To assist the reader, we now present a brief glossary of key terms which are the subject of this book.

Direct Sequence Code Division Multiple Access (DS-CDMA) -. A wireless access technique, where signals from different users are assigned a unique spreading code. Signals from different users occupy the same spectrum at the same time. The receiver separates signals using their codewords, as shown in Figure 1-6.

Figure 1-6. A simple Direct Sequence CDMA system. The signals from each user are spread by a spreading code, which is known at the transmitter and receiver. CDMA signals can occupy the same spectrum at the same time.

Adaptive Antenna -. An array of antennas which is able to change its antenna pattern dynamically to adjust to noise, interference, and multipath. Adaptive array antennas can adjust their pattern to track portable users. Adaptive antennas are used to enhance received signals and may also be used to form beams for transmission.

Switched Beam Systems -. Switched beam systems use a number of fixed beams at an antenna site. The receiver selects the beam that provides the greatest signal enhancement and interference reduction. Switched beam systems may not offer the degree of performance improvement offered by adaptive systems, but they are often much less complex and are easier to retro-fit to existing wireless technologies.

Smart Antennas -. Smart antenna systems can include both adaptive antenna and switched beam technologies, as shown in Figure 1-7.

Figure 1-7. Two smart antenna technologies.

Macrocells -. Large cells, covering several kilometers with each base station.

Microcells -. Smaller cells, used to provide increased capacity with cell spacing of a few hundred meters to a kilometer.

Picocells -. Very small cells, used to provide extremely high capacity indoors and in high-traffic pedestrian areas.

Low Tier Systems -. Wireless systems using picocells and microcells to provide low power service to pedestrian users indoors and in pedestrian areas. Typically, low tier systems, such as Digital European Cordless Telephone (DECT) and Personal Access Communications System (PACS), are not as well suited for high vehicle speeds as High Tier systems, and are more susceptible to multipath. However, low tier systems are usually able to support higher voice quality. Because low tier systems do not have to contend with high time delay spread, base stations and subscriber units can be less expensive, and low power requirements allow very long battery life. Low Tier systems excel at covering high density areas, but are less effective in rural, low density, and high speed environments.

High Tier Systems -. High Tier Systems use macrocells and microcells to provide wide area, universal coverage. High Tier Systems, such as IS-95 and GSM, use a variety of techniques to combat multipath.

Multipath -. In mobile and portable radio channels, as shown in Figure 1-8, there are multiple radio paths between the transmitter and receiver. The longer paths result in delayed versions of the desired signal arriving at the receiver. When the difference in delays between the different multipath components, quantified by the Time Delay Spread, is large, symbols spread into one another, leading to InterSymbol Interference (ISI) at the receiver. This can result in poor signal reception, even when the signal level is high, particularly in TDMA systems. Even when the time delay spread is small, if strong multipath is present, the phases of the multipath signal components can combine destructively over a narrow bandwidth, leading to fading of the received signal level [Rap96a].

Figure 1-8. Multipath results from scatterers in the mobile and portable radio environment.

Digital Modulation Techniques -. In digital modulation, transmitted signals are comprised of symbols from a finite alphabet. The key advantage of digital modulation techniques is that if the receiver correctly determines the transmitted symbol based on the received signal, then a perfect, noise-free copy of the transmitted signal can be recreated at the receiver. Unlike analog signals, error control coding can be easily applied to digital signals, providing the ability to add controlled redundancy, which provides robustness to any errors made at the receiver.

One of the simplest digital modulation techniques is Binary Phase Shift Keying (BPSK). In BPSK, a “1” is assigned to a phase shift of θ_i = 0°, and a “0” is assigned to a phase shift of θ_i = 180°, so that the transmitted signal is

Equation 1.1. 

In Quadrature Phase Shift Keying (QPSK) systems, θ_i can take one of four values, such as 45°, 135°, -45°, or -135°. A variation of this approach, called π/4 -shifted Differential QPSK or π/4 -DQPSK, is used in IS-136 and PACS. Another technique used in GSM and DCS-1900, is Gaussian Minimum Shift Keying (GMSK).

