The bandwidth of 1.25 MHz is a compromise between multipath mitigation, receiver
complexity, and receiver performance. Larger rates would require more Rake correlators
in order to utilize a large fraction of the multipath energy, while smaller
rates would suffer from an increased likelihood of so-called "flat fading"
and adverse "law of large numbers" effects.
That is, because there would be fewer users on each CDMA channel, the relative
power fluctuations, which are proportional to N-1/2, N=number of
users, would be larger. More operating margin is thus needed for stable operation,
entailing a penalty in capacity per megahertz.
Multipath delay spreads in urban areas are typically in the range of 2-3 microseconds.
Spreading bandwidths significantly larger than 1 MHz would resolve many more
multipath components. While there would be less likelihood of fading of each
correlator output, there would have to be more of them. The fraction of the
energy in each would be smaller, making time and frequency tracking more difficult.
Also the search function would have to find smaller signal components, which
would require more integration time and therefore degrade performance.
Smaller bandwidths suffer from two problems. First, they would tend to not resolve
common multipath situations. In this case, the fading behavior would be very
similar to the narrowband systems, exhibiting the so-called flat Rayleigh fading.
While some interference averaging might take place, the overall performance
would be adversely affected by the more severe fading.
A second consequence of too narrow a bandwidth is that too few users would be
serviced by each carrier. If fewer users are present the law-of-large numbers
averaging that takes place would be less effective in reducing power fluctuations.
The fluctuations in the sum of N random variables, such as the single-user power,
are proportional to N-1/2. With larger fluctuations, more operating
margin on the system operating point is needed. The capacity per MHz would be
poorer because each CDMA channel would be operating a smaller loading than would
be possible with a large bandwidth and a larger user population.
A spreading rate about 2-3 times the reciprocal delay spread is large enough
that 2 -3 correlators in a Rake receiver will collect nearly all signal energy,
on average. Also, some statistical independence of fading in the correlator
outputs can be expected.
Another consideration is the rollout of CDMA system into the existing AMPS infrastructure.
1.25 MHz is 1/8 of the original 10 MHz allocations. The relatively small bandwidth
permits an operator to replace about 15% of his AMPS channels with one CDMA
channel. But that one CDMA channel has many times the capacity of the AMPS channels
it replaced. This permits graceful, gradual, introduction of CDMA into the system.
And finally, after taking into account the frequency allocations for cellular
in North America, in which one of the band segments is only 1.5 MHz wide, the
choice of 1.25 MHz is seen to be a suitable compromise among all these conflicting
For more details, see Optimum Bandwidth.
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