Next generation wireless systems and networks phần 2 pot

36 FUNDAMENTALS OF WIRELESS COMMUNICATIONS or τ . Therefore, we obtain τ d ∼ = 1 B co (2.14) which states that a multipath channel always specifies a particular coherent bandwidth, beyond which the signal may suffer frequency-selective fading. The frequency-selectivity of the channel is relative to the signal bandwidth. For a particular multipath channel, its coherent bandwidth is always fixed. If the signal bandwidth B s is lager than the coherent bandwidth of the multipath channel B co ,a frequency-selective fading takes place; otherwise only a non-frequency-selective fading or flat fading will occur. The study of the techniques to mitigate MI has become a very popular research topic in the last 20 years, driven by a great demand for mobile cellular and wireless communications. Many papers [44–48] have been published as a result of great effort made by both academia and industry. Due to limited space, we will not dwell more on the theory of radio communication channels in this book. For more reading on this subject, the readers may refer to the following publications in the open literature [69–118]. 2.2 Spread Spectrum Techniques Spread spectrum (SS) techniques originated from the development of modern radar systems [119– 131] at the end of the second world war in the 1950s. The earlier radar systems employed continuous waves (CW) that were sent as a series of short bursts into the air. The delayed and attenuated echoes received from those short CW bursts were used to measure the distances and directions of the objects in the air as well as in the sea. Constrained by the maximal available peak power in the CW radio transmission, the earlier radar systems could not detect the incoming objects further than 100 kilometers, depending on the conditions in their operational environments. In order to improve the maximal detection range, pulse-compression techniques were introduced to the radar systems so that the detection range could be greatly extended beyond that range without increasing the peak transmitting power. The pulse-compression technique works on the principle that, instead of sending the CW radio signal directly, the carrier signal is first modulated by a coded waveform at the transmitter. When returned to radar receiver, this coded carrier waveform will then be matched filtered with the local coded waveform matched to what is used by the transmitter, yielding an autocorrelation peak that is very narrow in time and high in amplitude for easy detection. The commonly used pulse-compression waveforms in pulse radar systems include m-sequences [139–152], Barker codes [153–184], Kronecker sequences [185–189], GMW sequences [191], and so on. The operation of a communication system is different from that of a radar system in a way that the former works with the transmitter and receiver placed in different locations, whereas the latter works with them in the same place. Another distinction is that a communication system or network always works in a multiple-user environment, in which many users share a common air-link to communicate with one another without introducing excessive interference to them, while a radar system does not have such a problem as it usually works alone. Bearing these differences in mind, we can readily understand that the design concept for the coded pulse-compression radar systems can be borrowed to a communication system to improve signal detection efficiency by the use of pulse-compression and matched-filtering processes. Therefore, the application of pulse-compression techniques in a communication system yielded spread spectrum techniques. The introduction of the SS techniques in the later 1950s was due to the necessity to overcome some problems in communication systems, which appeared to be very hard to deal with when using conventional noise and interference suppression approaches. Although some communication channels FUNDAMENTALS OF WIRELESS COMMUNICATIONS 37 can be accurately modeled by AWGN channels, there are many other channels that do not fit this model. A typical example can be a battle field communication link that might be jammed by a continuous wave tone close to the signal’s center frequency or by a distorted retransmission of the enemy’s own transmitted signal. In this case, the interference cannot be modeled by a stationary AWGN process. Another possible jamming scenario is that the jammer just transmits wideband pulsed AWGN, which may not necessarily be stationary. In the later 1950s and early 1960s, many studies showed that there were other types of interfer- ences, which were not caused by enemy’s jamming signals or third party transmissions, but by its own transmitted signals, called self-interference. This type of self-interference is induced by multi- path propagation in the channels, and