In the mid 1990s, second generation Wireless Systems were widely deployed around the world. These systems replaced earlier analog technologies and provided improved voice quality, greater system capacity, and enhanced coverage and reliability. Table 1-2 summarizes the major Second Generation Wireless Systems deployed in Europe and the United States.

Wireless Local Loop (WLL) systems are used in lieu of wired access for fixed residential and business customers. In WLL deployments, base stations are deployed similar to a cellular service; however, instead of providing service to mobile subscribers, WLL services provide wireline-quality service to fixed users that have traditionally been served by wired links to the PSTN. At the fixed subscriber location, some systems use a wireless link directly to a handset or home base unit, whereas other systems use an antenna mounted outside of the house or business.

WLL systems have been deployed widely in emerging nations, where infrastructure is simply not available and providing access to remote populations would be prohibitively expensive. Whereas wired links to the PSTN can cost approximately $2000 per customer to install, WLL systems can be implemented at less than half that cost, making wireless access an attractive technology for Competitive Local Exchange Carriers (CLECs) hoping to compete with existing wired infrastructure.

Many of these systems use directional antennas mounted outside at the subscriber unit to minimize the impact of reverse link signals in adjacent cells. This technique, used in commercial CDMA Wireless Local Loop products, can help to maximize system capacity at the expense of wireless mobility. Other systems, particularly IS-95-based systems, use non-directional antennas at the subscriber unit. This sacrifices some capacity, but allows the Wireless Local Loop system to be completely compatible and inter-operable with mobile CDMA systems. A sampling of CDMA-based WLL systems is shown in Table 1-3.

Figure 1-9. Wireless Local Loop (WLL) systems are designed to provide wireline-quality voice and data services to residential and business customers. These systems may link to a Fixed Access Unit mounted on the outside of the subscriber building, or they may attempt to penetrate the structure to provide service directly to the subscriber handset.

These systems are deployed in North America, Europe, Asia, and South America in frequency bands allocated for cellular, PCS, and unlicensed operations from 800 MHz to 3.5 GHz.

In addition to voice services, other new wireless technologies can add broadband data, video, and high-speed Internet access for fixed users. The Multichannel Multipoint Distribution Service (MMDS) in 2150-2160 MHz, and 2500-2700 MHz provides “wireless cable television” service, with some limited uplink capability [Rap96a, Ch. 10]. Recently, Local Multipoint Distribution Service (LMDS) spectrum at 28 GHz has been allocated, promising 1300 MHz of spectrum to provide these services to fixed users, as shown in Figure 1-10 [Sei98].

Figure 1-10. The Local Multipoint Distribution Service (LMDS) provides 1300 MHz in the 28-31 GHz band [Sei98]

Just as second generation digital wireless networks have been widely deployed, work is well underway to develop third generation (3G) wireless networks. These networks will add broadband data to support video, Internet access, and other high speed data services for untethered devices.

As described in Chapter 1 of [Rap96a], in 1992 the World Administrative Radio Commission (WARC) of the International Telecommunications Union (ITU) formulated a plan to implement a global frequency band in the 2000 MHz range that would be common to all countries for universal wireless communication systems. This visionary concept, originally known as Future Public Land Mobile Telephone Systems (FPLMTS), was renamed International Mobile Telecommunications 2000 (IMT-2000) in 1995.

IMT-2000 was originally intended to define a single, ubiquitious wireless communication standard for all countries throughout the world, thereby promoting truly ubiquitious wireless communications systems and equipment for all citizens of the world through commonality in infrastructure and handset design. However, in the mid 1990s, it became clear that this vision of commonality would not be tenable due to the great commercial success of each of the various digital wireless technologies. Proponents of the leading European digital wireless technology, based upon TDMA and the GSM standard, and the leading North American digital technology, based upon IS-95 CDMA, have been unable, up until now, to come to agreement on a single united third generation (3G) wireless technology that could be standardized throughout the world. Thus, the ITU, in recent years, expressed a desire to determine a family of standards that would be implemented in a common frequency band throughout the globe.

