Position location techniques and applications - Part 4: Toward the cognitive radio paradigm

Wireless SISO Channel
We begin with the basic concepts of the common wireless channel, which differs from the wired channel because of such phenomena as multipath and interference. Let us first consider the simplest case, where we have a time-invariant channel. When we send signal s(t) over a channel with impulse response h(t), the received signal has the following expression:

where the * operator means convolution operation, n(t) is additive white Gaussian noise (AWGN), and j(t) is the interference from other users. The channel usually varies over time in stochastic fashion and attenuates the amplitude of our signal; thus, we define it as

where α is the attenuation coefficient of the channel, and δ(t - τ) is the Dirac's delta function with path delay τ. Now we can combine these equations to obtain

and in the frequency domain we have R(f) = H(f)S(f) + N(f). Note that here we do not comment on the nature of the signal s(t), and therefore it can be chosen by the designer of the transmitter-receiver. In addition, the interference j(t) has been ignored thus far.

The multiuser environment makes the transmission dilemma even more difficult because it adds interference to the system. For certain users, the signals of other users are seen as undesirable. In the mathematical sense, although very generally speaking, the multiuser environment in the frequency domain for K users is described as

where we can separate the desired user as

where the term is the aforementioned interference J(f). This multiuser aspect is valid also for multiantenna cases. Considering multipath propagation, the channel impulse response is given by

where k denotes the index of each multipath component and j is the imaginary unit. If these components with various phase delays are summed in the receiver, they cause multipath fading.

The worst-case scenario would be to have two components with 180-degree phase difference summed, in which case the sum is seen by the receiver as zero.

This phenomenon can be overcome somewhat with several techniques - for example, with the RAKE receiver used in CDMA systems [67, 68]. Mobility of the transmitter and/or receiver increases the complexity of the channel model because we need to take into consideration the Doppler shift. Often it is assumed that the user is stationary or moving very slowly, which is reasonable because typically the users of WLAN technology use their laptop when sitting somewhere and movement usually takes place at walking speeds.

When all the information discussed in this section is combined into a single channel model taking into consideration attenuation, path delay, noise, phase shift, fading, multiuser environment, and discrete-scatter Doppler phenomena, we get our channel model,

where A_k is the term that represents all those attenuation and phase-shift effects on the signal in each of the n multipath components, and v_k is the Doppler shift [68].

SISO is the traditional way of seeing multipath propagation. In SISO systems, we have only one transmit antenna and one receive antenna, and therefore we are not able to send multiple data streams to the channel and/or receive multiple copies of the signal on the various antennas, as in the multiantenna systems discussed in the following sections.

Wireless SIMO Channel
The difference between SISO and the more sophisticated, but still classic, approach called single-input multiple-output (SIMO) is, of course, multiple antennas on the reception (Rx) side. With more than one antenna at the Rx end the system gains benefits in spatial diversity. This is achieved by carefully combining the signal copies in the receiver. The price we pay for improved bit error rate (BER) and signal-to-noise ratio (SNR) is more complexity in the receiver [27, 68].

In the SIMO case, we send only one signal s(t) to the channel, but we receive the same signal (and multipath copies) at multiple antennas. As an illustration, consider a system with n receive antennas. The channel for each one of the n subsystems is given by

which gives the following for the vector of received signals:

Signal power fluctuates in wireless channels randomly; in other words it fades. By using several receive antennas, we achieve diversity, which is a good technique to combat fading. Diversity benefits derive from transmitting the signal over multiple (ideally) independently fading channels. It is possible to separate channels in time, frequency, or space. Spatial diversity is preferred, since it doesn't require more bandwidth or time.

If the transmitted signal is suitably constructed, the receiver is able to combine the received signals in such away that amplitude variability is significantly reduced. The diversity techniques do not directly increase the data rates, but they improve the quality of the received signal, and therefore they make it possible to use other techniques (e.g., modulation schemes) to increase data rates [64].