# Introduction to Wireless Communication Systems: Advanced Techniques for Signal Reception

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## 1.2 Wireless Signaling Environment

#### 1.2.1 Single-User Modulation Techniques

To discuss advanced receiver signal processing methods for wireless, it is useful first to specify a general model for the signal received by a wireless receiver. To do so, we can first think of a single transmitter, transmitting a sequence or frame {b[0], b[1], ..., b[M – 1]} of channel symbols over a wireless channel. These symbols can be binary (e.g., ±1), or they may take on more general values from a finite alphabet of complex numbers. In this treatment, we consider only linear modulation systems, in which the symbols are transmitted into the channel by being modulated linearly onto a signaling waveform to produce a transmitted signal of this form:

Equation 1.1

where wi(·) is the modulation waveform associated with the ith symbol. In this expression, the waveforms can be quite general. For example, a single-carrier modulation system with carrier frequency ωc, baseband pulse shape p(·), and symbol rate 1/T is obtained by choosing

Equation 1.2

where A > 0 and φ ∊ (-π, π) denote carrier amplitude and phase offset, respectively. The baseband pulse shape may, for example, be a simple unit-energy rectangular pulse of duration T:

Equation 1.3

or it could be a raised-cosine pulse, a bandlimited pulse, and so on. Similarly, a direct-sequence spread-spectrum system is produced by choosing the waveforms as in (1.2) but with the baseband pulse shape chosen to be a spreading waveform:

Equation 1.4

where N is the spreading gain, c0, c1, ..., cN−1, is a pseudorandom spreading code (typically, cj {+1, -1}), ψ(·), is the chip waveform, and is the chip interval. The chip waveform may, for example, be a unit-energy rectangular pulse of duration Tc:

Equation 1.5

Other choices of the chip waveform can also be made to lower the chip bandwidth. The spreading waveform of (1.4) is periodic when used in (1.2), since the same spreading code is repeated in every symbol interval. Some systems (e.g., CDMA systems for cellular telephony) operate with long spreading codes, for which the periodicity is much longer than a single symbol interval. This situation can be modeled by (1.1) by replacing p(t) in (1.2) by a variant of (1.4) in which the spreading code varies from symbol to symbol; that is,

Equation 1.6

Spread-spectrum modulation can also take the form of frequency hopping, in which the carrier frequency in (1.2) is changed over time according to a pseudorandom pattern. Typically, the carrier frequency changes at a rate much slower than the symbol rate, a situation known as slow frequency hopping; however, fast hopping, in which the carrier changes within a symbol interval, is also possible. Single-carrier systems, including both types of spread spectrum, are widely used in cellular standards, in wireless LANs, Bluetooth, and others (see, e.g., [42, 131, 150, 163, 178, 247, 338, 361, 362, 392, 394, 407, 408, 449, 523, 589]).

Multicarrier systems can also be modeled in the framework of (1.1) by choosing the signaling waveforms {ωi(·)} to be sinusoidal signals with different frequencies. In particular, (1.2) can be replaced by

Equation 1.7

where now the frequency and phase depend on the symbol number i but all symbols are transmitted simultaneously in time with baseband pulse shape p(·). We can see that (1.2) is the counterpart of this situation with time and frequency reversed: All symbols are transmitted at the same frequency but at different times. (Of course, in practice, multiple symbols are sent in time sequence over each of the multiple carriers in multicarrier systems.) The individual carriers can also be direct-spread, and the baseband pulse shape used can depend on the symbol number i. (For example, the latter situation is used in multicarrier CDMA, in which a spreading code is used across the carrier frequencies.) A particular case of (1.7) is OFDM, in which the baseband pulse shape is a unit pulse pT, the intercarrier spacing is 1/T cycles per second, and the phases are chosen so that the carriers are orthogonal at this spacing. (This is the minimal spacing for which such orthogonality can be maintained.) OFDM is widely believed to be among the most effective techniques for wireless broadband applications and is the basis for the IEEE 802.11a high-speed wireless LAN standard (see, e.g., [354] for a discussion of multicarrier systems).

An emerging type of wireless modulation scheme is ultra-wideband (UWB) modulation, in which data are transmitted with no carrier through the modulation of extremely short pulses. Either the timing or amplitude of these pulses can be used to carry the information symbols. Typical UWB systems involve the transmission of many repetitions of the same symbol, possibly with the use of a direct-sequence type of spreading code from transmission to transmission (see, e.g., [569] for a basic description of UWB systems).

