SPREAD SPECTRUM | DIRECT SEQUENCE SPREAD SPECTRUM (DS-SS) WITH BPSK | FREQUENCY HOPPED

A BASIC IDEA OF SPREAD SPECTRUM
An important aspect of spread-spectrum modulation is that it can provide protection against externally generated interfering (jamming) signals with finite power. The jamming signal may consist of a fairly powerful broadband noise or multitone waveform that is directed at the receiver for the purpose of disrupting communications. Protection against jamming waveforms is provided by purposely making the information-bearing signal occupy a bandwidth far in excess of the minimum bandwidth necessary to transmit it. This has the effect of making the transmitted signal assume a noiselike appearance so as to blend into the background. The transmitted signal is thus enabled to propagate through the channel undetected by anyone who may be listening. We may therefore think of spread spectrum as a method of “camouflaging” the ‘information-bearing signal.
One method of widening the bandwidth of an information-bearing (data) sequence involves the use of modulation. Let {b_k} denote a binary data sequence, and {c_k} denote a pseudo-noise (PN) sequence. Let the waveforms b(t) and c(t) denote their respective polar nonreturn-to-zero representations in terms of two levels equal in amplitude and opposite in polarity, namely, ± 1. We refer to b (1) as the information-bearing (data) signal, and to c (t) as the PN signal. The desired modulation is achieved by applying the data signal b(t) and the PN signal c(t)  to a product, modulator or multiplier, as in figure 11.4(a). We know from Fourier transform theory that multiplication of two signals produces a signal whose spectrum equals the convolution of the spectra of the two component signals. Thus, if the message signal b(t) is narrowband and the PN signal c(t) is wideband, the product (modulated) signal m(t) will have a spectrum that is nearly the same as the wideband PN signal. In other words, in the context of our present application, the PN sequence performs the role of a spreading code
diagram
FIGURE 11.4 Idealized model of baseband spread-spectrum system (a) Transmitter. (b) Channel. (c) Receiver
By multiplying the information-bearing signal b(t) by the PN signal c(t), each information bit is “chopped” up into a number of small time increments, as illustrated in the waveforms of figure 11.5. These small time increments are commonly, referred to as chips.
For baseband transmission, the product signal m(t) represents the transmitted signal. We may thus express the transmitted signal as under:
m(t) = c(t) b(t)                                                                    …(11.7)
The received signal r(t) consists of the transmitted signal nn(t) plus an additive interference denoted by i(t), as shown in the channel model of figure 11.4(b)
r (t) = m(t) + i(t)                                                                 …(11.8)
= c(t) b(t) + i(t)
DIAGRAM
FIGURE 11.5 Illustrating the wave-forms in the transmitter of figure 11.4(a)
To recover the original message signal b(t), the received signalr(t) is applied to a demodulator that consists of a multiplier followed by an integrator, and a decision device, as in figure 11.4(c). The multiplier is supplied with a locally generated PN sequence that is an exact replica of that used in the transmitter. Moreover, we assume that the receiver operates in perfect synchronism, with the transmitter, which means that the PN sequence in the receiver is lined up exactly with that in the transmitter. The multiplier output in the receiver is therefore given by
z(t) = c(t) r(t)
or                                               z(t) = c²(t) b (t) + c(t) i(t)                          …(11.9)
Equation (11.9) shows that the data signal b(t) is multiplied twice by the PN signal c(t) whereas the unwanted signal i(t) is multiplied only once. The PN signal c(t) alternates between the levels – 1 and + 1, and the alternation is destroyed when it is squared; hence, we have
c²(t) = 1 for all t                                     …(11.10)
Accordingly, we may simplify equation 11.9 as
z(t) = b(t) + c(t) i(t)                                   …(11.11)
Thus, we see from equation (11.11) that the data signal b(t) is reproduced at the multiplier output in the receiver, except for the effect of the interference represented by the additive term c(t) i(t). Multiplication of the interference i(t) by the locally generated PN signal c(t) means that the spreading code will affect the interference just as it did the original signal at the transmitter. We now observe that 0the data component b(t) is narrowband, whereas the spurious component c(t) i(t) is wideband. Hence, by applying the multiplier output to a baseband (low-pass) filter with a bandwidth just large enough to accommodate the recovery of the data signal b(t), most of the power in the spurious component c(t) i(t) is filtered out. The effect of the interference i(t) is thus significantly reduced at the receiver output.
In the receiver shown in figure 11.4(c), the low-pass filtering action is actually performed by the integrator that evaluates the area under the signal produced at the multiplier output. The integration is carried out for the bit interval 0 ≤ t ≤ T_b, providing the sample value v. Finally, a decision is made by the receiver : If v is greater than the threshold of zero, the receiver says that binary symbol 1 of the original data sequence was sent in the interval 0 ≤ t ≤ T_b, and if v is less than zero, the receiver says that symbol 0 was sent ; if v is exactly zero the receiver makes a random guess in favor of 1 or 0.
In summary, the use of a spreading code (with pseudo-random properties) in the transmitter produces a wideband transmitted signal that appears noiselike to a receiver that has no knowledge of the spreading code. We recall that (for a prescribed data rate), the longer we make the period of the spreading code, the closer will the transmitted signal be to a truly random binary wave, and the harder it is to detect. Naturally, the price we have to pay for the improved protection against interference is increased transmission bandwidth, system complexity, and processing delay. However, when out primary concern is the security of transmission, these are not unreasonable costs to pay.
DIRECT SEQUENCE SPREAD SPECTRUM (DS-SS) WITH BPSK

