Category: Capacity

Capacity could be number of users a system can accommodate or it can be the maximum throughput as predicted by Shannon capacity formula.

Capacity, LTE

LTE Data Rate Calculation

Peak LTE data rate can be calculated using the following parameters: 1 Time-slot=0.5 ms (i.e 1 Sub-frame = 1 ms) 1 Time-slot=7 Modulation Symbols (when normal CP length is used) 1 Modulation Symbol=6 bits; if 64 QAM is used as modulation scheme Data rate for a single carrier=Number of symbols per time slot*Bits per symbol/Duration of a time slot=7*6/0.5e-3=84kbps If 1200 carriers (100RBs) are used then the aggregated throughput would be=1200*84kbps=100.8Mbps If 4×4 MIMO is used then the capacity would increase four fold to=403.2Mbps With 3/4 channel coding the data rate would be reduced to=302.4Mbps Note: 1. A Resource Block […]

Read more
Capacity, LTE

Shannon Capacity of LTE (Effective)

In the previous post we calculated the Shannon Capacity of LTE as a function of bandwidth. We now calculate the capacity as a function of SNR (bandwidth fixed at 20MHz and signal power varied). We also use the concept of effective bandwidth to get a more realistic estimate of the capacity. The modified Shannon Capacity formula is given as: C=B_eff*log2(1+SNR) where B_eff=Bandwidth*eff1*eff2*eff3*eff4 eff1=0.9=due to adjacent channel leakage ratio and practical filter issues eff2=0.93=due to cyclic prefix eff3=0.94=due to pilot assisted channel estimation eff4=0.715=due to signalling overhead B_eff=0.57*B Therefore C=0.57*B*log2(1+SNR) Note: This is the capacity in a SISO channel with no […]

Read more
Capacity, Channel Capacity, Fundamentals, LTE

Shannon Capacity of LTE (Ideal)

Shannon Capacity of LTE in AWGN can be calculated by using the Shannon Capacity formula: C=B*log2(1+SNR) or C=B*log2(1+P/(B*No)) The signal power P is set at -90dBm, the Noise Power Spectral Density No is set at 4.04e-21 W/Hz (-174dBm/Hz) and the bandwidth is varied from 1.25MHz to 20MHz. It is seen that the capacity increases from about 10Mbps to above 70Mbps as the bandwidth is varied from 1.25MHz to 20MHz (keeping the signal power constant). It must be noted that this is the capacity with a single transmit and single receive antenna (MIMO capacity would obviously be higher).  

Read more
Capacity

Shannon Capacity of a GSM Channel in Fading Environment

In the previous post we calculated the Shannon Capacity of a 200kHz GSM channel in AWGN (Additive White Gaussian Noise). However, in a practical scenario the capacity is limited by time varying fading and interference. Let us consider a fading channel with four possible states corresponding to SNRs of 15dB, 10dB, 5dB and 0dB. The probability of these states is 0.50, 0.25, 0.15 and 0.10 respectively. The Shannon Capacity of such a channel is given as (assuming that the channel state information is known at the receiver): C=Σ B*log2(1+SNRi)* p(SNRi) C=B*(Σ log2(1+SNRi)* p(SNRi)) C=(200e3)*(log2(1+31.62)*0.50+log2(1+10.00)*0.25+log2(1+3.16)*0.15+log2(1+1)*0.10) C=757.43kbps Assuming that only one out […]

Read more
Capacity

Shannon Capacity of a GSM Channel

We know that GSM bit rates can vary from a few kbps to a theoretical maximum of 171.2kbps (GPRS). But what is the actual capacity of a 200kHz GSM channel. We can use the Shannon Capacity Theorem to find this capacity. C=B*log2(1+SNR) or C=B*log2(1+P/N) The noise power can be found by using the following formula: N=B*No=k*T*B=(1.38e-23)*(293)*(200e3)=8.08e-16W=-121dBm Let us now assume a signal power 0f -90dBm. This gives us an SNR of 31dB or 1258.9 on linear scale. The capacity can thus be calculated as: C=200e3*log2(1+1258.9)=2.06Mbps This is the capacity if all time slots are allocated to a single user. If […]

Read more
Capacity, WCDMA

WCDMA Uplink Capacity (N-pole)

The uplink capacity of a WCDMA cell also known as the pole capacity is given as: N=(W/R)/((Eb/Nt)*v*(1+a)) where W is the spreading bandwidth fixed at 3.84MHz R is the radio access bearer bit rate e.g. 12.2kbps Eb/Nt is the energy per bit to noise power spectral density ratio e.g. 5dB v is the voice activity factor which depends upon the vocoder, channel coding and actual application e.g. 0.5 a is the other-cell to in-cell interference ratio e.g. 0.65 Using the above values the pole capacity of the WCDMA cell is calculated as 120. In the case of a mobile UE […]

Read more
Capacity, WCDMA

CDMA vs FDMA Capacity (Mbps)

We saw previously that the channel capacity of a WCDMA system is severely limited by the Multiple Access Interference (MAI). Now let us consider the case where the 5MHz channel is divided equally among 20 users such that each user has a bandwidth of 250kHz. Keeping the transmit power for the narrow band signal the same as the wideband signal the signal to noise ratio would improve tremendously (since there is no MAI and the noise power is reduced by a factor of 20). Thus each narrowband channel would have a capacity of 2.99Mbps giving a combined capacity of 59.83Mbps […]

Read more
Capacity, WCDMA

WCDMA Capacity (Mbps)

The capacity of any wireless communication channel is given by the well known Shannon Capacity Theorem: C=B*log2(1+SNR) or C=B*log2(1+P/(NoB)) where C is the capacity of the channel in bits/sec, P in the noise power in Watts, No is the noise power spectral density in Watts/Hz and B is the channel bandwidth in Hz. It is obvious that the channel capacity increases with increase in signal power. However, the relationship with bandwidth is a bit complicated. The increase in bandwidth decreases the SNR (keeping the signal power and noise power spectral density same). Therefore the capacity does not increase linearly with […]

Read more