curve Omar Abu-Ella

Shannon Limit in AWGN channel What is the minimum SNR per bit (Eb/N0) for reliable communications? Omar Abu-Ella

Capacity of Flat-Fading Channels Capacity defines theoretical rate limit Maximum error free rate a channel can support Depends on what is known about channel CSI: channel state information CDI: channel distribution information Unknown fading: Worst-case channel capacity Fading Known at Receiver Only Omar Abu-Ella

Capacity of Fading Channels Omar Abu-Ella

Capacity of fading channel Omar Abu-Ella

Fading channel, only Rx knows CSI Omar Abu-Ella

Fading Known at both Transmitter and Receiver For fixed transmit power, same as only receiver knowledge of fading Transmit power P(g) can also be adapted Leads to optimization problem: Omar Abu-Ella

Optimal Adaptive Scheme Power Adaptation Capacity Waterfilling 1 g g0 Omar Abu-Ella

An equivalent approach: power allocation over time Omar Abu-Ella

Optimal Solution The water-filling solution is given by To define the water level, solve: Omar Abu-Ella

Asymptotic results Omar Abu-Ella

Performance Comparison At high SNR, water-filling does not provide any gain. Transmitter knowledge allows rate adaptation and simplifies coding. Omar Abu-Ella

Channel Inversion Fading inverted to maintain constant SNR Simplifies design (fixed rate) Greatly reduces capacity Capacity is zero in Rayleigh fading Truncated inversion Invert channel above cutoff fade depth Constant SNR (fixed rate) above cutoff Cutoff greatly increases capacity Close to optimal Omar Abu-Ella

Frequency Selective Fading Channels For time-invariant channels, capacity achieved by water-filling in frequency Capacity of time-varying channel unknown Approximate by dividing into subbands Each subband has width Bc (like MCM). Independent fading in each subband Capacity is the sum of subband capacities 1/|H(f)|2 Bc P f Omar Abu-Ella