The capacity of multiuser wireless communication systems and different multiple access technolo- gies are the topics of widespread interests and may have many practical implications for efficient system designs [22, 23]. Information Theoretic (IT) view of multiple access techniques and their capacity (number of bits per unit bandwidth) are discussed in early contributions by Gallager , El Gamal, Cover and Muelen, such as in [11], [24] and [13]. Unlike the IT approach, the user capacity centric approach [25], [26] are focused on maximizing the number of simultaneous users supported; which is more appealing in terms of generating more revenues i.e. users from limited
system resources. Since the spectral efficiency is the ultimate performance metric of any wireless systems, the information theoretic perspective of MAC and the achievable rate region of different MA schemes are shown here in a simplified manner. The orthogonal waveform MA (OWMA) schemes, although are optimum in terms of minimizing outage, are suboptimal in terms of achiev- able rates [9]. It is known that superposition coding transmission by several cooperating users and successive interference cancellation at the receiver achieves rates much higher than orthogonal schemes [27]. A brief review of capacity of multiuser systems are carried out next.
2.3.1 Information Theoretic Capacity
The performance of multiuser systems are often described in terms of capacity region . This is defined as the sum of each user’s maximum information rate that can be reliably transmitted over a unit bandwidth. For a K-user Gaussian multiple access channels (GMAC), the sum capacity CGM AC, can be given by [6] CGM AC = K X k=1 Rk; =⇒ CGM AC ≤ 1 2log2 " 1 + PK k=1Pk σ2 # (2.1)
where, Rkis rate of kthuser,Pσk2 is the signal to noise ratio with P denoting signal power and σ2is the variance of noise over the system bandwidth. As noticed in (2.1), the sum rate of the MAC is less than the sum of individual user’s rates. For example, the achievable rates for a 2-user GMAC is shown in Figure 2.1. Where, P1 and P2 are the power of user 1 and 2, respectively. The area
within the pentagon defines the rate region of the Gaussian MAC. As can be seen, the individual rate of users R1 and R2 are effected by their power P1 and P2 along with their AWGN terms.
Therefore the sum rate of the GMAC is always lower than that of single user system under the same power and bandwidth.
In CDMA communications , each user uses the entire spectrum of the system by spreading its low rate data using a distinct spreading sequence s spanned over N chips. The well known signal model of synchronous CDMA r = SAb+n, as in [28], [29] is used here. where, r, S, A, b and n, are the received signal vector of dimension 1 × N , matrix of users’ spreading sequences of size K × N , diagonal matrix of users’ amplitude, users’ data vector, and noise vector, respectively. The sum capacity Cspreadfor such a system is given by [6]
Cspread= 1 2N log2 " detI + N σ2SPS T # (2.2)
where, det denotes the determinant of a matrix, I is K × K identity matrix, ST denotes transpose of matrix S, and P=AAT is diagonal matrix of users powers.
The capacity formulae (2.1) and (2.2) of Gaussian MAC and CDMA multiuser system set an ultimate limit on how much information can be transmitted over the channels. The users in the uplink CDMA system usually employ random sequences to transmit their information to the basestation receiver. The asymptotic spectral efficiency of such systems for different type of mul- tiuser receivers at the basestation is investigated by Verdu and Shamai [6]. In Figure 2.2, the performance of different receivers obtained from [6] are shown. It can be seen that the spectral efficiency of the system with optimum receiver increases with number of users or system loading K/N . The conventional matched filter receiver shows much lower spectral efficiency and satu- rates after certain number of users. The performance of decorrelators and MMSE [29] are shown to be higher than MF at low system loading K/N ≤ 1.
Figure 2.2: Large system spectral efficiency of randomly spread CDMA for different receivers at Eb/N0=
10dB [6]
The information theory predicts that fading multiuser systems can offer higher sum capac- ity than that in AWGN channels, if the system resources (spreading sequences, channel power
distribution, transmitter power control) are utilized efficiently [23]. The author investigated the performance of conventional decision feedback also known as SIC receivers in different fading channels with and without power ordering. The spectral efficiency analysis similar to [23] will be used to assess the performance of improved IC receivers [16],[17] proposed in Chapter 3.
It has been seen earlier that the multiuser systems incur loss in the spectral efficiency compared with equivalent single user Gaussian channels. This is because, when multiple users simultane- ously access the common receiver, each user’s signal, that is regarded as the desired signal, also contribute to the noise and interference components for other users. The optimum receiver jointly detects the signals of all users and as K/N −→ ∞, converges asymptotically to the capacity of single user channels [6]. The practical multiuser systems have to accommodate several tens to hundreds of users within a given system bandwidth while ensuring minimum interference for detection of users’ data. In such cases, the employment of optimum receiver and SIC though they are known to achieve higher capacity, become impractical to implement due to their higher computational complexity. Therefore, the choice of a simple multiple access scheme that guaran- tees interference free access of users’ information has become one of the main focus of practical multiuser wireless systems.
2.3.2 User Capacity
The user capacity of multiple access scheme is defined by the ratio of total number of users K to the number of degree of freedom N , i.e. Cuser= K/N . The degree of freedom can be frequency
bands, time slots or user separating codes. The channel is said to be under-loaded if Cuser ≤ 1
and overloaded if Cuser > 1. When no multiple access scheme is employed and there are K
users in the system, the user capacity is Cuser = K. The conventional multiple access schemes,
e.g. FDMA and TDMA, support maximum N users. Therefore, their user capacity is simply Cuser= 1. Unlike these schemes, CDMA on the other hand, does not have hard limit on maximum
allowable number of users. The system performance, which is dependent on SINR , dictates the maximum number of users K. CDMA also has many attractive advantages in practical cellular wireless systems, such as, universal frequency reuse, high resilience to jamming and exploitation of multipath fading for performance improvement. To motivate the discussion of novel techniques that increase the user capacity, brief review of different MA schemes are provided next.