Further details on the modulation waveforms above and their properties will be introduced as needed throughout this treatment.

#### 1.2.2 Multiple-Access Techniques

In Section 1.2.1 we discussed ways in which a symbol stream associated with a single user can be transmitted. Many wireless channels, particularly in emerging systems, operate as multiple-access systems, in which multiple users share the same radio resources.

There are several ways in which radio resources can be shared among multiple users. These can be viewed as ways of allocating regions in frequency, space, and time to different users, as shown in Fig. 1.1. For example, a classic multiple-access technique is frequency-division multiple access (FDMA), in which the frequency band available for a given service is divided into subbands that are allocated to individual users who wish to use the service. Users are given exclusive use of their subband during their communication session, but they are not allowed to transmit signals within other subbands. FDMA is the principal multiplexing method used in radio and television broadcast and in first-generation (analog voice) cellular telephony systems, such as the Advanced Mobile Phone System (AMPS) and Nordic Mobile Telephone (NMT), developed primarily in the 1970s and 1980s (cf. [458]). FDMA is also used in some form in all other current cellular systems, in tandem with other multiple-access techniques that are used to further allocate the subbands to multiple users.

Figure 1.1. Multiple-access schemes.

Similarly, users can share the channel on the basis of time-division multiple access (TDMA), in which time is divided into equal-length intervals, which are further divided into equal-length subintervals, or time slots. Each user is allowed to transmit throughout the entire allocated frequency band during a given slot in each interval but is not allowed to transmit during other time slots when other users are transmitting. So, whereas FDMA allows each user to use part of the spectrum all of the time, TDMA allows each user to use all of the spectrum part of the time. This method of channel sharing is widely used in wireless applications, notably in a number of second-generation cellular (i.e., digital voice) sytems, including the widely used Global System for Mobile (GSM) system [178, 407, 408] and in the IEEE 802.16 wireless MAN standards. A form of TDMA is also used in Bluetooth networks, in which one of the Bluetooth devices in the network acts as a network controller to poll the other devices in time sequence.

FDMA and TDMA systems are intended to assign orthogonal channels to all active users by giving each, for their exclusive use, a slice of the available frequency band or transmission time. These channels are said to be orthogonal because interference between users does not, in principle, arise in such assignments (although, in practice, there is often such interference, as discussed further below). Code-division multiple access (CDMA) assigns channels in a way that allows all users to use all of the available time and frequency resources simultaneously, through the assignment of a pattern or code to each user that specifies the way in which these resources will be used by that user. Typically, CDMA is implemented via spread-spectrum modulation, in which the pattern is the pseudorandom code that determines the spreading sequence in the case of direct sequence, or the hopping pattern in the case of frequency hopping. In such systems, a channel is defined by a particular pseudorandom code, so each user is assigned a channel by being assigned a pseudorandom code. CDMA is used, notably, in the second-generation cellular standard IS-95 (Interim Standard 95), which makes use of direct-sequence CDMA to allocate subchannels of larger-bandwidth (1.25 MHz) subchannels of the entire cellular band. It is also used, in the form of frequency hopping, in GSM to provide isolation among users in adjacent cells. The spectrum spreading used in wireless LAN systems is also a form of CDMA in that it allows a number of such systems to operate in the same lightly regulated part of the radio spectrum. CDMA is also the basis for the principal standards being developed and deployed for 3G cellular telephony (e.g., [130, 361, 362, 407]).

Any of the multiple-access techniques discussed here can be modeled analytically by considering multiple transmitted signals of the form (1.1). In particular, for a system of K users, we can write a transmitted signal for each user as

Equation 1.8

where xk(·), {bk[0], bk[1], ..., bk[M−1]}, and wi,k(·) represent the transmitted signal, symbol stream, and ith modulation waveform, respectively, of user k. That is, each user in a multiple-access system can be modeled in the same way as in a single-user system, but with (usually) differing modulation waveforms (and symbol streams, of course). If the waveforms {wi,k(·)} are of the form (1.2) but with different carrier frequencies {ωk}, say, this is FDMA. If they are of the form (1.2) but with time-slotted amplitude pulses {pk(·)}, say, this is TDMA. Finally, if they are spread-spectrum signals of this form but with different pseudorandom spreading codes or hopping patterns, this is CDMA. Details of these multiple-access models will be discussed in the sequel as needed.