In June 1998, ITU received a total of 15 comprehensive IMT-2000 proposals from the leading governmental and industrial standards bodies throughout the world. Five of these proposals dealt with satellite communication systems and ten of these dealt with terrestrial PCS-like wireless systems. It is remarkable to note that most of the satellite and terrestrial proposals include some form of CDMA in the air interface protocol. The Outdoor IMT-2000 systems will be deployed with a Mobile Transmit Frequency of 1920-1980 MHz and a base station transmit band of 2110-2170 MHz. Indoor systems will use Time Division Duplexing (TDD).

At the time of this writing, the ITU is scheduled to select a family of “winning” world standards within the next few months. The leading U.S. proposal, cdma2000, will be backward-compatible with IS-95 systems (discussed in Chapter 2), but will support chip rates up to 12 times the 1.2288 Mchip/second rate used in the current standard, enabling higher capacity and user data rates [ITU98]. The cdma2000 standard will also incorporate auxiliary pilots to support smart antenna technology, which are discussed further in Chapter 4. It is likely that some variation of cdma2000 will be developed for U.S. markets, regardless of ITU actions [TIA98].

The European Telecommunications Standards Institute (ETSI) has developed the Universal Mobile Telecommunications System (UMTS) as an evolutionary path for GSM. The UMTS Terrestrial Radio Access (UTRA) standard is a Wideband CDMA (W-CDMA) technology that includes features that ensure easy integration with existing GSM Technology. The UTRA proposal shares a number of features, including direct sequence spreading rates, frame rate, and slot structure with other proposals from North America (W-CDMA/NA) and Asia (W-CDMA/Japan and CDMA-II from Korea), as illustrated in Table 1-4.

The UWC-136 proposal is designed to provide an upgrade path for both the North American TDMA digital technology (IS-136) and GSM. Unlike most of the other standards, UWC-136 is a TDMA technology, although frequency hopping is supported.

As government and industry bodies struggle over the complex technical and market issues surrounding these 3G proposals, the IMT-2000 vision is likely to be delayed. Nevertheless, the IMT-2000 proposals illustrate the flexibility of CDMA for providing high capacity, wideband user data, and multimedia transmission.

In DS systems, a narrowband signal, containing a message with bandwidth B₁, is multiplied by a signal with a much larger bandwidth B₂, which is called the spreading signal. Essential features of Direct Sequence Spread Spectrum are that

Thus, assuming that the bandwidth of the spreading signal is much larger than the bandwidth of the narrowband information signal, the transmitted signal will have a bandwidth which is essentially equal to the bandwidth of the spreading signal.

The spreading signal is comprised of symbols that are defined by a pseudo random sequence which is known to both the transmitter and receiver. These symbols are called chips. Typically, the rate of chips in the spreading code, R_c, is much greater than the symbol rate, R_d, of the original data sequence. The pseudo random chip sequence is also called a Pseudo Noise (PN) sequence because the power spectral density of the PN-sequence looks approximately like white noise filtered to have the same spectral envelope as a chip. The spreading factor, or processing gain, is defined as the ratio of the chip rate to the data symbol rate, or N = R_c/R_d.

To illustrate the operation of a DS spread spectrum system, consider an information signal b(t). This signal may be a voice or data signal. We will assume that b(t) is a digital signal composed of a sequence of symbols, b_j, each of duration T_s. The data signal is given by

Equation 1.2. 

where Ψ(t/T) is the unit pulse function:

Equation 1.3. 

This signal is multiplied by a spreading sequence a(t) which is composed of a sequence of chips:

Equation 1.4. 

where T_c is the chip period, and M is the number of PN symbols in the sequence before the sequence repeats. It should be noted that the chips serve to spread and identify the signal, whereas the data symbols convey information. In the IS-95 standard, spreading symbols are represented by quadrature chips having a carrier initial phase from the symbol set {e^jπ/4, e^−jπ/4, e^j3π/4, e^−j3π/4} [EIA93].

The multiplied signal, a(t)b(t), is upconverted to a carrier frequency f_c by multiplying a(t)b(t) by the carrier,

Equation 1.5. 

Let us assume, for the moment, that the channel does not distort the signal in any way, so that the received signal, r(t), consists of a weighted version of the transmitted signal with added white Gaussian noise, n(t):

Equation 1.6. 

