Welcome to the World of CDMA
Optimum Bandwidth for CDMA
Adapted from a presentation by Klein S. Gilhousen
at the International Conference on Personal, Mobile Radio, and
Spread Spectrum Communications
Beijing, China, October 12-14, 1994
The effects of multipath propagation on the CDMA signal
are quite different from those of narrowband signals. While increasing
spreading bandwidth leads to an asymptotic improvement in Erlang capacity
of CDMA per megahertz, multipath propagation phenomena have increasingly
detrimental effects. The direct sequence modulation and Rake receiver
do mitigate the multipath that leads to narrowband Rayleigh fading. However
the complexity of the Rake increases with bandwidth. So what is the "optimum"
spreading bandwidth? Why did the designers of IS-95A choose 1.25 MHz?
CDMA Capacity and the Law of Large NumbersIn reality, all CDMA systems are also, at least to a certain extent, Frequency Division Multiple Access (FDMA) systems. Usually, a given spectral allocation will be available for provision of a communications service. The system designer has the choice of filling the entire spectral allocation with a single spread spectrum waveform or of dividing the spectral allocation into a number of sub-bands, each of which is filled with a narrower bandwidth spread spectrum waveform. In this latter case, the resulting system is considered to be a hybrid of FDMA and CDMA. IS-95A is such a hybrid system because a number of 1.25 MHz bandwidth channels can be defined and used simultaneously. The radio channel capacity of a CDMA cellular system is defined as the number of subscribers that can access a particular base station of the system simultaneously. Calculation of the number, N, of equal power, fixed rate interfering users in an isolated cell of a CDMA system is generally accepted to be given by
The capacity of a CDMA system can be readily increased beyond that of (1) by applying additional techniques such as voice activity gating, sectorization and frequency reuse. Voice activity gating reduces the transmission data rate while a subscriber is not talking. Typical conversational speech is active only about 40% of the time, allowing a capacity increase of a factor of about 2.5. Sectorization typically divides the coverage area of a cell into three equal sectors which share the total offered load of the cell, allowing the total capacity of the cell to increase by a factor equal to the number of sectors.
Frequency reuse reduces the capacity of each cell slightly because of the interference from neighboring cells of the system, while multiplying the overall system capacity by the number of cells. The frequency reuse efficiency is about 65% in typical CDMA systems.
These capacity increasing techniques introduce statistical variation into the analysis of capacity. However, if the number of subscribers sharing a CDMA channel is large enough, then the performance will be very close to the average. This is known as a "law of large numbers" effect. Clearly, if the spread bandwidth is substantially reduced, the number of users sharing a given channel will not be "large" and performance will be degraded. Alternatively, as the spreading bandwidth is increased, there are diminishing returns as the capacity approaches its asymptotic maximum. This effect has been studied over a very large range of processing gains from 16 to 1024. In the table below, we show the loss of capacity versus processing gain. The computation is for a probability that the available capacity exceeds instantaneous demand greater than 90% of the time. Note that IS-95A has a processing gain of 128, while a system that filled, say, 10 MHz (the original cellular allocation) would have a processing gain of 1024. Note that the difference in capacity between these two is less than one-half dB. This small improvement in capacity for wider bandwidth can very easily be lost by inefficiencies arising from a variety of sources, as discussed below.
The extent to which a delayed signal adds coherently depends on the signal bandwidth. An impulse received with an infinite bandwidth totally resolves the multipath, as shown above. Each line represents a single path and does not fade, but it contains only a small fraction of the total signal energy. For a CW signal, all these components add up to a single stationary phasor that changes as the mobile (or the scatterers) move, producing fades. This effect is illustrated below for the narrowband case where all signal components are summed incoherently.
A signal with a finite bandwidth W has a time resolution associated with it
Figure 4 shows measured statistics for multipath dispersion in the CDMA test area of San Diego. This data shows the average behavior of the channel, not the impulse response at any particular time or place. This data is typical of many locations (see, for example, Cox). It shows an approximately exponential distribution with a delay spread of about 1.5 microseconds. A spread spectrum bandwidth of 1.25 MHz is well matched to the this channel condition, especially considering that three channel Rake receivers are typically employed in conjunction with IS-95A. It also shows the necessity for increasing the number of Rake receiver elements as the channel bandwidth increases.
Practical RAKE Receiver IssuesAs discussed above, a Rake receiver is necessary in order to capture a significant fraction of the received signal power of a spread spectrum signal in a multipath environment. A Rake receiver provides other benefits as well. It helps prevent the multipath signal components from combining noncoherently. Noncoherent combining occurs naturally, and unavoidably, in narrowband systems; it is the cause of the familiar Rayleigh fading. Given a finite spread bandwidth, however, one cannot expect the Rake to resolve all the multipath components all the time. This sometimes results in fading in each of the Rake channels (fingers). But to the extent that this residual fading behavior is uncorrelated between fingers, optimal diversity combining still improves performance over a single correlator receiver.
The Forward CDMA Channel is specifically designed to permit coherent combining of the multipath components. It includes an unmodulated pilot signal that gives the receiver a phase reference for demodulating data-bearing channels. The Rake fingers, in effect, remove the random, independent carrier phases from the multipath components. The resultant vector amplitudes then can be added in-phase.
The Reverse CDMA Channel uses non-coherent modulation and has no pilot. Diversity combining must be based on scalar symbol amplitudes and side information from the decoding. There is still diversity gain, however, over a receiver that collects only one component.
Figure 5. Rake receiver suitable for use in a base station receiver.
Frequency AllocationOne of the more interesting problems with fielding a wide bandwidth system is obtaining an adequate frequency allocation. In the United States, the FCC has allocated a total of 50 MHz in the 800 MHz band for cellular systems. The allocation is split in each service area between two competing carriers, the A (non-wireline) and B (wireline). Initially, the FCC had only allocated 40 MHz, 20 MHz to each carrier and then added 10 MHz later as cellular system proved themselves. This expansion was done in a complicated way, however. Initially, 825-835 MHz was allocated to A and 835-845 MHz was allocated to B for mobile transmit, with corresponding allocations from 870-890 MHz for base transmit. The expansion gave A the bands 824-825 MHz and 845-846.5 MHz; B was given 846.5-849 MHz, with corresponding upper band allocations.
The problem this causes CDMA systems is apparent. The
A' segment will contain at most a single 1.25 MHz bandwidth CDMA channel;
the B' segment will contain at most two CDMA channels. Even that is possible
only if the two CDMA channels are overlapped slightly, entailing some
loss of total capacity. So, if all portions of the cellular spectrum are
to be able to be utilized for CDMA, a 1.25 MHz bandwidth is the maximum
possible bandwidth for a non-overlay approach. While the situation in
the United States is somewhat unique, it is not unusual around the world
to find similar situations where very wide bandwidths simply cannot be
given exclusive frequency allocations. Typically, existing systems are
not very tolerant to a new system sharing the spectrum with them because
they were not designed to do so. Hence it is desirable to use relatively
narrow bandwidth CDMA in order to minimize the possibility of interference
to existing services and to minimize the amount of unusable spectrum allocation.
It should be clear that increasing spread bandwidth can only result in increased complexity of the systems. For example, increasing the spread bandwidth a factor of 8 from 1.25 MHz to 10 MHz will require the receiver correlators to operate 8 times faster. This increased speed will require both more silicon area and greater power consumption. In addition, many more correlators are required as shown above in order to adequately process the multipath signals.
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