OFDM principle and spread spectrum types

Principle of OFDM

Orthogonal Frequency Division Multiplexing splits a high-rate stream into N parallel low-rate streams, each on its own subcarrier. The subcarriers are spaced by Δf = 1/T_s, which makes them orthogonal: over one symbol period, the integral of the product of any two different subcarriers is zero.

∫₀^Ts cos(2π f_i t) cos(2π f_j t) dt = 0,  i ≠ j
f_k = f_0 + k/T_s

So the spectra may overlap, yet each subcarrier peak falls at the nulls of all others, and no inter-carrier interference occurs.

 |H|   /\  /\  /\  /\
      /  \/  \/  \/  \     overlapping sinc spectra
     /   /\  /\  /\   \    peak of one = null of others
 ---+---+---+---+---+---> f
       Δf=1/Ts

Key ideas:

• Long symbols: each subcarrier's symbol is N times longer than the original, so the delay spread is small compared with T_s and each subcarrier sees flat fading.
• IFFT/FFT: modulation and demodulation of all subcarriers is done by an N-point IFFT at the transmitter and FFT at the receiver.
• Cyclic prefix: a copy of the end of each symbol is placed at its start; if it is longer than the delay spread, ISI is removed and a one-tap equalizer per subcarrier is enough.

Types of spread spectrum modulation

1. Direct sequence SS (DSSS): data is multiplied by a fast PN chip sequence and BPSK modulated. The receiver multiplies by the same code to despread. Example: IS-95, 802.11b.
2. Frequency hopping SS (FHSS): the carrier of an FSK signal jumps among many frequencies in a PN-defined order; slow or fast hopping. Example: Bluetooth.
3. Time hopping SS (THSS): data is sent in short bursts in time slots chosen by a PN code within each frame. Example: impulse-radio UWB.
4. Hybrid systems: combinations such as DS/FH, which mix the advantages of both (e.g. military radios).