At the receiver, a local replica of the chip sequence, a(t − τ₀), is generated, where τ₀ is a random time offset between 0 and MT_c. To despread the signal at the receiver, the local chip sequence must be “delay locked” with the received signal. This means that the timing offset, τ₀, must be set to zero. One means of doing this is through the use of a Delay Locked Loop (DLL). Similarly, a Phase Locked Loop (PLL) may be used to create a replica of the carrier, cos(ω_ct). Using these two quantities, a decision statistic is formed by multiplying the received signal by the local PN sequence and the local oscillator and integrating the result over one data symbol:

Equation 1.7. 

Let us assume that a(t)a*(t) = 1, then

Equation 1.8. 

where η represents the influence of channel noise on the decision statistic. Assuming that the carrier frequency is large relative to the reciprocal of the bit period, then

Equation 1.9. 

Therefore, the decision statistic, Z_j, is an estimate, , of the transmitted data symbol b_j.

Figure 1-11. A direct sequence spread spectrum transmitter and receiver.

If the channel noise is additive white Gaussian noise with two-sided power spectral density N₀/2, then the variable η is a zero mean Gaussian random variable u_η = 0 with variance

Equation 1.10. 

The energy per symbol of the signal component of the decision statistic, Z_j, is

Equation 1.11. 

Let us assume that the symbols, b_j, being transmitted are from a binary symbol set such that b_j ∈ {−1, 1}. Then the energy per symbol, E_s, in (1.11) is the same as the energy per bit, E_b. The bit error rate at the output of the matched filter receiver is given by

Equation 1.12. 

where Q(x) is the standard Q-function which is given in Appendix B. The Q-function is a monotonically decreasing function, so that a larger ratio of symbol energy to noise power produces a smaller bit error rate.

The bit error rate given by (1.12) is the same as if we had used no spreading sequence. However, there are several differences between this case and the case where no spreading sequence is used. First of all, since the signal is spread over a large bandwidth with the same total power, the spectral density of the signal can be very small. This makes it difficult for a potential eavesdropper to detect the presence of the signal. This property is known as Low Probability of Detection (LPD). Additionally, if the eavesdropper does not know the PN-sequence used, then it will be very difficult to extract the information signal portion of r(t). This property is called Low Probability of Interception (LPI) [Proa89].

In mobile and portable radio channels, the fact that the DS signal is spread over a large bandwidth can significantly mitigate the effects of fading which can degrade the performance of narrowband systems. The coherence bandwidth of the channel quantifies the region of spectrum over which the amplitudes of all signal components at the receiver undergo approximately the same fading level. Typical values for coherence bandwidth are 3 MHz in indoor channels and 0.1 MHz for outdoor channels [Rap96a]. If the signal bandwidth is smaller than the coherence bandwidth of the channel and one part of the spectrum of the signal experiences a fade, then, in all likelihood, the entire signal spectrum experiences a fade and it is not possible to recover the lost data symbols except through error control coding. Using DS techniques, the signal can be made to cover a large enough bandwidth so that if one part of the signal spectrum is in a fade, other parts of the signal spectrum are not faded. One result of this is that the short-time variation of the total received power for a wide band DS signal is much less than that of the narrowband signal [Ste92]. Various techniques can be used to recover the signal as long as some portion of the received signal is not in a fade.

Finally, one property of the DS signal alluded to earlier is that many DS signals can be overlaid on top of each other in the same frequency band. Let us assume that there are two users in the system using the same frequency band at the same time. We assume that the PN sequence from user 0 is a₀(t) and the PN sequence from user 1 is a₁(t) where

Equation 1.13. 

The signals are said to be orthogonal over a symbol period if

Equation 1.14. 

Let us assume for the moment that the repetition rate of the PN-sequence is the same as the symbol period such that MT_c = T_s. When the length of the PN sequence, MT_c, is equal to the message symbol period, T_s, the system is called a code-on-pulse system. If the sequences are chip aligned, and bit aligned, then the orthogonality over a symbol period may be expressed as

Equation 1.15. 

If each user has a different orthogonal underlying code sequence, then many users can share the same medium without interfering with each other. This property may be used as a multiple access technique, namely Code Division Multiple Access. The case in which the user’s sequences are chip and bit aligned is called synchronous CDMA.

