Fixed Capacity by Channel Inversion q The traditional

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Fixed Capacity by Channel Inversion q The traditional channel inversion approach is the proper

Fixed Capacity by Channel Inversion q The traditional channel inversion approach is the proper choice for delay-limited transmissions (such as voice), when we have slow fading channels and can not wait for the channel to become better. q Similar to CDMA and GSM power control approach, fading inverted to maintain constant SNR at the receiver and fixed rate. q Mainly may used for slow-fading scenarios that we may not have i. i. d. channel samples over time. q Should use truncating to avoid large transmit powers for very poor channels. q Simplifies design: fixed rate

Optimal Capacity by Water-Filling in Time Domain (1) q However, in fast fading scenario,

Optimal Capacity by Water-Filling in Time Domain (1) q However, in fast fading scenario, we can adjust our transmission to get an overall optimum performance. q Leads to optimization problem of time-varying channel capacity: q In this case we will also get a parallel channel model and so the solution will be similar to traditional water-filling solution. q Power Adaptation: γ 0 chosen such that power constraint is met.

Optimal Capacity by Water-Filling in Time Domain (2)

Optimal Capacity by Water-Filling in Time Domain (2)

Optimal Capacity by Water-Filling in Time Domain (3) Variable Rate Coding q So, in

Optimal Capacity by Water-Filling in Time Domain (3) Variable Rate Coding q So, in practice, for each value of γ, we select an encoding scheme, send the codes and at receiver use proper decoding. q Obviously codes change over time as γ changes. q Code simplified since dealing with AWGN subchannels. q Optimum time varying rate, so more suitable for data applications, rather than fixed rate voice communications.

Optimal Capacity by Water-Filling in Time Domain (4) q How important is channel information

Optimal Capacity by Water-Filling in Time Domain (4) q How important is channel information at TX side for high and low SNRs? q Simple approximations to optimal water-filling: o High SNR: Allocating equal powers at all times is almost optimal. o Low SNR: Allocating all the power when the channel is strongest.

Optimal Capacity by Water-Filling in Time Domain (5) Water-filling does not provide any gain

Optimal Capacity by Water-Filling in Time Domain (5) Water-filling does not provide any gain at high SNR.

Optimal Capacity by Water-Filling in Time Domain (6) Water-filling provides a significant gain at

Optimal Capacity by Water-Filling in Time Domain (6) Water-filling provides a significant gain at low SNR.

Capacity of Fading Channel with no CSIT q At high SNRs capacity is less

Capacity of Fading Channel with no CSIT q At high SNRs capacity is less sensitive to power distribution over channels. q At low SNRs, performance is highly sensitive to received power and we get more degradation due to lack of information at transmitter. q Interesting note: CSI capacity is even higher than AWGN channel at low SNRs, because with fading we can “opportunistically” transmit at high rates when channel temporarily becomes very good!

Main Points q Fundamental capacity of flat-fading channels depends on what is known at

Main Points q Fundamental capacity of flat-fading channels depends on what is known at TX and RX. q In full CSI case, for optimum performance both power and rate should be adapted. q Capacity with TX/RX knowledge: variable-rate variable-power transmission (water-filling) is optimal. q Channel inversion (with truncation) is practical for slow fading fixed rate scenarios.