b-ISI (Backward inter-symbol interference)

Backward inter-symbol interference (b-ISI) is a phenomenon that occurs in digital communication systems when the symbols transmitted in a signal interfere with each other, causing errors in the received signal. In particular, b-ISI occurs when the symbols transmitted after a given symbol affect the detection of that symbol at the receiver.

In digital communication systems, information is transmitted by modulating a carrier signal with a sequence of symbols. The receiver demodulates the received signal to recover the transmitted symbols. However, due to various impairments in the communication channel, such as noise, interference, and distortion, the received signal may differ from the transmitted signal. These impairments can cause errors in the detection of the transmitted symbols, leading to a decrease in the quality of the communication.

One type of impairment that can cause errors in the detection of symbols is inter-symbol interference (ISI). ISI occurs when the symbols in a signal interfere with each other, causing the received symbols to be distorted. ISI can be classified into two types: forward ISI (f-ISI) and backward ISI (b-ISI). f-ISI occurs when the symbols transmitted before a given symbol affect the detection of that symbol at the receiver. On the other hand, b-ISI occurs when the symbols transmitted after a given symbol affect the detection of that symbol at the receiver.

b-ISI is particularly problematic in digital communication systems because it can cause errors in the detection of symbols that were transmitted correctly. This is because the interference from the subsequent symbols can cause the received symbol to be distorted in such a way that it is misinterpreted at the receiver. This can lead to a decrease in the data rate, an increase in the error rate, and a decrease in the overall quality of the communication.

One way to mitigate b-ISI is to use equalization techniques. Equalization is a process that tries to estimate the effect of the communication channel on the transmitted signal and compensate for it. There are two main types of equalization techniques: linear equalization and decision-feedback equalization.

Linear equalization is a technique that tries to estimate the channel impulse response (CIR) and invert it to recover the transmitted symbols. The CIR is the response of the communication channel to a delta function input. It describes how the channel modifies the transmitted signal as it propagates through the channel. Linear equalization involves multiplying the received signal by the inverse of the estimated CIR to cancel out the effect of the channel.

Decision-feedback equalization is a more advanced technique that uses feedback to improve the equalization performance. Decision-feedback equalization involves not only estimating the CIR but also estimating the previous symbols and using them to improve the equalization. The previous symbols are estimated using a feedback loop that feeds back the detected symbols to the equalizer. The estimated symbols are then used to improve the equalization and cancel out the effect of b-ISI.

Another way to mitigate b-ISI is to use advanced modulation schemes that are less susceptible to ISI. Advanced modulation schemes use more complex signaling schemes that allow for higher data rates and better performance in the presence of ISI. Examples of advanced modulation schemes include quadrature amplitude modulation (QAM), orthogonal frequency-division multiplexing (OFDM), and multiple-input multiple-output (MIMO) systems.

QAM is a modulation scheme that uses both amplitude and phase modulation to encode information. QAM uses a constellation diagram to represent the possible symbol values. Each point on the constellation diagram represents a different symbol value. QAM can achieve high data rates and good performance in the presence of ISI.

OFDM is a modulation scheme that uses multiple subcarriers to transmit the data. OFDM divides the available bandwidth into multiple subcarriers, each of which is modulated with a different symbol. The subcarriers are orthogonal to each other, which means that they do not interfere with each other. This allows for better performance in the presence of ISI, as the symbols on each subcarrier do not interfere with each other.

MIMO systems use multiple antennas at both the transmitter and receiver to improve the performance of the communication system. MIMO systems can achieve higher data rates and better performance in the presence of ISI by exploiting the spatial diversity provided by multiple antennas.

In addition to equalization and advanced modulation schemes, there are other techniques that can be used to mitigate b-ISI. These include pre-coding, time-domain equalization, and pulse shaping.

Pre-coding is a technique that involves modifying the transmitted signal to reduce the effect of the communication channel. Pre-coding can be used to improve the performance of the communication system by reducing the impact of b-ISI.

Time-domain equalization is a technique that involves equalizing the signal in the time domain rather than the frequency domain. Time-domain equalization can be used to improve the performance of the communication system by canceling out the effect of b-ISI in the time domain.

Pulse shaping is a technique that involves modifying the shape of the transmitted pulse to reduce the effect of ISI. Pulse shaping can be used to improve the performance of the communication system by reducing the impact of b-ISI and other types of ISI.

In conclusion, b-ISI is a phenomenon that occurs in digital communication systems when the symbols transmitted after a given symbol affect the detection of that symbol at the receiver. b-ISI can cause errors in the detection of symbols, leading to a decrease in the data rate, an increase in the error rate, and a decrease in the overall quality of the communication. To mitigate b-ISI, equalization techniques, advanced modulation schemes, and other techniques can be used. These techniques can improve the performance of the communication system by reducing the impact of b-ISI and other types of ISI.