capacity of wireless channel

8/12/2019 Capacity of Wireless Channel

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CAPACITY OFWIRELESS CHANNELS

Presented

chrisTO ja

GEC Thris



INTRODUCTION

The growing demand of wireless communication.

The maximum data rate that can be transmitted with minimum errorprobability.

Shannon’s theory.

Channel capacity is the tightest upper bound on the rate of informatiocan be reliably transmitted over a communications channel.

The coding theorem proved that a code did exist that could achieve a rate close to capacity with negligible probability of error.

The converse proved that any data rate higher than capacity could noachieved without an error probability bounded away from zero.

CHRISTO JACOB K, G



INTRODUCTION

Depending upon 2 types of channels Time invariant: AWGN channels

Time variant: Fading channels

CHRISTO JACOB K, G



Consider a discrete time AWGN noise channel with input output relatio = +

Assume channel bandwidth B, transmit power P.

The received signal-to-noise ratio (SNR) is given by

=

The capacity of this channel is given by

= 1 +

CAPACITY IN AWGNCHANNELS

CHRISTO JACOB K, G



CAPACITY IN AWGNCHANNELSShannon’s coding theorem and converse theorem are proved using the concmutual information between the channel input and output.

For a discrete memoryless time-invariant channel with random input x and randooutput y , the channel’s mutual information is defined as

; = , log( (,) ())

,

Mutual information can also be written in terms of the entropy in the channel outpconditional output y | x as

; = − (/) Shannon proved that channel capacity equals the mutual information of the chanmaximized over all possible input distributions

= () ; = () , log( (,) ())

,

CHRISTO JACOB K, G



PROBLEM

Consider a wireless channel where power falloff with distance follo

formula Pr(d) = Pt(d 0 /d ) 3 for d 0 = 10 m. Assume the chann

bandwidth B = 30 kHz and AWGN with noise PSD N 0 / 2, where N

W/Hz. For a transmit power of 1W, find the capacity of this chann

transmit – receive distance of 100 m and 1 km.

CHRISTO JACOB K, G



SOLUTION

The received SNR is γ = Pr (d )/N 0 B = .13/(10-9 ·30 ·103) = 33 = 15 dB for d = 100 m

γ = .013/(10-9 ·30 ·103) = .033 = −15 dB for d = 1000 m.

The corresponding capacities are

C = B log2(1+γ) = 30000 log2(1+33) = 152.6 kbps for d = 100 m

C = 30000 log2(1+ .033) = 1.4 kbps for d = 1000 m.

CHRISTO JACOB K, G



CAPACITY OF FLAT FADINGCHANNELS

CHRISTO JACOB K, G



CAPACITY OF FLAT FADINGCHANNELS

The channel gain g [i ], also called the channel side information (CSI),changes during the transmission of the codeword.

The capacity of this channel depends on what is known about g [i ] at ttransmitter and receiver. We will consider three different scenarios regthis knowledge as follows. Channel distribution information (CDI): The distribution of g [i ] is known to the transm

receiver.

Receiver CSI: The value of g [i ] is known to the receiver at time i , and both the transand receiver know the distribution of g [i ].

Transmitter and receiver CSI: The value of g [i ] is known to the transmitter and receitime i , and both the transmitter and receiver know the distribution of g [i ].

CHRISTO JACOB K, G



CHANNEL DISTRIBUTIONINFORMATION KNOWN

Channel gain distribution p(g) is known at txr and rxr.

For iid fading capacity given by

= () ; = () , log( (,) ())

,

But solving for capacity can be complicated depending on nature of faddistribution.

For iid Rayleigh fading channel power gain is exponentially distributed changes independently with each channel use.

CHRISTO JACOB K, G



CHANNEL SIDEINFORMATION AT RECEIVER

The value of g[i] is known at the receiver at the time i, and both thetransmitter and receiver know the distribution of g[i]

There are two channel capacity definitions that are relevant to the systdesign Shannon capacity, also called ergodic capacity, and capacitoutage

For Shannon capacity the rate transmitted over the channel is constantransmitter cannot adapt its transmission strategy relative to the CSI. Tcapacity reduces.

An alternate capacity definition for fading channels with receiver CSI iscapacity with outage

This is defined as the maximum rate that can be transmitted over a channe

outage probability corresponding to the probability that the transmission candecoded with negligible error probability. CHRISTO JACOB K, G

capacity of wireless channel

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