Channel capacity

When we look at Shannon’s formula (also known as Shannon’s limit), first thing we notice is the limit for channel capacity is proportional to the available channel bandwidth. Certainly channel bandwidth is closely tied to the center frequency used; i.e., lower the center frequency lower the potential channel bandwidth. Going back to the days of Marconi, his first transatlantic transmission is estimated to be using a center around 820-980 KHz. At those frequencies building a wide-band receiver or transmitter was rather impossible. Instead his design depended on an inductor/capacitor combination as shown in ( Between Newfoundland, Canada and Cornwall, UK (where I write this blog now), Marconi claimed to transmit letter S on December 12th, 1901. Certainly at that frequency, it is difficult to ascertain whether he received a reflection of the original wave or that of a harmonic.

Again fast forwarding to today where typical transmitters for LTE using a 10 MHz bandwidth allow channel capacity figures closer to 100 Mbit/s. In order to achieve such wider bandwidth and more importantly to be able to provide mobile communications services to handheld devices, modern wireless communications systems typically use frequency ranges above 500 MHz. Going to much higher frequency ranges such as over 2 GHz allow much wider channel capacity figures at the expense of reduced range due to higher attenuation in free-space as well as higher penetration loss for covering indoors when transmitters happen to be outdoors.

We can summarize the Goldilocks effect of first parameter in Shannon’s law: if the center frequency happens to be too low then available channel bandwidth is too small and building a handheld device is rather difficult. On the other hand, if the center frequency happens to be too high then available channel bandwidth is high but the propagation and building-penetration losses become too high to end up requiring too many transmitters.

In the next post, let’s look at the progression of efficiency in terms of bit/s versus the available channel bandwidth, and in turn the impact of signal and noise power.

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