does not fit the stationary AWGN model either. The receiver can be interfered by the sent signal itself via delayed reception of its own transmitted signal. This phenomenon is called multipath effect or Multipath Interference and was a problem first found in the LOS microwave digital radio relay transmission systems, such as those used for earlier long-haul telephone trunk transmission as well as in urban mobile radio system in the later 1960s. In extensive research on mitigating those interference problems which could not be reduced by the typical AWGN channel model, it was found out that SS techniques were extremely effective in dealing with the non-AWGN channel interferences in communication systems. Therefore, the invention and further development of the SS techniques were driven mainly by the applications of the then emerging communication systems and services, such as long-haul microwave relay systems, satellite, and terrestrial land mobile communications, and so on. Before defining a spread spectrum system, we would like to make sure that we understand what the spectrum of a signal is. Any modulation scheme in a communication system carries two most important characteristic parameters, one being the center frequency at which the signal is modulated; the other the bandwidth of the signal modulated by the carrier waveform. A spectrum, as we are discussing here, is the frequency-domain representation of the signal and especially the modulated signal. We most often see signals presented in the time domain (that is, as the functions of time). Any signal, however, can also be presented in the frequency domain, and different transforms (mathematical operators) are available for converting frequency-domain or time-domain functions from one domain to the other and vise versa. The most frequently used transform operation is the Fourier transform, for which the relationship between the time and frequency domains is defined by the pair of Fourier integrals defined as F(ω) =  ∞ −∞ f(t)e −iωt dt (2.15) where f(t) is a time-domain representation of the signal, F(ω) is defined as the spectrum of the signal f(t),andω is the radian frequency of the spectral index variable. The Equation (2.15) is always called the Fourier transform of the signal f(t).Theinverse Fourier transform also exists, which can be used to convert the frequency-domain spectral expression F(ω) back to the time-domain signal representation f(t),or f(t)= 1 2πi  ∞ −∞ F(ω)e −iωt dω (2.16) Therefore, the spectrum of a time-domain signal f(t) is defined as the width and shape of its spectral occupancy in the frequency domain, defined by Equation (2.15). Tables of Fourier and Laplace transform pairs for different types of time-domain functions can be found in many references (e.g., see [1–3]). Here, we just mention some of the Fourier transforms that are most commonly employed in our analysis of SS systems. For instance, we will be, in particular, interested in the spectra of carriers modulated by pseudorandom binary data streams. Also of interest will be the spectra of frequency hopped carriers, especially where those carriers are to be used in multiple access applications, and it is necessary to restrict any interference between multiple users 38 FUNDAMENTALS OF WIRELESS COMMUNICATIONS working in the same band of frequencies. Note that the frequency spectrum produced by modulation with a time-domain square pulse waveform is a sin x x function, while modulation with a sin x x envelope produces a square-shaped spectrum. The Fourier transform pair for square time waveform and sin x x function can be written as f(t)= sin  πt τ  πt τ ⇔ F(ω) =      τ,|ω|≤ π τ 0, |ω| > π τ (2.17) where the notation ⇔ indicates the Fourier-transform-pair relation between f(t) and F(ω),andτ is the first zero points beside the main lobe of the function sin  πt τ  πt τ . Other spectra that will be of special interest to us are those that are produced by square, triangular, and Gaussian-shaped waveforms, whose Fourier transforms are given as f(t)=      1, |t|≤ τ 2 0, |t| > τ 2 ⇔ F(ω) = τ sin  ωτ 2  ωτ 2 (2.18) where τ is the width of the square waveform, and f(t)=    1 − |t| τ , |t|≤τ 0, |t| >τ ⇔ F(ω) = τ sin 2  ωτ 2   ωτ 2  2 (2.19) where the base of the triangular pulse is 2τ ,and f(t)= e − ( t τ ) 2 2 ⇔ F(ω) = τ √ 2πe (τ ω) 2 2 (2.20) respectively. More signal-spectrum Fourier transform pairs can be found in the literature [1–3]. To give some visual examples of real Fourier transforms, we have shown three most commonly referred time waveforms and their Fourier transforms in Figure 2.9, where the square function, the triangular function and the Gaussian function and their frequency-domain Fourier transforms are illustrated. As they were generated from real spectrum plots from MATLAB, they are shown exactly as they should appear in real applications. Just