Spread Spectrum Communications

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Spread Spectrum Communications

1、 Shannon – Hartley Theorem

No discussion on spread spectrum techniques would be complete without a brief recap of the Shannon– Hartley Theorem.

In information theory, the Shannon–Hartley theorem states the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.

The theorem establishes Shannon's channel capacity for a communication link and defines the maximum data rate (information) that can be transmitted within a specified bandwidth in the presence of noise interference:

        Equation 1

Where:

C = channel capacity (bit/s)

B = channel bandwidth (Hz)

S = average received signal power (Watts)

N = average noise or interference power (Watts)

S/N = signal to noise ratio (SNR) expressed as a linear power ratio

By rearranging Equation 1 from log base 2 to the natural log, e, and by noting that we can  manipulate the equation as follows:

       Equation 2

For spread spectrum applications the signal to noise ratio is small, since the signal power is often below  the noise floor. Assuming a noise level such that S/N << 1, Equation 2 can be re-written as:

Or: Equation 3

From equation 3  it can be seen that to transmit error free information in a channel of fixed noise-to-signal ratio, only the transmitted signal bandwidth need be increased.

2、 Spread-Spectrum Principles

As has been noted above, by increasing the bandwidth of the signal we can compensate for the degradation of the signal-to-noise (or noise-to-signal) ratio of a radio channel.

In traditional Direct Sequence Spread Spectrum (DSSS) systems, the carrier phase of the transmitter  changes in accordance with a code sequence. This process is generally achieved by multiplying the wanted data signal with a spreading code, also known as a chip sequence. The chip sequence occurs at a much faster rate than the data signal and thus spreads the signal bandwidth beyond the original bandwidth occupied by just the original signal. Note that the term chip is used to distinguish the shorter coded bits from the longer un-coded bits of the information signal.

Figure 1: Modulation / Spreading Process

At the receiver, the wanted data signal is recovered by re-multiplying with a locally generated replica of the spreading sequence. This multiplication process in the receiver effectively compresses the spread signal back to its original un-spread bandwidth, as illustrated below in  Figure 2. It should be noted that the same chip sequence or code must be used in the receiver as in the  transmitter to correctly recover the information.

Figure 2: Demodulation / De-spreading Process

The amount of spreading, for direct sequence, is dependent on the ratio of "chips per bit" - the ratio of  the chip sequence to the wanted data rate, is referred to as the processing gain (Gp), commonly  expressed in dB.

Where:

RC = chip rate (Chips/second)

Rb = bit-rate (bits/second

As well as providing inherent processing gain for the wanted transmission (which enables the receiver to correctly recover the data signal even when the SNR of the channel is a negative value); interfering  signals are also reduced by the process gain of the receiver. These are spread beyond the desired information bandwidth and can be easily removed by filtering.

DSSS is widely used in data communication applications. However, challenges exist for low-cost or power-constrained devices and networks.

Often, as is the case with GPS or the DSSS PHY of IEEE Standard 802.15.4k, the system will require a highly accurate and expensive reference clock source. In addition, the longer the spreading code or sequence, the longer the time required by the receiver to perform a correlation over the entire length of the code sequence, or by either searching sequentially through code sequences or implementing multiple correlators in parallel

This is especially of concern for power-constrained devices that cannot be “always-on” and thus need to repeatedly and rapidly synchronize.