#### 1.2.3 Wireless Channel

From a technical point of view, the greatest distinction between wireless and wireline communications lies in the physical properties of wireless channels. These physical properties can be described in terms of several distinct phenomena, including ambient noise, propagation losses, multipath, interference, and properties arising from the use of multiple antennas. Here we review these phenomena only briefly. Further discussion and details can be found, for example, in [38, 46, 148, 216, 405, 450, 458, 465].

Like all practical communications channels, wireless channels are corrupted by ambient noise. This noise comes from thermal motion of electrons on the antenna and in the receiver electronics and from background radiation sources. This noise is well modeled as having a very wide bandwidth (much wider than the bandwidth of any useful signals in the channel) and no particular deterministic structure (structured noise can be treated separately as interference). A very common and useful model for such noise is additive white Gaussian noise (AWGN), which as the name implies, means that it is additive to the other signals in the receiver, has a flat power spectral density, and induces a Gaussian probability distribution at the output of any linear filter to which it is input. Impulsive noise also occurs in some wireless channels. Such noise is similarly wideband but induces a non-Gaussian amplitude distribution at the output of linear filters. Specific models for such impulsive noise are discussed in Chapter 4.

Propagation losses are also an issue in wireless channels. These are of two basic types: diffusive losses and shadow fading. Diffusive losses arise because of the open nature of wireless channels. For example, the energy radiated by a simple point source in free space will spread over an ever-expanding spherical surface as the energy propagates away from the source. This means that an antenna with a given aperture size will collect an amount of energy that decreases with the square of the distance between the antenna and the source. In most terrestrial wireless channels, the diffusion losses are actually greater than this, due to the effects of ground-wave propagation, foliage, and so on. For example, in cellular telephony, the diffusion loss is inverse square with distance within line of sight of the cell tower, and it falls off with a higher power (typically, 3 or 4) at greater distances. As its name implies, shadow fading results from the presence of objects (buildings, walls, etc.) between the transmitter and receiver. Shadow fading is typically modeled by an attenuation (i.e., a multiplicative factor) in signal amplitude that follows a log-normal distribution. The variation in this fading is specified by the standard deviation of the logarithm of this attenuation.

Many of the advanced signal transmission and processing methods that have been developed for wireless systems are designed to contravene the effects of multipath. For example, wideband signaling techniques such as spread spectrum are often used as a countermeasure to frequency-selective fading. This both minimizes the effects of deep frequency-localized fades and facilitates the resolvability and subsequent coherent combining of multiple copies of the same signal. Similarly, by dividing a high-rate signal into many parallel lower-rate signals, OFDM mitigates the effects of channel dispersion on high-rate signals. Alternatively, high-data-rate single-carrier systems make use of channel equalization at the receiver to counteract this dispersion. Some of these issues are discussed further in Section 1.3.

Interference, also a significant issue in many wireless channels, is typically one of two types: multiple-access interference and co-channel interference. Multiple-access interference (MAI) refers to interference arising from other signals in the same network as the signal of interest. For example, in cellular telephony systems, MAI can arise at the base station when the signals from multiple mobile transmitters are not orthogonal to one another. This happens by design in CDMA systems, and it happens in FDMA or TDMA systems due to channel properties such as multipath or to nonideal system characteristics such as imperfect channelization filters. Co-channel interference (CCI) refers to interference from signals from different networks, but operating in the same frequency band as the signal of interest. An example is the interference from adjacent cells in a cellular telephony system. This problem is a chief limitation of using FDMA in cellular systems and was a major factor in moving away from FDMA in second-generation systems. Another example is the interference from other devices operating in the same part of the unregulated spectrum as the signal of interest, such as interference from Bluetooth devices operating in the same 2.4-GHz ISM band as IEEE 802.11 wireless LANs. Interference mitigation is also a major factor in the design of transmission techniques (e.g., the above-noted movement away from FDMA in cellular systems) as well as in the design of advanced signal processing systems for wireless, as we shall see in the sequel.

The phenomena we have discussed above can be incorporated into a general analytical model for a wireless multiple-access channel. In particular, the signal model in a wireless system is illustrated in Fig. 1.2. We can write the signal received at a given receiver in the following form:

Equation 1.9

where gk(t,u) denotes the impulse response of a linear filter representing the channel between the kth transmitter and the receiver, i(·) represents co-channel interference, and n(·) represents ambient noise. The modeling of the wireless channel as a linear system seems to agree well with the observed behavior of such channels. All of the quantities gk(·, ·), i(·), and n(·) are, in general, random processes. As noted above, the ambient noise is typically represented as a white process with very little additional structure. However, the co-channel interference and channel impulse responses are typically structured processes that can be parameterized.