as an oscilloscope is like a window in the time domain for observing signal waveforms, a spectrum analyzer is a window in the frequency domain, generated by sweeping a filter across the band of interest and detecting the power falling within the filter as it is swept. This power level can then be plotted on the display of an oscilloscope. Usually, all spectra referred to in this book are power spectra density (PSD) functions of the signals concerned. The relation between the PSD of a signal and its Fourier transform can be written as P(ω)=|F(ω)| 2 (2.21) It is to be noted that the power of a signal can be calculated from either the time domain or the frequency domain, and the results should be exactly the same as a consequence of power conservation law.Thatis 1 2π  ∞ −∞ P(ω)dω =  ∞ −∞ |f(t)| 2 dt (2.22) It is to be noted that the change of physical appearance in the time domain goes in the opposite direction to that in the frequency domain. For instance, if we extend the duration of a signal waveform FUNDAMENTALS OF WIRELESS COMMUNICATIONS 39 f(t) f(t) f(t) 1 1 1 F (w) = t sin (wt/2) wt/2 F (w) = t F (w) = t sin (wt/2) wt/2 2p t 2p t 4p t 4p t 1 t 1 t 4p t t 2 t 2 4p t 2p t t t − 2p t − − − − t t − t − t − t w 0 0 0 0 0 0 t t t 2 w w √ √ 2pe 2p (tw) 2 2 (a) (b) (c) Figure 2.9 Fourier transform pairs for three commonly referred time waveforms. (a) Square wave- form. (b) triangular waveform. (c) Gaussian waveform. in the time domain, its Fourier transform will be compressed in the frequency domain, as stated exactly in the scaling property of Fourier transform as follows: f(at) ⇔ 1 2π|a| F  ω 2πa  (2.23) where a is a scaling factor of time index variable t. The scaling factor a can be either more or less than one, resulting in either compressed or extended original signal waveform of f(t)in the time domain. The spectral bandwidth of a time-domain signal f(t) can be perfectly defined by the width in frequency, at which its power is distributed. Therefore, the signal bandwidth is very much related to the shape or appearance of its power spectra density function. Based on how much power is included in its bandwidth, we have several different definitions of the signal bandwidth. The most commonly used signal bandwidth is 3 dB signal bandwidth, which is defined as the width, over which the power spectral density function falls from its peak value to a level 3 dB lower than the peak. This bandwidth 40 FUNDAMENTALS OF WIRELESS COMMUNICATIONS is also called 3-dB bandwidth. The signal bandwidth can also be defined as the spectral width, over which the included signal power becomes a fixed percentage of the total signal power. This can be easily shown using the following expression as 99% × 1 2π  ∞ −∞ P(ω)dω = 1 2π  B 99% −B 99% P(ω)dω (2.24) where B 99% is the 99 percentage power bandwidth. Similarly, we can also define other percentage power bandwidths,suchas90 percentage power bandwidth, 50 percentage power bandwidth,and so on. After having defined the signal bandwidth, we are ready to describe what an SS communication system is in the sequel. Literally, an SS technique can be defined as any method for a transmitter to spread the signal spectrum to a much wider extent than necessary to send the baseband signal itself in a channel. At the receiver side, an SS receiver will be able to effectively collect most, if not all, of the signal energy in a bandwidth spanned by the sent SS signal for effective detection. For instance, a voice signal can be sent with amplitude modulation in a bandwidth roughly twice that of the voice information itself. Other forms of modulation, such as low deviation FM or single sideband AM, also permit information to be transmitted in a bandwidth comparable to the bandwidth of the sent information itself. An SS system, however, often takes a baseband signal (e.g., a voice channel) with a bandwidth of only a few kilohertz, and distributes it over a band that may span many megahertz width in frequency. This is accomplished by modulating the information to be sent together with a wideband encoding waveform, also called spread modulating signal. The most familiar example of spectrum spreading is observed in conventional frequency modulation (FM), in which deviation ratios greater than one are used. As a result, the bandwidth occupied by an FM modulated signal is dependent on not only the information bandwidth but also the amount of modulation. As in all other spectrum spreading systems, a signal-to-noise 6 advantage is gained by the modulation and demodu- lation process. To measure the magnitude of this gained advantage, the terminology of process gain is always used in an SS system. Wideband FM could be considered as an SS technique from the standpoint that the carrier spec- trum produced in the frequency modulation process is much wider than the transmitted information. However, in