Spread-Spectrum Techniques

DIRECT-SEQUENCE SPREAD-SPECTRUMThe message x(t) is multiplied by a wideband PN waveform c(t) prior to modulation

The PN generator produces a pseudorandom binary wave c(t) consisting of rectangular pulses called chips. Each chip has a duration of Tc and an amplitude of ±1 so that c²(t) = 1 ( an essential condition for message recovery)

DSS transmitter system and spectra

Pseudrandom binary wave: (a) waveform; (b) autocorrelation and power spectrum.

If we assume that c(t) has the same properties as the random digital wave with ak=±1, then the autocorrelation and power spectral density of c(t) are

PN bandwidth

Chipped message

Independent of c(t) ( Sx is message power or energy)

G = Power spectral density

x~(t) has a spread spectrum whose bandwidth essentially equals the PN bandwidth Wc.

Bandwidth expansion factor = Wc / Wx

This wideband, noise-like signal would be hard to distinguish from background noise at an unauthorized receiver; accordingly, we say that spread-spectrum transmission has a low probability of intercept.

An authorized receiver will recover the message without increased output noise, despite the increased bandwidth. Moreover, the receiver structure suppresses stray interference or hostile jamming.

DSS receiver system and the effects of a single-tone jammer.

additive noise or interference

Synchronous detection after bandpass filtering yields

Notice that this multiplication spreads the spectrum of zi(t) but de-spreads and recovers x(t), assuming near perfect synchronization of the local PN generator.

If the message is digital and sent via BPSK one can use the correlation detector. In the presence of white noise, the probability of error

Eb= Energy per bit No= Noise power spectral density

Note: When z(t) stands for white noise n(t)

DSSS correlation receiver for BPSK.

DSSS Performance in Presence of Interference

Let z(t) stand for an interfering sinusoid or CW jamming signal

In-phase component is

Signal-to-jamming ratio

The single-tone jammers spectrum has been spread and thus, relative to the output signal power, has been reduced by a factor Wx/Wc˂˂1

Process gain (Pg) = bandwidth expansion ratio

One can treat the jammer as just another source of noise

BPSK

If the channel is corrupted by both broadband white noise and a CW jammer

Received power

Jammer power

When rb = Wx

The jamming margin is used as a measure of a system’s ability to operate in the presence of interference. If, in a given system, we specify a minimum Pe or minimum Eb>NJ ratio and a relatively large Pg, then the system will exhibit rejection of interference.

Let the channel is shared with M-1 other spread-spectrum users—as is the case with code division multiple access (CDMA) — each one would have their own unique spreading code and arrival times at the receiver

Multiple Access

where Am, cm(t), tm, and Ѳm denote the signal amplitude, spreading code, time delay, and phase, respectively, of the mth user

In the case of BPSK, the output of the correlation receiver

z(tk)=cumulative interference of the additional M-1 CDMA users

If for simplicity Am is set to 1, then after despreading

Notice that since xm(t) = ± 1, the integration term becomes the crosscorrelation between the desired and the interferer’s PN codes. Therefore, minimizing the cross-correlation between spreading codes minimizes the interference between CDMA users. Ideally, each PN code would be chosen to be orthogonal to the other, thereby making z(tk) = 0. Unfortunately, with practical systems this is not completely possible.

All interfering signals appear to the system as broadband noise. Therefore, unlike TDMA and FDMA, in which additional users manifest themselves as crosstalk, each CDMA user merely adds to the ambient noise floor.

Multipath and the Rake Receiver

M - 1 users sharing the channel + delayed or multipath versions of the desired signal

Model of multipath channel whereby the transmitted signal travels on three distinct paths

Each path introduces a delay ti and attenuation factor Ai.

To overcome the effects of multiple versions of the signal interfering with each other, and to take advantage of path diversity for improved signal-to-noise ratio (SNR) and signal-to-interferance ratio ( SIR), a scheme of separate receivers for each signal path is used and then incorporate delay and gain adjustments to each one to enable constructive addition of the multiple signal versions.

