delivered the opinion of the court:
The defendant, Edgar W. Green, was convicted of three counts of attempted first degree murder (720 ILCS 5/8 — 4(a), 9 — 1 (West 1994)). He was sentenced to concurrent terms of imprisonment of 30, 20 and 50 years. On appeal, the defendant argues that: (1) he was not proven guilty beyond a reasonable doubt of the attempted murder of victims Mason and May; (2) his trial attorney rendered ineffective assistance; (3) the trial court improperly considered as an aggravating factor that the defendant knew or should have known that May was a police officer; and (4) the trial court erred in accepting the defendant’s waiver of his right to a jury trial. We affirm.
On August 2, 1995, the defendant had an altercation with victim Davis outside a bar. The two scuffled, and the defendant claimed that Davis pulled out a knife. The defendant, who was carrying a gun loaded with four bullets, chased Davis and shot him in the back. The shooting occurred outside another bar, and Davis fell into the bar after being shot. As Davis was falling into the bar, victim Mason was leaving. The defendant and Mason had crossed paths earlier, and Mason had fired a gun at the defendant. When they met this time, Mason began to run away from the defendant and the defendant gave chase.
Mason ran past victim May, an off-duty police officer who was not in uniform and was not using a marked vehicle. When Mason alerted May to the defendant’s presence, May turned and saw the defendant holding the gun. The defendant pointed the gun at May and pulled the trigger three times. The gun did not discharge. During this time, May identified himself as a police officer and called for the defendant to put down the weapon. The defendant momentarily pointed the gun at Mason, then moved the weapon back toward May and pulled *404the trigger two more times. Again, the gun did not fire. May chased the defendant and subdued him.
At the police station following his arrest, the defendant was read his Miranda warnings. The defendant was shown a sheet of paper that explained those rights. Because the defendant indicated that he could not read well, an officer read the sheet to him and the defendant initialed each portion, indicating that he understood what had been read to him. Thereafter, he gave a statement in which he admitted shooting Davis and admitted shooting at Mason and pointing the gun at May.
Prior to trial, the defendant was evaluated by a clinical psychologist to determine whether he was fit to stand trial. The psychologist determined that the defendant exhibited borderline intellectual functioning. However, he was unable to administer several of the tests he sought to give the defendant because the defendant responded in a manner that made it impossible to get any significant answers from him.
The defendant signed a written jury waiver, and the matter proceeded to a bench trial. Following the presentation of the State’s case, the defendant moved for a directed finding. He claimed that the State had not proved that he took a substantial step toward the murder of either Mason or May and claimed that the State had not proved that he intended to murder either Mason or May. The trial judge stated that he did not know what the defendant was thinking at the time of the shootings. Based on the evidence presented by the State, however, the court found that it would be possible to conclude that the defendant had intended to murder Mason and May and had taken a substantial step toward completing that act. The court therefore denied the defendant’s motion. After hearing all the evidence, the trial court found the defendant guilty of the attempted murders of Davis, Mason and May.
The presentence investigation report contained statements from the defendant that he was drinking and smoking marijuana "all day” prior to the shooting. The report also stated that the defendant was receiving social security payments based on his mental retardation.
The trial court sentenced the defendant to 30 years’ imprisonment for the attempted murder of Davis and 20 years’ imprisonment for the attempted murder of Mason. The court found as an aggravating factor that the defendant knew or should have known that May was a police officer. Consequently, the court sentenced the defendant to 50 years’ imprisonment for the attempted murder of May.
The defendant argues that the State failed to prove him guilty of *405the attempted murder of Mason and May because: (1) he did not take a substantial step toward murdering Mason because he did not pull the trigger of the gun while the gun was pointed at Mason; and (2) when he pointed the gun at Mason and May he knew that there were no bullets left in the gun. The defendant further claims the trial judge admitted in his remarks in response to the motion for directed finding that the State had not proved that he had the intent to murder Mason and May.
A defendant is guilty of attempted murder when he, with the intent to kill, does any act which is a substantial step toward committing murder. People v. Burrage, 269 Ill. App. 3d 67, 645 N.E.2d 455 (1994). When a defendant challenges the sufficiency of the evidence against him, this court must determine whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found that the essential elements of the crime were proved beyond a reasonable doubt. People v. Collins, 106 Ill. 2d 237, 478 N.E.2d 267 (1985). The reviewing court may not substitute its judgment for that of the trier of fact with regard to the weight of the evidence and the credibility of the witnesses and should not reverse a conviction unless the evidence is so improbable, unreasonable or unsatisfactory as to justify a reasonable doubt concerning the defendant’s guilt. People v. Singletary, 237 Ill. App. 3d 503, 604 N.E.2d 1009 (1992).