the context of this section only those techniques are of interest in which some signal or operation, other than the information being sent, is used for spreading the transmitted signal. Many different spread spectrum techniques exist, in which the spreading codes or spreading sequences will be used to control the frequency or time of transmission of the data-modulated carrier, thus indirectly modulating the data-modulated carrier by the spreading codes or spreading sequences. Several basic spread spectrum techniques available to the communications system designer will be described and discussed in a general way in this part of Chapter 2. This section gives some detailed descriptions of the various techniques and the signals generated. In addition to the most important (or at least most prevalent) forms of SS modulation schemes (i.e., direct sequence (DS) spreading schemes), other useful techniques such as frequency hopping (FH), time hopping, chirping and various hybrid combinations of modulation forms will be described. Each is important in the sense that each has useful applications. The historical tendency has been to confine each form to a particular application scenario. Direct-sequence spreading, for instance, has been found most commonly used in civilian applications. FH is more widely employed in military communication systems. Chirp modulation has been used almost exclusively in radar. These systems will be discussed in the later subsections. The digital codes or sequences used for the spreading signal will also be discussed in detail in Section 2.3 in this chapter. There are four major techniques that will be accepted here as examples of SS signaling methods: • Modulation of a carrier by a digital code sequence whose chip rate is much higher than the information signal bandwidth. Such systems are called direct-sequence modulated systems. 6 Here, what we mean in “signal-to-noise” ratio is in fact “signal-to-interference” ratio, as no SS technique will help to suppress noise, it will help suppress only interferences. FUNDAMENTALS OF WIRELESS COMMUNICATIONS 41 • Carrier frequency shifting in discrete increments in a pattern determined by a code sequence. This technique is called frequency hopping spread spectrum. The transmitter jumps from one frequency to another in some predetermined sequence; the order of appearance of the frequen- cies is determined by a controlling code sequence. • The transmitted signal appears in different time slots within a fixed time frame, resulting in the so called time hopping spread spectrum technique. 7 • Pulsed-FM or chirp modulation technique, in which a carrier is swept over a wide band during a given pulse interval. On the basis of the above four different SS techniques, many hybrid versions can be derived, such as time-frequency hopping system, where the code sequence determines both the transmitted frequency and the time of transmission, instead of only one as in the case of either FH or time hopping. Also, it is to be noted that the pulse-FM or chirp modulation scheme was a direct derivation from the earlier radar applications and not many applications have been found in modern communication networks and systems due to its relatively low processing gain (PG) achievable and hard to use digital technique for its signal processing. Recently emerging UWB technologies have a lot in common with a time hopping SS system. The UWB techniques will also use PPM to modulate digital signal (usually binary) with very nar- row pulses. Therefore, the UWB technology is a further development of traditional SS systems. More detail discussions on UWB technologies can be found in Section 7.6. Obviously, spread spec- trum techniques form a foundation for modern CDMA technologies, which have been playing an extremely important role in current 3G (and maybe beyond 3G as well) wireless networks and communications. In the following subsections, we will discuss the three major spread spectrum techniques, namely, DS, FH, and time hopping techniques. 2.2.1 Direct-Sequence Spread Spectrum Techniques The simplest method to spread the spectrum of a data-modulated signal is to modulate the signal a second time using a wideband spreading signal, which always takes some forms of sequences, that is, a pseudorandom sequence or PN sequence for short. This second modulation usually takes some form of digital phase modulation, although analog amplitude or phase modulation is conceptually possible. This spread spectrum (SS) scheme is called the direct sequence spread spectrum (DSSS) system, (or, more exactly, directly carrier-modulated, code sequence modulation system) which is the best known and most widely used spread spectrum system. This is because of their relative simplicity from the point of view that they do not require a high-speed, fast-settling frequency synthesizer. Nowadays, DS