OFDM For 4G Wireless Communications

OFDM For 4G Wireless Communications 

4G Communications

Time domain analysis:

Assume a channel that has the following impulse response h(t).

If we send a pulse S(t) over this channel, the pulse shape would be

convoluted with the channel impulse response as shown in the Figure. 

Note that the pulse becomes dispersed or extended in time interfering 

                     with surrounding pulses and causing inter-symbol interference (ISI).  

Now compare the two cases of T >> τ and T < τ :

First case:

T < τ  

Pulse completely distorted.

ISI is significant in this case. As shown in the figure

Second case:

T >>τ 

Pulse extended but the extension are much smaller than T the output behaves like the transmitted rectangular pulse. As shown in the figure

Frequency domain analysis:

Channel Frequency Response H(f).

High rate signal spectrum (narrow pulse).

Low rate Signal spectrum (wide pulse).

A wide-band (High rate) signal is completely distorted.

A narrow band (Low rate) signal is essentially seeing a flat channel.

Discussion

A high data rate transmitted signal has a consequent large bandwidth. 

This means that it subjected to frequency selective or frequency dependent fading, which can distort the signal significantly.

One solution is to divide the bandwidth available for transmission into many narrow-band sub channels .

Low data rate sub channel‘s frequency component encounter an almost flat channel. (The band over which the channel is almost constant is called the coherence bandwidth of the channel) Relative to the narrow sub channel, the channel is basically a frequency-independent complex number, i.e.; amplitude and a phase shift.

Conclusion from Both analyses

Short pulses suffer severely from channel. But we need these short pulses in order to send a greater number of them in given time period, i.e., to increase data or bit transmission rate. One solution is to use short pulses (high data rate) and an equalizer at receiver. 

The equalizer is a filter that compensates for the distortion induced by channel characteristics.

For very high data rates a sophisticated equalizer is needed and may not be ever feasible. Is there another solution? Yes, stick to long pulses. But how can we then increase the data rate? We can use many frequency channels (called sub channels), and hence the name FDM (Frequency Division Multiplexing). Over each of these sub channels the data rate is low, but taken together and since they operate in parallel, a very high data rate can be achieved while circumventing the dispersive influence of the channel.

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