In the instant case, the defendant shot Davis, then immediately began chasing Mason. He pointed the gun at May and pulled the trigger and then pointed the gun at Mason before turning to May and pulling the trigger again. From the evidence adduced at trial, the judge could have concluded that the defendant took a substantial step toward murdering Mason by chasing him down while carrying a gun and then pointing the gun at him. Moreover, the judge could have concluded that the defendant did not realize that the bullets in the gun were spent. Finally, the judge’s remarks in response to the defendant’s motion for directed finding merely indicated that the defendant had not yet told his side of the story. The judge indicated that he was keeping an open mind to hear what the defendant had to say but, given only the evidence produced by the State, a directed finding was not in order. Considering the entire circumstances of the alleged crime, we find that the evidence is not so improbable, unreasonable or unsatisfactory that it justifies a reasonable doubt as to the defendant’s guilt.
Next, the defendant claims that his trial counsel rendered ineffective assistance because she failed: (1) to move to suppress his statement to the police; and (2) to argue that the defendant was too intoxicated to form the intent to commit murder.
*406Ineffectiveness of counsel is proven when: (1) counsel’s representation falls below an objective standard of reasonableness such that the trial results were unreliable; and (2) the defendant is prejudiced by the unprofessional conduct. People v. Albanese, 125 Ill. 2d 100, 531 N.E.2d 17 (1988). If the court can determine that the defendant suffered no prejudice, then it need not decide whether counsel’s representation was deficient. Strickland v. Washington, 466 U.S. 668, 80 L. Ed. 2d 674, 104 S. Ct. 2052 (1984).
The defendant cites no specific authority to support his argument that his trial counsel should have moved to suppress his statement to the police. Thus, the argument is waived. See Spinelli v. Immanuel Lutheran Evangelical Congregation, Inc., 118 Ill. 2d 389, 515 N.E.2d 1222 (1987) (arguments not supported by relevant authority and coherent argument are waived).
With regard to the defendant’s claim that he was too intoxicated to form the intent to murder Davis, Mason and May, the record contains absolutely no support for this theory. The only indication that the defendant was in such an inebriated state comes from the defendant’s self-serving statements in the presentence investigation report. If the defendant was as drunk as he claims to have been, surely someone — a witness, a police officer — would have testified that he appeared to be under the influence of alcohol or drugs.
The defendant claims that the dearth of evidence supports his theory of ineffectiveness. We do not agree. Indeed, the lack of evidence leads us to conclude that the attempt to raise such a defense would have failed. With no prejudice to the defendant by the failure to raise the defense, there can be no ineffective assistance of counsel. Thus, we hold that the defendant’s trial attorney did not render ineffective assistance to the defendant.
Third, the defendant contends that the trial court improperly considered as an aggravating factor at sentencing that the defendant knew or should have known that May was a police officer.
At trial, Officer May testified that he identified himself to the defendant at the same time as the defendant was first aiming the gun at him and pulling the trigger. After that, the defendant turned the gun on Mason and then turned the gun back toward May and pulled the trigger again. Even if we were to conclude that the events happened so quickly that the defendant did not initially realize what May was trying to communicate, we still would agree with the trial court that the defendant knew or should have known of May’s profession when he turned the gun on May for the second time. Therefore, we hold that the trial court properly considered this aggravating factor in sentencing the defendant.
*407Finally, the defendant contends that the trial court erred in accepting his waiver of a jury trial. He argues that, because he is retarded, he could not knowingly waive this right unless it was explained to him in open court. The defendant claims that since the record contains no evidence that such an explanation occurred, the written jury waiver is insufficient proof that the defendant intended to forego his constitutional right to trial by jury.
We note that the record on appeal contains a written jury waiver signed by the defendant. The docket entry for the date in question provides that the court accepted the waiver as knowingly and voluntarily given. Thus, the record on appeal supports the trial court’s decision to accept the defendant’s waiver. In order to contest that, the defendant would have had to provide us with some additional documentation which would suggest that the defendant did not understand the right he was waiving. Yet, the defendant has provided this court with no transcript and no bystander’s report to support his contentions. Having failed to do so, the defendant has not met his burden of providing an adequate record upon which to evaluate his claim. See Foutch v. O’Bryant, 99 Ill. 2d 389, 459 N.E.2d 958 (1984).
Moreover, the defendant has cited no authority for his contention that, because of his alleged mental retardation, the trial court was required to explain in open court his right to a jury trial and the consequences of waiving that right. Thus, he has waived this claim of error. See Spinelli, 118 Ill. 2d 389, 515 N.E.2d 1222.
Consequently, we must hold that the trial court was correct in accepting his jury waiver.
For the foregoing reasons, the judgment of the circuit court of Knox County is affirmed.
Affirmed.
LYTTON, P.J., and SLATER, J., concur.