Figure 1.2. Signal model in a wireless system.

An important special case is that of a pure multipath channel, in which the channel impulse responses can be represented in the form

Equation 1.10

where Lk is the number of paths between user k and the receiver, αℓ,k and τℓ,k are the gain and delay, respectively, associated with the th path of the kth user, and δ(·) denotes the Dirac delta function. Note that this is the situation illustrated in Fig. 1.2, in which we have written the time-invariant impulse response as gk(t) ≡ gk(t, 0). This model is an idealization of the actual behavior of a multipath channel, which would not have such a sharply defined impulse response. However, it serves as a useful model for signal processor design and analysis. Note that this model gives rise to frequency-selective fading, since the relative delays will cause constructive and destructive interference at the receiver, depending on the wavelength of propagation. Often, the delays {τℓ, k} are assumed to be known to the receiver or are spaced uniformly at the inverse of the bulk bandwidth of the signaling waveforms. A typical model for the path gains {αℓ, k} is that they are independent complex Gaussian random variables, giving rise to Rayleigh fading.

Note that, in general, the receiver will see the following composite modulation waveform associated with the symbol bk[i]:

Equation 1.11

If these waveforms are not orthogonal for different values of i, ISI will result. Consider, for example, the pure multipath channel of (1.10) with signaling waveforms of the form

Equation 1.12

where sk(·) is a normalized signaling waveform [∫ |sk(t)|2 dt = 1], Ak is a complex amplitude, and T is the inverse of the single-user symbol rate. In this case, the composite modulation waveforms are given by

Equation 1.13

with

Equation 1.14

If the delay spread (i.e., the maximum of the differences of the delays {τℓ, k} for different values of ) is significant relative to T, ISI may be a factor. Note that for a fixed channel, the delay spread is a function of the physical geometry of the channel, whereas the symbol rate depends on the data rate of the transmitted source. Thus, higher-rate transmissions are more likely to encounter ISI than are lower-rate transmissions. Similarly, if the composite waveforms for different values of k are not orthogonal, MAI will result. This can happen, for example, in CDMA channels when the pseudorandom code sequences used by different users are not orthogonal. It can also happen in CDMA and TDMA channels, due to the effects of multipath or asynchronous transmission. These issues are discussed further in the sequel as the need arises.

This model can be further generalized to account for multiple antennas at the receiver. In particular, we can modify (1.9) as follows:

Equation 1.15

where the boldface quantities denote (column) vectors with dimensions equal to the number of antennas at the received array. For example, the pth component of gk(t, u) is the impulse response of the channel between user k and the pth element of the receiving array. A useful such model is to combine the pure multipath model of (1.10) with a model in which the spatial aspects of the array can be separated from its temporal properties. This yields channel impulse responses of the form

Equation 1.16

where the complex vector aℓ, k describes the response of the array to the th path of user k. The simplest such situation is the case of a uniform linear array (ULA), in which the array elements are uniformly spaced along a line, receiving a single-carrier signal arriving along a planar wavefront and satisfying the narrowband array assumption. The essence of this assumption is that the signaling waveforms are sinusoidal carriers carrying narrowband modulation and that all of the variation in the received signal across the array at any given instant in time is due to the carrier (i.e., the modulating waveform is changing slowly enough to be assumed constant across the array). In this case, the array response depends only on the angle φℓ, k at which the corresponding path’s signal is incident on the array. In particular, the response of a P-element array is given in this case by

Equation 1.17

where j denotes the imaginary unit and where , with λ the carrier wavelength and d the interelement spacing (see [126, 266, 269, 404, 445, 450, 510] for further discussion of systems involving multiple receiver antennas).

It is also of interest to model systems in which there are multiple antennas at both the transmitter and receiver, called multiple-input/multiple-output (MIMO) systems. In this case the channel transfer functions are matrices, with the number of rows equal to the number of receiving antennas and the number of columns equal to the number of transmitting antennas at each source. There are several ways of handling the signaling in such configurations, depending on the desired effects and the channel conditions. For example, transmitter beamforming can be implemented by transmitting the same symbol simultaneously from multiple antenna elements on appropriately phased versions of the same signaling waveform. Space-time coding can be implemented by transmitting frames of related symbols over multiple antennas. Other configurations are of interest as well. Issues concerning multiple-antenna systems are discussed further in the sequel as they arise.