The received signal at user 0’s receiver consists of the desired signal, multiple access interference from user 1, and noise

Equation 1.16. 

where

Equation 1.17. 

The decision statistic for user 0 is obtained using Equation (1.7). The component of the decision statistic due to the desired signal is A₀T_sb_0,j/2, just as before. The component of the decision statistic due to the noise component is again a zero mean Gaussian random variable with variance N₀T_s/4. In synchronous CDMA, the component due to the interference is

Equation 1.18. 

Thus if the spreading sequences of user 0 and user 1 are orthogonal, so that they satisfy (1.15)ch01equ1,5 then the component of the decision statistic due to interference will be zero. In this case, the addition of the users in the same time and frequency slots will not affect the performance of other users. In most cases, it is possible to operate only in a synchronous CDMA mode on the forward link since the base station can simultaneously modulate and spread the signals for all users. On the reverse link, since it is difficult to synchronize spatially separated mobile users on the bit and chip level, and since the signals travel different path lengths from the transmitter to the base station, it is not feasible to operate in a synchronous mode.

In the asynchronous case, where usually the sequence for user 1 is delayed by τ₁ seconds relative to the chip sequence for user 0, the expression describing the interaction between the signals from two users at the receiver for user 0 becomes considerably more complicated. We may express the delay as an integer number of chip periods γ₁ such that τ₁ = γ₁T_c + Δ₁ where 0 ≤ Δ₁ < T_c. We will further assume that for values of i ≥ M and i < 0 that a_{1, i} = a_{1, i−mM}, so that 0 ≤ i − mM < M − 1. Then the signals from user 0 and 1 will not interfere with each other if

Equation 1.19. 

It is not possible to select useful spreading codes which satisfy (1.19) over all possible values of b_{1, j}, Δ₁ and γ₁. Thus, in an asynchronous CDMA system, the signals from different users interfere with each other, resulting in higher bit error rates as compared with orthogonal CDMA. Therefore, in asynchronous CDMA systems, every user contributes interference, called Multiple Access Interference (MAI), to the decision statistic for other users.

Consider a CDMA system in which K users occupy the same frequency band at the same time. These users may share the same cell, or some of the K users may communicate with other base stations.

The signal received at the base station from user k is given by [Pur77]

Equation 1.20. 

where b_k(t) is the data sequence for user k, a_k(t) is the spreading (or chip) sequence for user k, τ_k is the delay of user k relative to a reference user 0, P_k is the received power of user k, and φ_k is the phase offset of user k relative to a reference user 0. Since τ_k and φ_k are relative terms, we can define τ₀ = 0 and φ₀ = 0.

Let us assume that both a_k(t) and b_k(t) are binary sequences having values of −1 or +1. As noted earlier, the IS-95 CDMA system, which we will discuss in the next section, uses a somewhat different waveform, with quadrature spreading. The binary values used here, however, are useful for demonstrating some fundamental concepts in DS-CDMA.

The chip sequence a_k(t) is of the form,

Equation 1.21. 

where M is the number of chips sent in a PN sequence period and T_c is the chip period. MT_c is the repetition period of the PN sequence.

For the data sequence, b_k(t), T_b is the bit period. As noted in the introduction to this chapter, it is assumed that the bit period is an integer multiple of the chip period such that T_b = NT_c. Note that M and N do not need to be the same. The binary data sequence b_k(t) is given by

Equation 1.22. 

At the receiver, illustrated in Figure 1-12, the signal available at the input to the correlator is given by

Equation 1.23. 

Figure 1-12. Model for CDMA multiple access interference [Pur77]

where n(t) is additive Gaussian noise with two-sided power spectral density N₀/2. It is assumed in (1.23) that there is no multipath in the channel with the possible exception of multipath that leads to flat fading such that the coherence time of the channel is considerably larger than a symbol period.

At the receiver, the received signal is mixed down to baseband, multiplied by the PN sequence of the desired user (user 0 for example) and integrated over one bit period. Thus, assuming that the receiver is delay and phase synchronized with user 0, the decision statistic for user 0 is given by

Equation 1.24. 

