- Open Access
An analytical expression for the BER of optimal single user detection of a BPSK signal contaminated by multiple CCIs
© Chung; licensee Springer. 2012
- Received: 7 January 2012
- Accepted: 8 June 2012
- Published: 8 June 2012
We derive an analytical expression for the bit-error rate (BER) of optimal single user detection of a binary phase-shift keying signal corrupted by multiple cochannel interferers. The channel capacity is also calculated to investigate the BER performance.
- multiple cochannel interference
- channel capacity
- error probability
- maximum likelihood detection
The problem of detecting a binary phase-shift keying (BPSK) signal corrupted by a single cochannel interferer (SCI) and additive white Gaussian noise (AWGN) has been investigated [1–11]. In , a suboptimal receiver is derived that utilizes the carrier frequency difference. In , an optimal BPSK receiver is derived assuming Rayleigh fading and no receiver knowledge of signal parameters. In , a suboptimal BPSK receiver structure is proposed for a non-faded channel. In , the optimum receiver is derived for a two-user synchronous BPSK channel. The bit-error rate (BER) performance of the optimum receiver was compared with that of the conventional matched-filter receiver in  and the jointly optimal receiver (JOR) in . The exact probability of error of an SCI-JOR was first obtained in [6, 7]. An exact expression for the BER of an individually optimal receiver (IOR) used to detect a BPSK signal corrupted by a similar SCI and AWGN was derived in . When a BPSK signal corrupted by an SCI and AWGN is detected, the IOR is the optimal multiuser detector . The JOR is also analyzed in . On the other hand, the optimal single user detection (OSUD) in an SCI and AWGN is investigated and the BER of the OSUD is calculated in . However, the number of cochannel interferers (CCIs) can increase for multiuser communications such as cellular mobile systems, in which the domain degradation is the interference due to other users communicating on the same channel, as the number of users increases. In this article, we propose the OSUD for a BPSK signal detection in the presence of AWGN and multiple cochannel interferers (MCIs). In addition, while in , the real roots were obtained by the equation of the product tanh functions, we solve the equation specifically, which is obtained by equating log-likelihood ratios (LLRs) with zero. The channel capacity is also calculated to investigate the BER performance.
It is easy to show that the MCI-OSUD of (7) simplifies to the SCI-OSUD in  for I1 ≠ 0 and I k = 0, k = 2, 3,...,N I .
where 2 ≤ i ≤ N c .
3.1. BER derivation for N I = 2
Then, the BER can be calculated by (14) or (17).
3.2. BER derivation for N I > 2
the updated set F i is obtained from the set D i by removing ±(μ-1(d m (-c-1)+1)-μ-1(-c-1))/2, except the biggest element (-b-1)∈E i , for (-c-1)≠(-b-1), (-c-1)∈E i , and the updated set R i is obtained from the set F i by removing , except the smallest element (-s-1)∈E i , for (-c-1)∈E i , (-c-1)≠(-s-1).
Figure 1. Procedure of generating a table with conditions for various real roots. The number N I of interferers is 4.
In summary, with the set C i of marginal conditions, we obtain the set R i of real roots corresponding to C i by solving (11). For the case C i , 1≤i≤N c , the real roots p j (i)∈R i , , and the center -c-1, , we obtain the condition p j -1(i)<μ-1(-c-1)<p j (i). Then conditional BER is calculated by (16) and the BER is calculated by (14) or (17).
where by using (3) and (4), and . Then the capacity is computed by (26).
We derived an analytical expression for the BER of the MCI-OSUD. The effect of MCIs on the BER was analyzed. To investigate the BER performance, the channel capacity was also calculated. The capacity, the analytical result, and the simulation are in good agreement.
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