Input y(t) is fed to the dispreading multipliers, each one having a PN source that is in phase with one of the multipath components. The output of each ith dispreading multiplier

Three-finger Rake receiver

Rake receiver for signals that have three multipath components

i = 0, 1, 2

i = 0, 1, 2pseudonoise

The output of each of the i multipliers is then fed to a diversity combiner that consists of a set of adjustable delay and gain elements so that the outputs add constructively, since the signal from each finger will have identical delays. The signal from each path is scaled so as to increase the level of signals from the fingers with high signal-to-noise ratios and reduce the level of those with low signal-to-noise ratios. This naturally scales the paths according to the received-signal quantities. Both the gain and scaling adjustments can be done dynamically according to the path conditions. The diversity combiner output is

i = 0, 1, 2

Three-finger Rake receiver that incorporates separate correlation stages for each signal path.

HOMEWORK

FREQUENCY-HOPPING SPREAD-SPECTRUM

The message is spread out over numerous carrier frequencies, the jammer has a reduced probability of hitting any one in particular. Otherwise the jammer has to spread its power over a wider frequency range in order to be effective.

Slow-hopping SS: one or more message symbols are transmitted per hop

Fast-hopping SS : there are two or more frequency hops per message symbol.

With slow-hopping SS, the receiver demodulatesthe signal like any other M-ary FSK signal. However, with fast hop SS there are several hops per symbol, so the detector determines the value based on either a majority vote or some decision rule such as maximum likelihood.The message is usually M-ary FSK modulated to some carrier frequency fc, although some systems use BPSK. The modulated message is then mixed with the output of a frequency synthesizer. The frequency synthesizer’s output is one of Y 2k values, where k equals the number of outputs from the PN generator. The BPF selects the sum term from the mixer for transmission on the channel.

FHSS transmitter

FHSS receiver

FHSS Performance in the Presence of Interference

Types of jamming for FHSS systems: (a) barrage; (b) partial-band; (c) singletone; (d ) multiple-tone.

PN generationIn order for a receiver to properly recognize a transmitter’s signal and, in particular, prevent false synchronization, it is important that the PN code’s autocorrelation function have the largest peak possible at τ=0 and τ = kTc and as be low as possible everywhere else. This objective is met if the PN generator produces a maximal-length (ML) sequence.

To minimize jamming and/or casual eavesdropping, the PN sequence should be as long as possible; the longer the sequence, the more effort it takes for an unauthorized listener to determine the PN sequence. However, with linear codes, an eavesdropper only requires the knowledge of 2˄n chips to determine the shift register connections. Therefore vulnerability to unauthorized listening can be reduced by either making frequent changes in the PN sequence during transmission or by using some nonlinear scheme for the feedback connections. PN codes that are both secure and have desirable correlation characteristics are generally difficult to find, and thus if the goal is secure communications, then the message should be encrypted separately.

Shift register sequence generator with [5, 2] configuration

If the appropriate feedback tap connections are made, then an n-bit register can produce a maximal-length (ML)

second and fifth cells are tapped

1. Balance. The number of ones generated is one more than the number of zeros generated.2. Run. A run is a sequence of a single type of digit. An ML sequence will have one-half of its runs of length 1, one-quarter of its runs of length 2, one-eighth of its runs of length 3, and so on.3. Autocorrelation. Its autocorrelation function has properties similar to the correlation properties of random noise, in that there is a single autocorrelation peak.4. The mod-2 addition of an ML sequence and any shifted version of it results in a shifted version of the original sequence.5. Except for the zero state, all of the 2n possible states will exist during the sequence generation.

ML sequence

Let a PN sequence sk be used to form a binary polar NRZ signal

where p(t) is a rectangular pulse and the amplitude of the kth pulse is

The signal s(t) is deterministic and periodic, with period NTc, and has a periodic autocorrelation function

If N is very large and Tc very small

s

so the PN signal acts essentially like white noise with a small DC component

Example: Autocorrelation of a [3,1] Shift RegisterA 3-bit, [3, 1] shift register configuration with values of 111 produces a periodic ML sequence of 1110100 with N =7.

Cross-correlation of [3,1] and [3,2] PN sequences

Auto- and crosscorrelation of [3, 1] and [3, 2] PN sequences.

Cross-correlation ratios for various ML sequence lengths and feedback connections (produced from a single shift register).

Sequences generated from a single shift register do not have good cross-correlation properties, making them unsuitable for CDMA systemsTo generate a different output sequence requires changing the feedback connections; therefore, a given shift register length will give us relatively few unique output sequences.

Preferred pairs, Gold Codes

Gold code generator.