            As a matter of fact, a direct sequence spread spectrum (DS—SS) system spreads the baseband data by directly multiplying the baseband data pulses with a pseudo-noise sequence. This PN sequence is produced by a pseudo-noise code generator. A single pulse or symbol of the PN waveform is known as a chip. Figure 11.6 shows a basic block diagram of a DS system with binary phase modulation. Synchronized data symbols, i.e., information bits or binary channel code symbols, are added in modulo-2 fashion to the chips before they are phase modulated. A coherent or differentially coherent phase-shift keying (PSK) demodulation is utilized in the receiver.
diagram
FIGURE 11.6 Block diagram of a DS-SS system with binary phase modulation; (a) transmitter and (b) receiver
The received spread spectrum signal for a single user can be represented as
z(t) =  m(t) p(t) cos (2pf_ct + q)                             …(11.12)
where m (t) is the data sequence,
p(t) is the PN spreading sequence,
f_c is the carrier frequency,
and q   is the carrier phase rangle at t = 0
The data waveform is a time sequence of nonoverlapping rectangular pulses, each of which has an amplitude equal to +1 or -1. Each symbol in m (t) represents a data symbol and has duration T_s.
Each pulse in p(t) represents a chip, is usually rectangular with an amplitude equal to +1 or -1, and has a duration of T_c.
The transitions of the data symbols and chips coincide such that the ration T_s or T_c is an integer.
If B_z is bandwidth of z(t) and B is the bandwidth of a conventionally modulated signal m (t) cos (2pfct), the spreading due to p(t) gives B_z >> B.
diagram
FIGURE 11.7 Spectra of desired received signal with interference : (a) wideband filter output and (b) correlator output after despreading.
Figure 11.6 (b) illustrates a DS receiver. Assuming that code synchronization has been achieved at the receiver, the received signal passes through the wideband filter and is multiplied by a local replica of the PN code sequence p(t). If p(t) = + 1, then p²(t) = 1, and this multiplication yields the despread signal s(t) given by
s₁(t) =  m(t) cos (2pf_ct + q)                                   …(11.13)
at the input of the demodoulator. Because s₁ (t) has the form of a BPSK signal, the corresponding demodulation extracts m (t).
Figure 11.7 shows the received spectra of the desired spectrum signal and the interference at the output of the receiver wideband filter. Multiplication by the spreading waveform produces the spectra of figure 11.7(b) at the demodulator input. The signal bandwidth is reduced to B, while the interference energy is spread over an RF bandwidth exceeding B_z. The filtering action of the demodulator removes most of the interference spectrum that does not overlap with the signal spectrum. Thus, most of the original interference energy is eliminated by spreading and minimally affects the desired receiver signal. An approximate measure of the

