# BER performance for BPSK and QPSK

Started by October 5, 2006
```Hi,

I read this statement from a book "The bit error probability for QPSK
modulation is the same as for BPSK, and hence, the results for BPSK can be
used also for the QPSK case". The author of the book simulated the BER
performance for BPSK modulation in multipath and AWGN channel.

May I know how true is this statement? Under what scenario can I make such
an approximation? Where can I find the analytical prove for this statement?
As I understood, the bit to noise ratio (Eb/No) for this two modulation
schemes (BPSK & QPSK) are totally different. Thus, would it be reasonable
to make such an assumption if the transmitted power and bandwidth
allocated to this 2 systems are the same?

Many thanks.

```
```
Richard_K wrote:

> Hi,
>
> I read this statement from a book "The bit error probability for QPSK
> modulation is the same as for BPSK, and hence, the results for BPSK can be
> used also for the QPSK case".  The author of the book simulated the BER
> performance for BPSK modulation in multipath and AWGN channel.
> May I know how true is this statement?

Very true.

Under what scenario can I make such
> an approximation?

If the bandwidth and the E/No are the same.

Where can I find the analytical prove for this statement?

2 x 2 = 2 + 2
:)

> As I understood, the bit to noise ratio (Eb/No) for this two modulation
> schemes (BPSK & QPSK) are totally different.

QPSK is comprised of the two orthogonal BPSK signals.

Thus, would it be reasonable
> to make such an assumption if the transmitted power and bandwidth
> allocated to this 2 systems are the same?

Not quite. The BPSK with the bit rate A and transmit power P has the
same BER as that of QPSK with the bit rate 2A and power 2P. The
bandwidth is the same in both cases.

This is fairly trivial. What is interesting the 3-PSK has somewhat
0.5dB better performance then that of QPSK or BPSK. However I have never
heard of the communication systems which make use of the 3-PSK.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

```
```"Vladimir Vassilevsky" <antispam_bogus@hotmail.com> wrote in message
news:h%9Vg.8905\$GR.7778@newssvr29.news.prodigy.net...
>
>
> Richard_K wrote:
>
>> Hi,
>>
>> I read this statement from a book "The bit error probability for QPSK
>> modulation is the same as for BPSK, and hence, the results for BPSK can
>> be
>> used also for the QPSK case".  The author of the book simulated the BER
>> performance for BPSK modulation in multipath and AWGN channel.
>> May I know how true is this statement?
>
> Very true.
>
>  Under what scenario can I make such
>> an approximation?
>
> If the bandwidth and the E/No are the same.
>
>  Where can I find the analytical prove for this statement?
>
>  2 x 2 = 2 + 2
>  :)
>
>> As I understood, the bit to noise ratio (Eb/No) for this two modulation
>> schemes (BPSK & QPSK) are totally different.
>
> QPSK is comprised of the two orthogonal BPSK signals.
>
>  Thus, would it be reasonable
>> to make such an assumption if the transmitted power and bandwidth
>> allocated to this 2 systems are the same?
>
> Not quite. The BPSK with the bit rate A and transmit power P has the same
> BER as that of QPSK with the bit rate 2A and power 2P. The bandwidth is
> the same in both cases.
>
> This is fairly trivial. What is interesting the 3-PSK has somewhat 0.5dB
> better performance then that of QPSK or BPSK. However I have never heard
> of the communication systems which make use of the 3-PSK.
>
Provided the I and Q streams stay orthogonal it's o.k.  A phase offset on
the recovered carrier leads to cross-talk between the two streams.

Best of Luck - Mike

```