# Relationship between symbol error rate and bit calculator

### Symbol rate - Wikipedia

Using Gray coding and assuming that for high signal to noise ratio the errors Table 1: Approximate symbol and bit error probabilities for coherent modula- tion. In digital communications, symbol rate, also known as baud rate and modulation rate, is the The symbol rate is related to the gross bitrate expressed in bits per second. The difference between baud (or signalling rate) and the data rate (or bit rate) is like a . In digital television transmission the symbol rate calculation is: . Oct 5, The analysis provides means to calculate the optimal ring ratio (RR) and phase difference (PD) for several possible results in a simple tractable symbol error rate (SER) ter, the information data bits are generated using.

Relationship to bit error rate[ edit ] The disadvantage of conveying many bits per symbol is that the receiver has to distinguish many signal levels or symbols from each other, which may be difficult and cause bit errors in case of a poor phone line that suffers from low signal-to-noise ratio. In that case, a modem or network adapter may automatically choose a slower and more robust modulation scheme or line code, using fewer bits per symbol, in view to reduce the bit error rate.

An optimal symbol set design takes into account channel bandwidth, desired information rate, noise characteristics of the channel and the receiver, and receiver and decoder complexity. Modulation[ edit ] Many data transmission systems operate by the modulation of a carrier signal.

For example, in frequency-shift keying FSKthe frequency of a tone is varied among a small, fixed set of possible values. In a synchronous data transmission system, the tone can only be changed from one frequency to another at regular and well-defined intervals. The presence of one particular frequency during one of these intervals constitutes a symbol.

The concept of symbols does not apply to asynchronous data transmission systems. In a modulated system, the term modulation rate may be used synonymously with symbol rate. Binary modulation[ edit ] If the carrier signal has only two states, then only one bit of data i. The bit rate is in this case equal to the symbol rate.

For example, a binary FSK system would allow the carrier to have one of two frequencies, one representing a 0 and the other a 1. A more practical scheme is differential binary phase-shift keyingin which the carrier remains at the same frequency, but can be in one of two phases. Again, only one bit of data i.

### Bit error rate - Wikipedia

This is an example of data being encoded in the transitions between symbols the change in phaserather than the symbols themselves the actual phase. The reason for this in phase-shift keying is that it is impractical to know the reference phase of the transmitter.

N-ary modulation, N greater than 2[ edit ] By increasing the number of states that the carrier signal can take, the number of bits encoded in each symbol can be greater than one. The bit rate can then be greater than the symbol rate.

For example, a differential phase-shift keying system might allow four possible jumps in phase between symbols. Then two bits could be encoded at each symbol interval, achieving a data rate of double the symbol rate. In a more complex scheme such as QAMfour bits of data are transmitted in each symbol, resulting in a bit rate of four times the symbol rate. Not power of 2[ edit ] Although it is common to choose the number of symbols to be a power of 2 and send an integer number of bits per baud, this is not required.

Line codes such as bipolar encoding and MLT-3 use three carrier states to encode one bit per baud while maintaining DC balance. For this configuration, use the Computation mode parameter default value, Entire frame. If both data signals are vectors, then this block compares some or all of the Tx and Rx data: If you set the Computation mode parameter to Entire frame, then the block compares all of the Tx frame with all of the Rx frame.

If you set the Computation mode parameter to Select samples from mask, then the Selected samples from frame field appears in the dialog. This parameter field accepts a vector that lists the indices of those elements of the Rx frame that you want the block to consider. For example, to consider only the first and last elements of a length-six receiver frame, set the Selected samples from frame parameter to [1 6].

If the Selected samples from frame vector includes zeros, then the block ignores them. If you set the Computation mode parameter to Select samples from port, then an additional input port, labeled Sel, appears on the block icon. The data at this input port must have the same format as that of the Selected samples from frame parameter described above. If one data signal is a scalar and the other is a vector, then this block compares the scalar with each entry of the vector.

Note This block does not support variable-size signals. If you choose the Select samples from port option and want the number of elements in the subframe to vary during the simulation, then you should pad the Sel signal with zeros.

The Error Rate Calculation block ignores zeros in the Sel signal. Output Data This block produces a vector of length three, whose entries correspond to: If you set the Output data parameter to Workspace and fill in the Variable name parameter, then that variable in the base MATLAB workspace contains the current value when the simulation ends. Pausing the simulation does not cause the block to write interim data to the variable.

Instead, use the Port option and connect the output port to a Simulink To Workspace block. If you set the Output data parameter to Port, then an output port appears. This output port contains the running error statistics. Delays The Receive delay and Computation delay parameters implement two different types of delays for this block.

One delay is useful if you want this block to compensate for the delay in the received signal. The other is useful if you want to ignore the initial transient behavior of both input signals.

**BER vs SNR in BPSK - simulink**

The Receive delay parameter represents the number of samples by which the received data lags behind the transmitted data. The transmit signal is implicitly delayed by that same amount before the block compares it to the received data. This value is helpful when you delay the transmit signal so that it aligns with the received signal. The receive delay persists throughout the simulation.

## Symbol rate

The Computation delay parameter represents the number of samples the block ignores at the beginning of the comparison. If you do not know the receive delay in your model, you can use the Align Signals block, which automatically compensates for the delay. If you use the Align Signals block, set the Receive delay in the Error Rate Calculation block to 0 and the Computation delay to the value coming out of the Delay port of the Align Signals block.

Alternatively, you can use the Find Delay block to find the value of the delay, and then set the Receive delay parameter in the Error Rate Calculation block to the delay value. If you use the Select samples from mask or Select samples from port option, then each delay parameter refers to the number of samples that the block receives, whether the block ultimately ignores some of them or not. Stopping the Simulation Based on Error Statistics You can configure this block so that its error statistics control the duration of simulation.

This is useful for computing reliable steady-state error statistics without knowing in advance how long transient effects might last. To use this mode, check Stop simulation. The block attempts to run the simulation until it detects the number of errors the Target number of errors parameter specifies. However, the simulation stops before detecting enough errors if the time reaches the model's Stop time setting in the Configuration Parameters dialog boxif the Error Rate Calculation block makes Maximum number of symbols comparisons, or if another block in the model directs the simulation to stop.

To ignore either of the two stopping criteria in this block, set the corresponding parameter Target number of errors or Maximum number of symbols to Inf. For example, to reach a target number of errors without stopping the simulation early, set Maximum number of symbols to Inf and set the model's Stop time to Inf. Examples The figure below shows how the block compares pairs of elements and counts the number of error events.

### channelcoding - Calculate symbol rate for QAM modulation - Signal Processing Stack Exchange

The Tx and Rx inputs are column vectors. This example assumes that the sample time of each input signal is 1 second and that the block's parameters are as follows: However, the schematic arranges each column vector horizontally and aligns pairs of vectors so as to reflect a receive delay of two samples.

At each time step, the block compares elements of the Rx signal with those of the Tx signal that appear directly above them in the schematic.