interference rejection capability is given by the ratio , which is equal to the processing gain defined as
PG =  =  =                                 …(11.14)
The greater the processing gain of the system, the greater will be its ability to suppress in hand interference.
11.4     FREQUENCY HOPPED SPREAD SPECTRUM (FH—SS).
(i) Basic Fundamentals
Frequency hopping involves a periodic change of transmission frequency. A frequency hopping signal may be regarded as a sequence of modluated data bursts with time-varying, pseudorandom carrier frequencies. The set of possible carrier frequencies is called the hopset. Hopping occurs over a frequency band that includes a number of channels. Each channel is defined as a spectral region with a narrowband modulation burst (usually FSK) having the corresponding carrier frequency. The bandwidth of a channel used in the hopset is called the instantaneous bandwidth. The bandwidth of the spectrum over which the hopping occurs is called the total hopping bandwidth. Data is sent by hopping the transmitter carrier to seemingly random channels which are know only to the desired receiver. On each channel, small bursts of data are sent using conventional narrowband modulation before the transmitter hops again.
(ii)        Single Channel Modulation
If only a single carrier frequency (single channel) is used on each hop, digital data modulation is called single channel .modulation. Figure 11.8 shows a single channel FH—SS system. The time duration between hops is called the hop duration or the hopping period and is denoted by T_h. The total hopping bandwidth and the instantaneous bandwidth are denoted by B_z and B, respectively.
The processing gain ;  for FH system.
(iii)       Dehopped Signal
After frequency hopping has been removed from the received signal, the resulting signal is said to be dehopped. If the frequency produced by the receiver synthesizer in figure 11.8 (b) is
diagram
FIGURE 11.8 Block diagram of frequency hopping (F11) system with single channel modulation
synchronized with the frequency pattern of the received signal, then the mixer output. is a dehopped signal at a fixed difference frequency. Before demodulation, the dehopped signal is applied to a conventional receiver. In FH, whenever an undesired signal occupies a particular hoping channel, the noise and interference in that channel are translated in frequency so that they enter the demodulator. Thus, it is possible to have collisions in an FH system where an undesired user transmits in the same time as the desired user.
(iv)       Classification of Frequency Hopping
Frequency hopping may be classified as fast or slow. Fast frequency hopping occurs if there is more than one frequency hop during each transmitted symbol. Thus, fast frequency hopping implies that the hopping rate equals or exceeds the information symbol rate. Slow frequency hopping occurs if one or more symbols are transmitted in the time interval between frequency hops.
(v)        Transmission Channel
If binary frequency shift keying (FSK) is used, the pair of possible instantaneous frequencies changes with each hop. The frequency occupied by a transmitted symbol is called the transmission channel. The frequency hop rate of an FH—SS system is determined by the frequency agility of receiver synthesizers, the type of information being transmitted, the amount of redundancy used to code against collisions, and the distance to the nearest potential interferer.
11.5     PERFORMANCE OF DIRECT SEQUENCE SPREAD SPECTRUM SYSTEM
(i) Transmitted signal
A direct sequence spread spectrum system with K multiple access users is shown in figure 11.9. Assume each user has a PN sequence with N chips per message symbol period T such that NT_c = T.
The transmitted signal of the kth user can be expressed as under
s_k(t) =  m_k(t) pk (t) cos (2pf_ct + f_k)                                   …(11.15)
where p_k (t) is the PN code sequence of the kth user, and m_k (t) is the data sequence of the kth user. The received signal will consist of the sum of K different transmitted signals (one desired user and K – 1 undesired users) plus additive noise.
(ii) Reception
Reception is accomplished by correlating the received signal with the Transmitted signale appropriate signature sequence to produce a decision variable. The decision variable for the ith transmitted bit of User 1 is
equation
If m₁, _i = – 1, then the bit will be received in error if Z_i⁽¹⁾ > 0. The probability of error canmbinatino of signals plus additive noise, equation (11.5) can be rewritten as
equation
 
where                                      equation                               …(11.18)
is the response of the receiver to the desired signal from User 1,
equation                          …(11.19)
is a Gaussian random variable representing noise with mean zero and variance
E[x²] =                                                                                     …(11.20)
and                                                                  equation                   …(11.21)
represents the multiple across interference from User k.
diagram
FIGURE 11.9       A simplified diagram of a DS—SS system with K users.
(a) Model of K users in a CDMA spread spectrum system;
(b) receiver structure for User 1.
(iii)       Average Probability of Bit Error