modulation has been used for commercial communication systems and measurement instruments, and even laboratory test equipments that are capable of producing a choice of a number of code sequences or operating modes. It is reasonable to expect that DS modulation will become a familiar form of the spreading modulation scheme in many areas in the years to come due to its unique and desirable features. Even now, commercial applications of DSSS systems are being explored. Characteristics of DS spreading modulation is exactly the modulation of a carrier by a code sequence. In the general case, the format may be AM, FM, or any other amplitude- or angle-modulation form. Very often, however, the binary phase-shift keying (BPSK) is used, because it can be implemented at a very low cost: only two balanced multiplication units are required, plus a low-pass filter followed by a decision 7 It has to be noted that one type of emerging ultra-wideband (also called UWB) technology works in a very similar way as a time hopping SS. It is also called TH-UWB technology. Most commonly used modulation scheme in the TH-UWB is pulse position modulation (PPM). 42 FUNDAMENTALS OF WIRELESS COMMUNICATIONS device. The basic form of a DS signal is that produced by a simple and biphase-modulated (BPSK) carrier. The details about the BPSK DSSS system will be introduced later. The selection of spreading signals is of great importance in a DSSS system as it should have certain properties that facilitate demodulation of the transmitted data signal by the intended receiver, and make demodulation by an unintended receiver as hard as possible. These same properties will also make it possible for the intended receiver to discriminate between the intended signal and jam- ming, which usually appears quite differently from what is used for spreading the signal at the transmitter. If the bandwidth of the spreading signal is much larger than the original data signal bandwidth, the SS transmitting signal bandwidth will be dominated by the spreading signal and is nearly independent of the original data signal. Each element of the spreading sequences or codes is usually called a chip; its width will determine the bandwidth of the signal after spreading modula- tion. Before discussing any DSSS communication systems, we have to introduce the most important characteristic parameter, namely, PG, which is defined as a function of the RF bandwidth of the DS signal transmitted, compared with the bandwidth of its data information before carrier modulation. The PG is exhibited as a signal-to-interference improvement resulting from the RF-to-information bandwidth trade-off. It will also govern its capability to mitigate many other undesirable factors appearing in the communication medium and signal detection processes, such as antijamming property, and so on. The usual assumption is that the RF bandwidth is assumed to be equal to the main lobe of the DS spectrum, which is always a sin x x function. In many practical applications, the ratio between the chip rate and original data information rate can also be used as the PG. Therefore, for a DSSS system having a 10 Mcps chip rate and a 1 kbps information rate the PG will be (10 7 )/(10 3 ) = 10 4 or about 40 dB. A more strict definition of the PG is given as PG DS = RF bandwidth of DS/SS signal Baseband bandwidth of user data signal (2.25) ∼ = Chip rate of DS/SS signal User data rate The question arises then, whether the PG can be raised to a very high level to improve the performance of a DSSS system. This question can be answered best by addressing the limitations that exist with respect to expanding the bandwidth ratio to a arbitrarily large value so that the PG may be increased indefinitely. Obviously, two parameters are available to adjust PG. The first is the RF bandwidth, which depends on the chip rate used. For instance, if we have an RF (null-to-null) bandwidth 100 MHz wide, the chip rate should be at least 50 Mcps. On this basis, how wide should we make the system RF bandwidth and how much benefit can we obtain from the increase of the chip rate? To double the RF bandwidth defined by the chip rate, we can only increase 3 dB PG. However, the price is in its system complexity. With double the chip rate, the sampling rate at a digital receiver has to be at least doubled. This will substantially increase the signal processing load at a DSP chip or CPU. It is to be noted that the increase in the computation load is not linear with the increase in the sampling rate. In other words, the doubling chip rate will probably result in trebling, quadrupling or yielding an even higher computation load in a DSP chip. This imposes a great challenge to implement real-time based communication applications, such as multimedia services. With the decrease in chip duration (or increase in the chip