For convenience and simplicity of notation, the remainder of the analysis will be presented for the case of bit 0 (j = 0 in (1.24)). Substituting (1.20) and (1.23) into (1.24),

Equation 1.25. 

which may be expressed as

Equation 1.26. 

where I₀ is the contribution to the decision statistic from the desired user (k = 0), ζ is the multiple access interference, and η is the noise contribution. The contribution from the desired user is given by

Equation 1.27. 

As shown in Appendix A, the noise term, η is given by

Equation 1.28. 

where it is assumed that n(t) is white Gaussian noise with two-sided power spectral density, N₀/2. The mean of η is

Equation 1.29. 

From (1.10), the variance of η is

Equation 1.30. 

The third component in (1.26), ζ, represents the contribution of multiple access interference to the decision statistic. ζ is the summation of K − 1 terms, I_k,

Equation 1.31. 

each of which is given by

Equation 1.32. 

If the spreading sequences are not orthogonal, then the cross correlation properties of the sequences determine the degree to which one DS signal interferes with another DS signal. For a given length of PN-sequence, there is generally a much larger number of different sequences with low cross-correlation properties than mutually orthogonal sequences. From (A.49), it follows that

Equation 1.33. 

where N is the spreading factor,

Equation 1.34. 

where R_c is the chip rate of the PN sequence and R_b is the message bit rate.

In Appendix A it is shown that, using the Gaussian Approximation, the Multiple Access Interference can be approximated as a Gaussian random variable. Then we approximate the Bit Error Rate using (A.51) as

Equation 1.35. 

in the interference limited case, where , this becomes

Equation 1.36. 

Consider the CDMA uplink where multiple subscribers are transmitting signals that are received at a single base station receiver. Generalizing (1.36), the bit error rate for user p can be expressed as

Equation 1.37. 

where N is the spreading factor and γ_p represents the Carrier-to-Interference-Ratio (CIR) for subscriber p. Letting P_p represent the received power from user p, γ_p is

Equation 1.38. 

As the CIR increases, the bit error rate for a subscriber decreases.

Recall that P_k represents the power received at the base station from a particular subscriber. If every user transmits at the same power level, then the received power from users closer to the base station will tend to be higher than the received power from subscribers that are farther away from the base station. This leads to a different performance for subscriber links, depending on where the subscribers are located in the cell. More importantly, a few subscribers closest to the base station may contribute so much Multiple Access Interference that they prevent other uplink signals from being successfully received at the base station. This is the near-far effect [Rap96a].

To solve this problem, power control is used in CDMA systems. Power control forces all users to transmit the minimum amount of power needed to achieve acceptable signal quality at the base station. Power control typically reduces the power transmitted by subscribers closest to the base station, while increasing the power of subscribers farthest away from the base station. Compared with the case where all users transmit at the same power level, power control reduces the denominator of (1.38), increasing the CIR, and lowering the error rate for all subscribers.

If all subscribers in a system have the same bandwidth, data rate, and other signal characteristics, then one reasonable approach to power control is to set all of the received power levels, P_k, to a constant value, P_c. Then (1.38) can be rewritten as

Equation 1.39. 

This is called perfect power control. In practice, this sort of perfect power control is not achievable and under many circumstances, despite its name, may not even be desirable.

Perfect power control requires exact knowledge of the loss in the radio propagation channel between the subscriber transmitter and the base station receiver, commonly referred to as path loss. As shown later in this chapter, there are a number of factors that impact the path loss between the transmitter and receiver, causing signal levels to fluctuate with time. In practical systems, the path loss between the uplink path is estimated through a combination of techniques. These include Open Loop Power Control, where the path loss on the downlink is measured, and it is assumed that the path loss is approximately the same on the uplink, so the subscriber unit adjusts its power accordingly. To account for the time varying nature of the channel, and the fact that path loss in the forward and reverse directions may not be the same, practical systems also use Closed Loop Power Control, where the base station instructs the subscriber unit to raise or lower its transmit power to meet some targeted received power level. This allows the mobile to adjust its transmit power to track the time varying nature of the channel.