Assuming that I_k is composed of the cumulative effects of N random chips from the kth interferer over the integration period T of one bit, the central limit theoren implies that the sum of these effects will tend toward a Gaussian distribution. Since there are K – 1 users which serve as identically distributed interferes, the total multiple access interference I =  may be approximated by a Gaussian random variable. Also the Gaussian approximation assumes that each I_k is independent, but in actuality they are not. The Gaussian approximation yields a convenient expression for the average probability of bit error given by
P_e = Q                                                                …(11.22)
 
(iv)       Bit Error Rate (BER)
For a single user, K = 1, this expression reduces to the BER expression for BPSK modulation. For the interference limited case, where thermal noise is not a factor,   tends to infinity, and the BER expression has a value equal to
P_e = Q                                                             …(11.23)
This is the irreducible error floor due to multiple access interference and assumes that all interferers provide equal power, the same as the desired user, at the DS-SS receiver. In practice, the near-far problem presents difficulty for DS-SS systems. Without careful power control of each mobile user, one close-in user may dominate the received signal energy at a base station, making the Gaussian assumption inaccurate. For a large number of users, the bit error rate is limited more by the multiple access interference than by thermal noise.
11.6     PERFORMANCE OF FREQUENCY HOPPING SPREAD SPECTRUM
(i)         Probability of Error for BFSK
In FH-SS systems, several users independently hop their carrier frequencies while using BFSK modulation. If two users are not simultaneously utilizing the same frequency band, the probability of error for BFSK can be given by
P_e =  exp                                            …(11.24)
However, if two users transmit simultaneously in the same frequency band, a collision, or hit, occurs. In this case, it is reasonable to assume that the probability of error is 0.5. Thus, the overall probability of bit error can be modulated as under:
P_e =  exp        (1 – p_n) +        P_h                     …(11.24)
where p_h is the probability of a hit, which must be determined.
(ii)        Probability of a Hit
If there are M possible hopping channels (called slots), there is a  probability that a given interferer will be present in the desired users slot. If there are K – 1 interfering user’s  the probability that at least one is present in the desired frequency slot is equal to one mm vs. the probability of no hits, given as under:
p_h = 1 –                            …(11.26)
assuming M is large.
Substituting this in equation (11.25), we have
P_e =  exp                       …(11.27)
Now, let us consider the following special cases.
If K = 1, the probability of error reduces to equation (11.24), the standard probability of error for BFSK.
Also, if     approaches infinity, then, we have
Equation                                           …(11.28)
which illustrates the irreducible error rate due to multiple access interference.
The previous analysis assumes that all users hop their carrier frequencies synchronously. This is called slotted frequency hopping. This may not be a realistic scenario for many FH-SS systems. Even when synchronization can be achieved between individual user clocks, radio signals will not arrive synchronously to each user due to the various propagation delays.
(iii)       Probability of a hit in Asynchronous Case
The probability of a hit in the asynchronous case is given by
p_h = 1 –                          …(11.29)
where N_b is the number of bits per hop. Comparing equation (11.27) to (11.29), we see that for the asynchronous case, the probability of a bit is increased (this would he executed). Using equation (11.29) in equation (11.26), the probability of error for the asynchronous FH-SS case will be
P_e =  exp  …(11.29)
(iv) Advantage Over DS-SS

            FH-SS has an advantage over DS-SS in that it is not as susceptible to the near-far problem. Because signals are the not utilizing the same frequency simultaneously, the relative power levels of signals are not as critical as in, DS-SS. The near-far problem is not totally avoided, however, since there will be some interference caused by stronger signals bleedings into weaker signals due to imperfect filtering of adjacent channels. To combat the occasional hits, error-correction coding is required on all transmissions.