rate) the smallest interval to make a decision at a receiver is also reduced, leaving a result that the hardware and software have to catch up with the data rate to make a sensible decision for each received bit on the basis of the chips. We should remember that the channel characteristics never change with the increase of chip rate, as discussed in Section 2.1. With each chip received at a receiver, all necessary algorithms, such as channel estimation, decision feedback, equalization, and so on, have to be carried out and finished in time before the end of the chip in question. It is still a great challenge to implement a full digital receiver at a chip rate 10 Gcps using the state-of-the-art microelectronics technology. Thus, it is not a wise approach to increase the PG FUNDAMENTALS OF WIRELESS COMMUNICATIONS 43 by using a higher chip rate. On the other hand, we can easily understand that it is not sensible to increase the PG by reducing the user data rate either. The most commonly used techniques for DS spreading are discussed below. BPSK direct-sequence spread spectrum The simplest form of DSSS employs BPSK as the spreading modulation. It has to be noted that here we are talking about two modulations, that is, the spreading modulation and carrier modulation.The former denotes the modulation of data information with a predetermined spreading code or sequence to result in a bandwidth spreading, and the latter stands for modulating the baseband signal with a high frequency radio carrier, only shifting the spectrum of the original baseband signal to a certain RF frequency without yielding any bandwidth spreading. Therefore, for a BPSK DSSS system we imply that the spreading modulation must be done using a BPSK modem. However, it is not certain whether the carrier modulation in a BPSK DSSS system also employs the BPSK modem. As a matter of fact, a BPSK DSSS system can also use any modem, such as BPSK, QPSK, MSK, and so on, for its carrier modulation purpose. Yet another important point we have to mention here is that the order of the spreading modulation and carrier modulation is irreversible in most cases, and usually the spreading modulation happens before the carrier modulation. In other words, the data signal should first be modulated by a spreading signal, and then the spread signal will be further modulated by a radio frequency (RF) carrier before being fed into the antenna for transmission. However, if both spreading modulation and carrier modulation use BPSK modems, the order of the two become interchangeable. Ideal BPSK modulation yields instantaneous phase shifts of the carrier by zero or 180 degrees according to the signs of the binary data signal as a modulating signal. It can be mathematically expressed by a multiplication of the carrier by a function c(i) that takes on the values ±1. Let us con- sider a constant-envelope data-modulated carrier with power P , carrier radian frequency ω c ,definedby f d (t) = √ 2P cos [ ω c t +φ d (t) ] (2.26) where φ d (t) stands for the data-modulated phase, which should take two different values, either zero or 180 degrees depending on the signs (either +1or−1) of binary data information, and the term √ 2P is to give an average power P. This signal occupies a bandwidth typically between one-half and twice the data rate prior to DS spreading modulation, depending on the details of the data modulation and the pulse shapes used in shaping the original data pulses. The BPSK spreading is accomplished by simply multiplying f d (t) by a time-domain signal c(i) that is also called the spreading signal or spreading sequence, as illustrated in Figure 2.10. Binary data signal RF Carrier signal Spreading signal c(t) BPSK carrier modulation BPSK spreading modulation (2) (3)(2) (1) 2P cos(w c t + f d ) √ 2Pc(t)cos(w c t + f d ) √ 2P cos w c t √ Figure 2.10 Illustration of a BPSK DSSS transmitter. 44 FUNDAMENTALS OF WIRELESS COMMUNICATIONS The transmitted signal after spreading modulation becomes f s (t) = √ 2Pc(t)cos [ ω c t +φ d (t) ] (2.27) whose bandwidth is basically determined by the spectral span of the spreading signal c(t),which usually is a wideband spreading sequence. It is to be noted that the process of multiplication of c(t) with f d (t) will not alter the power of the f d (t), but only extend the bandwidth of f d (t). This is what an SS signal means. Then, we look back at the scaling property of the Fourier transform, which tells us that the extension of the spectral span of a signal will equivalently make its time-domain waveform shrink, just as expressed in Equation (2.23). From the power conservation law (Equation (2.22)), the expansion in the bandwidth span of a signal in the frequency domain will reduce its peak amplitude if the total power remains the same. This effect makes an SS signal appear like a wideband noise- like interference to