Rather than adjust the subscriber transmitter power to meet a desired received power level at the base station, practical CDMA systems use other criteria for adjusting power levels. These include adjusting the power level to meet specific error rate or Carrier-to-Interference-and-Noise-Ratio (CINR) requirements. Chapter 2 illustrates that the IS-95 CDMA standard uses a complex power control mechanism that adjusts the subscriber transmitter power 800 times per second.

Assuming perfect power control, (1.36) can be used to illustrate how the addition of subscribers to a CDMA system increases the bit error rate seen by the receiver for any particular subscriber.

In the non-interference limited case, for perfect power control where P_k = P₀ for all k = 0...K − 1, we have

Equation 1.40. 

In the interference limited case with perfect power control, equation (1.40) may be approximated by

Equation 1.41. 

Equation (1.41) is plotted in Figure 1-13. As the number of users increases, the raw bit error rate seen by the uplink receiver for any particular receiver increases. CDMA systems use error control coding so they are tolerant of bit errors introduced by Multiple Access Interference. Note that the agreement is excellent for average bit error rates larger than 10^-3, where most voice systems operate. However, due to the tail of the Gaussian distribution, the approximation slightly over estimates capacity for bit error rates less than 10^-3.

Figure 1-13. The bit error rate for an asynchronous reverse link obtained through computer simulation and through application of the Gaussian Approximation given in (1.41). The spreading factor is N = 31 and perfect power control is applied such that all users have the same power level. Omni-directional antennas are used at the base station.

An alternative to Direct Sequence (DS) is Frequency Hop Spread Spectrum (FH-SS). In many ways, these systems are similar to an FDMA system, in which the bandwidth available for multiple users is divided into N channels. At any point in time, a frequency hopping signal for a particular user occupies only a single frequency channel. The difference between this system and a traditional FDMA system is that the frequency hopping signal changes frequency carriers, or hops, at rapid periodic intervals. If the signal hops at, or close to, the symbol rate, the system is termed a fast frequency hopping system. If hopping occurs at a lower rate, it is called slow frequency hopping. The sequence of frequency slots occupied by the FH signal is a pseudo random sequence.

The pseudo random sequence is recreated at the receiver which retunes to the proper channel to match the transmitted signal. It is assumed that not all of the channels are continuously occupied. If two multiple access users are using the same channel set, each using a different pseudo random channel sequence, the signals will occasionally be transmitted in the same frequency slot. A bit error may occur in this case, but the effects of this can be minimized through the use of error control coding [Lin83][Rap96a].

A frequency hopping system provides a level of security, especially when a large number of channels are used, since an unintended receiver that does not know the pseudo random sequence of frequency slots must constantly retune to search for the signal that it is attempting to intercept. FH systems also have the effect of randomizing interference which can be beneficial [Par89]. In today’s emerging wireless CDMA technology, DS spread spectrum has been widely accepted, and the remainder of this text focuses on Direct Sequence rather than Frequency Hop Spread Spectrum.

The mechanisms behind electromagnetic wave propagation are diverse, but they can generally be attributed to reflection, diffraction, and scattering. Most cellular radio systems operate in urban areas where there is often no direct line-of-sight path between the transmitter and the receiver, and where the presence of high-rise buildings causes severe diffraction loss. Due to multiple reflections from various objects, the electromagnetic waves travel along different paths of varying lengths. The interaction among these waves causes multipath fading, and the strengths of the waves decrease as the distance between the transmitter and receiver increases.

Propagation models have traditionally focused on predicting the average received signal strength at a given distance from the transmitter, as well as the variability of the signal strength in close spatial proximity to a particular location. Propagation models that predict the mean signal strength for an arbitrary transmitter-receiver (T-R) separation distance are useful in estimating the radio coverage area of a transmitter and are called large-scale propagation models, since they characterize gross path loss characteristics that apply over scales that are large compared to a wavelength. On the other hand, propagation models that characterize the rapid fluctuations of the received signal strength over very short travel distances (a few wavelengths) or short time durations (on the order of seconds) are called small-scale or fading models.

Both theoretical and measurement-based propagation models indicate that average received signal power decreases by the logarithm of the distance between the transmitter and the receiver, whether in outdoor or indoor radio channels. Such models have been used extensively in the literature. The average large-scale path loss for an arbitrary T-R separation is expressed as a function of distance by using a path loss exponent, n.