an unintended receiver. It is obvious that a conventional (non-spread-spectrum) receiver would not be useful for detecting the wideband noise-like signal here because it is well below the level of the real noise observed at the receiver. The signal given in Equation (2.27) is transmitted into an AWGN channel with a transmission delay τ d . The signal is received and contaminated by interference and channel AWGN noise. Demod- ulation is accomplished in part by demodulating or remodulating with the spreading code locally generated and appropriately delayed, c(t −˜τ d ), as shown in Figure 2.11. This demodulation or corre- lation of the received signal with the delayed spreading waveform is called the despreading process and is an important function in any SS system. The signal after despreading the module in Figure 2.11 will become r 1 (t) = √ 2Pc(t − τ d )c(t −˜τ d ) cos [ ω c t +φ d (t −τ d ) + θ ] (2.28) where ˜τ d is the estimated delay at the receiver, τ d is the propagation delay that the transmitted signal experienced, and θ is the phase delay caused by the propagation delay. If the estimated delay at the receiver is exactly the same as the real delay, or ˜τ d = τ d , Equation (2.28) will yield √ 2P cos [ ω c t +φ d (t −τ d ) + θ ] (2.29) as c(t −τ d )c(t −˜τ d ) = 1if ˜τ d = τ d . This despread signal has been restored into a narrowband signal, which is very similar to the original transmitted phase modulated data signal with only some difference in the delay τ d and an extra phase θ caused by the propagation delay from the transmitter to the receiver. This despreading process plays a crucial role here to transform the received wideband signal into its original narrowband data signal. Bandpass filter Recoverd binary data signal Decision device Despreading signal c(t − t d ) r 2 (t)r 1 (t) Local carrier signal + noise + interference 2P cos(w c t) √ √ ~ 2Pc(t − t d )cos[w c t + f d (t − t d ) + q] ~~ (4) (5) (6) Figure 2.11 Illustration of a BPSK DSSS receiver. FUNDAMENTALS OF WIRELESS COMMUNICATIONS 45 On the other hand, if the receiver uses a wrong spreading signal or spreading sequence, say c  (t −˜τ d ), to despread the received wideband signal √ 2Pc(t −τ d ) cos [ ω c t +φ d (t −τ d ) + θ ] ,it will never accomplish the despreading process to restore the narrowband signal correctly, because c(t − τ d )c  (t −˜τ d ) will be another wideband sequence no matter whether ˜τ d = τ d or not and thus the signal √ 2Pc(t − τ d )c  (t −˜τ d ) cos [ ω c t +φ d (t −τ d ) + θ ] (2.30) will remain a wideband modulated signal. Therefore, the spreading signal c(t) is usually also called the signature sequence or signature code as it behaves like a key to decode or despread the received signal for recovering the original sent narrowband data signal. There are six different time-domain waveforms observed at the transmitter and the receiver, as shown in (1) to (6) in Figure 2.12. We can also allocate the corresponding observation points from Figure 2.10 and Figure 2.11 accordingly, assuming that the binary data information in this case (shown in Figure 2.12) is a constant value of +1 for illustration simplicity. We can then see how a BPSK DSSS communication transceiver works step by step from the time-domain perspective. The block diagrams shown in Figure 2.10 and Figure 2.11 illustrate a typical DSSS commu- nications transceiver structure. It shows that a DSSS system can be viewed as a conventional AM or FM communications link with only an extra part added to implement spreading modu- lation and demodulation functionalities. In real applications the carrier modulation usually does not happen before spreading modulation. The baseband information is digitized and added to the spreading sequence first. For the discussion given in this section, however, we assume that the RF carrier has already been data modulated before spreading modulation, because this can sim- plify the discussion of the modulation-demodulation process in a BPSK DSSS system. After having been amplified, a received signal is multiplied by a reference sequence generated at the receiver locally and, given that the transmitter’s sequence and receiver’s sequence are synchronous and the same, the carrier inversion phases (as shown in (3) and (4) in Figure 2.12) will be removed successfully and the original carrier waveform will be restored. This narrowband restored car- rier can then pass through a bandpass filter designed to pass only the original data-modulated carrier. (1) Carrier Signals in DS transmitter Signals in DS receiver (2) Spreading sequence (3) Spreading modulated carrier (4) Received DS modulated signal (5) Local despreading sequence (6) Recovered carrier Figure 2.12 Conceptual illustration of time-domain signal waveforms for a BPSK DSSS transceiver. The waveforms shown in this graph correspond to the observation points (1) to (3) in Figure 2.10 and the points (4) to (6) in Figure 2.11, respectively. [...]