Equation 1.58. 

or

Equation 1.59. 

where n is the path loss exponent which indicates the rate at which the path loss increases with distance, d₀ is the close-in reference distance which is determined from measurements close to the transmitter, and d is the T-R separation distance. The bars in equations (1.58) and (1.59) denote the ensemble average of all possible path loss values for a given value of d. When plotted on a log-log scale, the modeled path loss is a straight line with a slope equal to 10n dB per decade. The value of n depends on the specific propagation environment. For example, in free space, n is equal to 2, and when obstructions are present, n will have a larger value.

It is important to select a free space reference distance that is appropriate for the propagation environment. In large coverage cellular systems, 1 km reference distances are commonly used [Lee89], whereas in microcellular systems, much smaller distances (such as 100 m or 1 m) are used. The reference path loss is calculated by using the free space path loss formula given by equation (1.54) or through field measurements at distance d₀. Table 1-5 lists typical path loss exponents and log normal shadowing standard deviations obtained in various mobile radio environments.

The model in equation (1.59) does not consider the fact that the surrounding environmental clutter may be very different at two different locations having the same T-R separation. This leads to measured signals which are much different than the average value predicted by equation (1.59). Measurements have shown that at any value of d, the path loss PL(d) at a particular location is random and distributed log-normally (normal in dB) about the mean distance-dependent value [Cox84], [Ber87]. We can therefore express the path loss as

Equation 1.60. 

and

Equation 1.61. 

where X_σ is a zero-mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB).

The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation, but have different levels of clutter on the propagation path. This phenomenon is termed log-normal shadowing. Simply put, log-normal shadowing implies that measured signal levels at a specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean of (1.59), where the measured signal levels have values in dB units. The standard deviation of the Gaussian distribution that describes the shadowing also has units in dB. Thus, the random effects of shadowing are accounted for, using the Gaussian distribution which lends itself readily to evaluation.

The close-in reference distance d₀, the path loss exponent n, and the standard deviation σ, statistically describe the path loss model for an arbitrary location having a specific T-R separation; this model may be used in computer simulation to provide received power levels for random locations in communication system design and analysis. An example of an IS-95 link design using (1.60) is provided in Chapter 2.

In practice, the values of n and σ are computed from measured data, using linear regression where the difference between the measured and estimated path losses is minimized in a mean square error sense over a wide range of measurement locations and T-R separations. The value of in (1.60) is based on either close-in measurements or on a free space assumption from the transmitter to d₀. An example of how the path loss exponent is determined from measured data follows. Figure 1-17 illustrates actual measured data in several cellular radio systems and demonstrates the random variations about the mean path loss (in dB) due to shadowing at specific T-R separations.

Figure 1-17. Plot of Path Loss vs. Distance at 1900 MHz for measurements performed with a receiver at microcell antenna heights (13 meters), and a mobile transmitter with an antenna height of 1.5 meters, in several different cluttered environments. The MMSE estimated path loss exponent for the collection of measurements is n = 4.6 with σ = 12.5 dB.

Since PL(d) is a random variable with a normal distribution in dB about the distance-dependent mean, so is P_r(d), and the Q-function or error function (erf) may be used to determine the probability that the received signal level will exceed (or fall below) a particular level. The Q-function is defined as

Equation 1.62. 

where

Equation 1.63. 

The probability that the received signal level will exceed a certain value γ can be calculated from the cumulative density function as

Equation 1.64. 

Similarly, the probability that the received signal level will be below γ is given by

Equation 1.65. 

Usually, shadowing is taken into account by determining a link margin that is required to achieve a certain coverage probability. For example, to achieve a 95% coverage probability at the cell edge with a shadowing standard deviation of σ = 10 dB, we find that we need or 16.5 dB. In other words, there is only a 5% probability that Pr(d) will be less than γ, as long as the mean received power, , is 16.5 dB above γ. We call this 16.5 dB value the shadowing margin. The link budget example in Chapter 2 uses shadowing margins to account for coverage probability due to shadowing.