... the I and Q channels after despreading and carrier demodulation become u1 (t) = Ad(t − τ ) sin2 2 fc t + θ + Ad(t − τ )c1 (t − τ )c2 (t − τ ) sin 2 fc t + θ cos 2 fc t + θ = A d(t − τ ) 1 − cos(4πfc t + 2 ) 2 A + d(t − τ )c1 (t − τ )c2 (t − τ ) sin(4πfc t + 2 ) 2 and u2 (t) = Ad(t − τ ) cos2 2 fc t + θ + Ad(t − τ )c1 (t − τ )c2 (t − τ ) sin 2 fc t + θ cos 2 fc t + θ (2. 41) FUNDAMENTALS OF WIRELESS. .. (t) Asin (2 pfct + q) Sequence generator 1 + 90° shift d(t) QPSK DS SS signal Sequence generator 2 Acos (2 pfct + q) c2 (t) s2 (t) d(t)c2 (t) s(t) = s1 (t) + s2 (t) = √ 2A sin(2pf + q+g (t)) BPSK Figure 2. 16 A generic QPSK DSSS transmitter w1 (t) u1 (t) u(t) c1 (t − t) A sin (2 pfct + q′) c2 (t − t) A cos (2 pfct + q′) s(t−t) w2 (t) t + li + T Zi (.) dt t + li ∫ + − Recovered data u2 (t) Figure 2. 17 A generic... = s1 (t) + s2 (t) = √ 2A sin(2pf + q+g (t)) A cos (2 pfct + q) c2 (t) s2 (t) d2(t)c2 (t) BPSK Figure 2. 20 An alternative structure of QPSK DSSS transmitter with double transmission rate w1 (t) u1 (t) c1 (t − t) s(t−t) + − A sin (2 pfct + q′) c2 (t − t) Zi t + li + T (.) dt ∫t + li A cos (2 pfct + q′) w2 (t) u2 (t) P/S Zi t + li + T (.) dt ∫t + li Recovered data + − Figure 2. 21 An alternative structure... = 53 A d(t − τ ) 1 + cos(4πfc t + 2 ) 2 A + d(t − τ )c1 (t − τ )c2 (t − τ ) sin(4πfc t + 2 ) 2 (2. 42) respectively The summation of the signals from the I and Q channels will become u(t) = u1 (t) + u2 (t) = Ad(t − τ ) + Ad(t − τ )c1 (t − τ )c2 (t − τ ) sin(4πfc t + 2 ) (2. 43) Obviously, after the low-pass filtering, the second term in Equation (2. 43) will vanish and only the term Ad(t − τ ) reflecting... if c1 (t)d(t) = −1 and c2 (t)d(t) = +1 (2. 39) if c1 (t)d(t) = −1 and c2 (t)d(t) = −1 if c1 (t)d(t) = +1 and c2 (t)d(t) = −1 FUNDAMENTALS OF WIRELESS COMMUNICATIONS 51 1 d(t) t −1 T 0 2T 1 c1(t) t −1 0 1 c2(t) t −1 0 1 d(t)c1(t) −1 t 0 1 d(t)c2(t) −1 t 0 A t s1(t) −A 0 A t s2(t) −A 0 √ 2A s(t) − √ 2A 0 g = 7p/4 3p/4 t 5p/4 p/4 3p/4 7p/4 p/4 5p/4 3p/4 7p/4 Figure 2. 18 Signal waveforms in a generic QPSK... Figure 2. 16, the QPSK DSSS signal can be expressed as s(t) = s1 (t) + s2 (t) = Ad(t)c1 (t) sin (2 fc t + θ ) + Ad(t)c2 (t) cos (2 fc t + θ ) √ = 2A sin (2 fc t + θ + γ (t)) (2. 38) where the phase modulated component can be written into γ (t) = arctan c2 (t)d(t) c1 (t)d(t)  π  ,    4   3π    ,  4 =  5π    4 ,    7π    , 4 if c1 (t)d(t) = +1 and c2 (t)d(t) = +1 if c1 (t)d(t) = −1 and c2... is the chip width for both c1 (t) and c2 (t) Thus, s1 (t) and s2 (t) will have the same bandwidth equal to T2c This QPSK DSSS system has 1 T its data transmission rate of T and the PG of PG = Tc The bandwidth of this QPSK DSSS system is determined by the chip width of c1 (t) and c2 (t) It is to be noted that the I and Q channels in the transmitter shown in Figure 2. 16 send the same 1 information bit... or bandwidth, PG and SNR (or transmission power) In order to compare the performance of two DSSS systems, such as a BPSK system and a QPSK DSSS system, we have to concentrate on one particular parameter, with the other two fixed, to make the comparison easily and objectively For instance, if we want to compare BPSK and QPSK DSSS systems shown in Figures 2. 10 and 2. 20, we should fix the data rate and. .. a generic QPSK DSSS transmitter and a receiver, as shown in Figure 2. 16 and Figure 2. 17, respectively d(t) is the input information data stream defined in Equation (2. 31) with its duration being T , c1 (t) and c2 (t) are two spreading sequences generated in the transmitter for I and Q channel spreading modulations, A sin (2 fc t + θ ) and A cos (2 fc t + θ ) are in-phase and quadrature carriers for QPSK... price in bandwidth efficiency as both the I and Q channels occupy the same bandwidth, which is exactly the same as the bandwidth for a BPSK DSSS system This is really wonderful and can happen only using the two unique orthogonal carriers sin (2 fc t) and cos (2 fc t) It is a pity that we cannot find any more such ideal orthogonal carriers The two spreading sequences c1 (t) and c2 (t) applied to the I and Q . waveform, and f(t)=    1 − |t| τ , |t|≤τ 0, |t| >τ ⇔ F(ω) = τ sin 2  ωτ 2   ωτ 2  2 (2. 19) where the base of the triangular pulse is 2 ,and f(t)= e − ( t τ ) 2 2 ⇔ F(ω) = τ √ 2 e (τ ω) 2 2 (2. 20) respectively −cos(4πf c t +2  )  + A 2 d(t − τ)c 1 (t −τ)c 2 (t −τ)sin(4πf c t +2  ) (2. 41) and u 2 (t) = Ad(t − τ)cos 2  2 f c t +θ   + Ad(t − τ)c 1 (t −τ)c 2 (t −τ)sin  2 f c t +θ   cos  2 f c t +θ   FUNDAMENTALS. waveform FUNDAMENTALS OF WIRELESS COMMUNICATIONS 39 f(t) f(t) f(t) 1 1 1 F (w) = t sin (wt /2) wt /2 F (w) = t F (w) = t sin (wt /2) wt /2 2p t 2p t 4p t 4p t 1 t 1 t 4p t t 2 t 2 4p t 2p t t t − 2p t − − − − t t − t − t − t w 0 0 0 0 0 0 t t t 2 w w √ √ 2pe 2p (tw) 2 2 (a) (b) (c) Figure